Probing strong with gravitational waves

Chris Van Den Broeck

Theory of Relativity Seminar, June 4th, 2021 Advanced LIGO and Advanced Virgo The coalescence of compact binaries The first 50 detections

• Mostly binary black holes • Binary neutron stars: GW170817, GW190425

LIGO + Virgo, arXiv:2010.14527 Access to strongly curved, dynamical Curvature of spacetime spacetime of Curvature

Characteristic timescale Yunes et al., PRD 94, 084002 (2016) The nature of gravity Ø Lovelock’s theorem: “In four spacetime dimensions the only divergence-free symmetric rank-2 tensor constructed solely from

the metric gμν and its derivatives up to differential order, and preserving diffeomorphism invariance, is the Einstein tensor plus a cosmological term.”

Ø Relaxing one or more of the assumptions allows for a plethora of alternative theories:

Berti et al., CQG 32, 243001 (2015)

Ø Most alternative theories: no full inspiral-merger-ringdown waveforms known § Most current tests are model-independent Fundamental physics with gravitational waves

1. The strong-field dynamics of spacetime • Is the inspiral-merger-ringdown process consistent with the predictions of GR?

2. The propagation of gravitational waves • Evidence for dispersion?

3. What is the nature of compact objects? Are the observed massive objects the “standard” black holes of classical ? • Are there unexpected effects during inspiral? • Is the remnant object consistent with the no-hair conjecture? Is it consistent with Hawking’s area increase theorem? • Searching for echoes 1. The strong-field dynamics of spacetime

Ø Inspiral-merger-ringdown process • Post-Newtonian description of inspiral phase

• Merger-ringdown governed by additional parameters βn, ⍺n Ø Place bounds on deviations in these parameters:

LIGO + Virgo, PRL 118, 221101 (2017) Ø Rich physics: Dynamical self-interaction of spacetime, spin-orbit and spin-spin interactions

Ø Can combine information from multiple detections

• Bounds will get tighter roughly as 1/ Ndet p

✓ 1 ' 1 = ⇡ rad 180

/ =( )/ 0 A A0 Af A0 A0

R D = tan ✓ 365000 km '

1 2. The propagation of gravitational waves

Ø Dispersion of gravitational waves? E.g. as a result of non-zero mass: • Dispersion relation:

2 2 2 2 4 E = p c + mgc g = h/(mgc) • Group velocity:g = h/(mgc) 2 4 2 vg/c =1 mgc /2E 1 2 h h (t) 1 i'0 i(2⇡fts(f) (ts(f))) 2 42 2 ix + A(ts(f)) e e vg/c =1 mgc /E dx e ⇥ 2 ¨(ts(f)) • Modification to gravitational2✓ ◆ waveZ1 phase: = ⇡Dc/[g(1 + z) f] 2 1 = ⇡Dc/[g(11 + z) f] g = h/(mgc) int 1 1 L = QLQL = QL L 2`!` 2`! E Ø Bound on`=1 graviton> 1.6 10mass:13 km`=1 Xg ⇥ X 23 2 dxµm=(g dx10.76,dx1,dx102,dxeV3)/c  ⇥ 23 2 m 7.7 10 eV/c g  ⇥ 2/3 4 G 5/3 ⇡f (s)(tret) h (tret)= Mc s c s a(t )r c2 c emis ✓ ◆ ✓ ◆ !220(Mf ,af ) x =0 LIGO + Virgo, arXiv:2010.14529 ⌧220(Mf ,af ) dnˆ F A(nˆ) F A(nˆ) 4⇡ 1 2 A Z X  =1 >0  20 150 <0 t ⇠

R D = tan ✓ 365000 km '

1 1

1

1

1 I I M˜ = 1 2 cos(2! t)+const 11 2 rot I I M˜ = 1 2 cos(◆)sin(2! t)+const 12 2 rot I I M˜ = 1 2 cos2(◆)cos(2! t)+const 22 2 rot

m2 µ x1(t)= R eˆ(t)= R eˆ(t) m1 + m2 m1 m1 µ x2(t)= 2. TheR eˆ (propagationt)= R eˆ(t) of gravitational waves m1 + m2 m2 E2 = p2c2 + Ap↵c↵ ØE2 =Morep2c 2general+ Ap↵ formsc↵ of dispersion: E2 = p2c2 + Ap↵c↵ E2 = p2c2 + Ap↵c↵ E2 = p2c2 + Ap↵c↵ § ↵ =0 corresponds to violation of local Lorentz invariance § ↵ 6=2.5 multi-fractal spacetime 1 2 1 i'0 i§(2⇡↵ft=3s(f) (tsdoubly(f))) special2 relativity ix A(ts(f)) e e dx e 2 § ↵ =4 higher-dimensional¨(ts(f)) theories ✓ ◆ Z1

1 1 int 1 1 L = QLQL = QL L 2`!` 2`! E X`=1 X`=1 dxµ =(dx0,dx1,dx2,dx3)

2/3 4 G 5/3 ⇡f (s)(tret) h (tret)= Mc s c s a(t )r c2 c emis ✓ ◆ ✓ ◆ x =0 LIGO + Virgo, arXiv:2010.14529 dnˆ F A(nˆ) F A(nˆ) 4⇡ 1 2 A Z X t

1

11

1 1 2. The propagation of gravitational waves

Ø Does the speed of gravity equal the ? Ø The binary neutron star coalescence GW170817 came with gamma ray burst, 1.74 afterwards

Ø With a conservative lower bound on the distance to the source: -15 -16 -3 x 10 < (vGW – vEM)/vEM < +7 x 10

Ø Excluded certain alternative theories of gravity designed to explain dark matter or dark in a dynamical way LIGO + Virgo + Fermi-GBM + INTEGRAL, ApJ. 848, L13 (2017) LIGO + Virgo, PRL 123, 011102 (2019) 3. What is the nature of compact objects?

Ø Black holes, or still more exotic objects?

• Boson stars

• Dark matter stars

• Gravastars

•

• Firewalls, fuzzballs

• The unknown 3. What is the nature of compact objects?

Anomalous effects during inspiral

Ringdown of newly formed object

Gravitational wave echoes Anomalous effects during inspiral

Ø Tidal field of one body causes quadrupole deformationQ in =the other:(EOS; m ) ij Eij Qij = (EOS; m) ij Q = E(EOS; m) where (EOS; ij m ) depends0 > on0 ij < 0 ⌘ E (EOS; m) 0 > 0 Q 0 < 0 E ⌘ • Boson stars, (EOS;dark matterm) stars:0 > 0 < 0 ⌘ (EOS; m)• Gravastars0 > 0: < 0 × 1000 ⌘ 500 Ø Enters inspiral phase at 5PN order, through 5 5 |[%] (m)/m (R/m)

100 / /

50

| 2 3 • O(10 - 10 ) for neutron stars × (EOS; m) 0 > 0 < 0 × × ⌘ × • Can also be measurable for 10 × × × × 5 × × × × × mimickers, e.g. boson stars 10 20 30 40 50

M [M] Cardoso et al., PRD 95, 084014 (2017) Johnson-McDaniel et al., arXiv:1804.0826 FIG. 1. Relative percentage errors on the average tidal deformability ⇤ for BS-BS binaries observed by AdLIGO (left panel), ET (middle panel), and LISA (right panel), as a function of the BS mass and for di↵erent BS models considered in this work (for each model, we considered the most compact configuration in the stable branch; see main text for details). For terrestrial interferometers we assume a prototype binary at d = 100Mpc, while for LISA the source is located at d =500Mpc.The horizontal dashed line identifies the upper bound ⇤/⇤ = 1. Roughly speaking, a measurement of the TLNs for systems which lie below the threshold line would be incompatible with zero and, therefore, the corresponding BSs can be distinguished from E BHs. Here ⇤ is given by Eq. (72), the two inspiralling objects have the same mass, and ⇤/⇤ kE /k2 . ⇠ 2

TABLE I. Tidal Love numbers (TLNs) of some exotic compact objects (ECOs) and BHs in Einstein-Maxwell theory and modified theories of gravity; details are given in the main text. As a comparison, we provide the order of magnitude of the TLNs for static NSs with compactness C 0.2(theprecisenumberdependsontheneutron-starequationofstate;seeTableIIIformoreprecisefits).ForBSs, the table provides the⇡ lowest value of the corresponding TLNs among di↵erent models (cf. Sec. III A) and values of the compactness. In the polar case, the lowest TLNs correspond to solitonic BSs with compactness C 0.18 or C 0.20 (when the radius is defined as that containing 99% or 90% of the total mass, respectively). In the axial case, the lowest⇡ TLNs correspond⇡ to a massive BS with C 0.16 or C 0.2(againforthetwodefinitionsoftheradius,respectively)andinthelimitoflargequarticcoupling.ForotherECOs,weprovide⇡ ⇡ expressions for very compact configurations where the surface r0 sits at r0 2M and is parametrized by ⇠ := r0/(2M) 1; the full results are available online [65]. In the Chern-Simons case, the axial l =3TLNisa⇠↵ected by some ambiguity and is denoted by a question mark [see Sec. IV C for more details]. Note that the TLNs for Einstein-Maxwell and Chern-Simons gravity were obtained under the assumption of vanishing electromagnetic and scalar tides. Tidal Love numbers E E B B k2 k3 k2 k3 NSs 210 1300 11 70 Boson star 41.4402.8 13.6 211.8 4 8 16 16 ECOs 5(8+3 log ⇠) 105(7+2 log ⇠) 5(31+12 log ⇠) 7(209+60 log ⇠) 8 8 32 32 Perfect mirror 5(7+3 log ⇠) 35(10+3 log ⇠) 5(25+12 log ⇠) 7(197+60 log ⇠) 16 16 32 32 Gravastar 5(23 6log2+9log⇠) 35(31 6log2+9log⇠) 5(43 12 log 2+18 log ⇠) 7(307 60 log 2+90 log ⇠) 1 Einstein-Maxwell 00 0 0 Scalar-tensor 00 0 0 BHs 2 2 ↵CS ↵CS Chern-Simons 001.1 M 4 11.1 M 4 ? 1

TLNs as [6, 8]

1 l(l 1) 4⇡ M kE l , l ⌘2 M 2l+1 2l +1 r El0 (3) B 3 l(l 1) 4⇡ Sl kl 2l+1 , ⌘2 (l + 1)M 2l +1 l0 selection rules that allow to define a wider class of “rotational” r B TLNs [22, 23, 75, 76]. In this paper, we neglect spin e↵ects to 1 leading order. where M is the mass of the object, whereas l0 (respec- 1 E 1

1 Q = 2m3

2 3 !2202(M3f ,af ) Q =  m Q =  m Q = 2m3 ⌧220(Mf ,af ) Q = 2m3 Anomalous effects during inspiral !220(Mf ,af ) Ø Spin of an individual compact object also !220(Mf ,af ) !220(Mf ,af ) induces a quadrupole moment:⌧220(Mf ,af ) ~ !220(Mf ,af ) ⌧ (M ,a ) ⌧220(Mf ,af ) Q = 2m3 220 f f ⌧220(Mf ,af ) • Black holes:  =1 >0  20 150 <0 ⇠ • Boson stars,A darkt matter wstars:=1⌧t>f 0  20 150 <0 0 0 0 ⇠ m R  =1 >•0  Gravastars20 150: <0 D = !⇠220(Mf ,af ) R tan ✓ D = Ø Allow⌧220 for(M deviationsf ,af ) from Kerr value:tan ✓ R 365000 km R 2 3 D = D =Q = (1 + ) m 365000 km tan ✓ ' R !220(M' f ,af ) D = tan ✓ 365000 km tan ✓ 365000 km ' ' ⌧220(Mf ,af ) 365000 km m ' Possible theoretical !220(Mf ,af ) values for boson stars:

⌧R220(Mf ,af )  10 150 D = ⇠ tan ✓ … hence constraints 365000 km ' are already of interest!  =1 >0  20 150 <0R ⇠ D = tan ✓ Krishnendu et al., PRD 100, 104019 (2019) 365000 km ' R D = tan ✓ 365000 km '

1 1 1

1

1 1

1 1 t/⌧ Ringdown of newly formedh(t)= black holee lmn cos(! t + ) Almn lmn lmn t/⌧ lmn h(t)= e lmn cos(! Xt + ) Ø Ringdown regime: Kerr metricAlmn + linear perturbationslmn lmn lmn • Ringdown signal is a superpositionX of quasi-normal modes t/⌧ h(t)= e lmn cos(! t + ) ! = ! (M ,a ) Almn lmn lmn!nlm ⌧nlm lmn lmn f f lmn ! ⌧ X nlm nlm • Characteristic frequencies ! lmn and= ! dampinglmn(Mf ,a timesf ) ⌧lmn = ⌧lmn(Mf ,af ) !nlm = !nlm(Mf ,af ) ⌧nlm = ⌧nlm(Mf ,af ) !nlm = !nlm(Mf ,af ) ⌧nlm = ⌧nlm(Mf ,af ) t/⌧lmn ⌧lmn = ⌧lmn(Mf ,af ) h(t)= e cos(! t + ) Ø No-hairAlmn conjecture:!lmn =stationary,lmn!lmn(Mlmnf ,af )electrically neutral black hole lmn X M a completely characterized⌧lmn = ⌧lmn( Mbyf ,a massf ) f M, spinf f af / 0 =( f 0)/ 0 0 • Linearized Einstein equations around Kerr backgroundA A enforceA specificA A dependences: / 0 =( f 0)/ 0 0 A A A A A ! = ! (M ,a ) lmn lmn/ =(f f )/ 0 0 f 0 0 Berti et al., PRD 73R, 064030 (2006) A A A A A D = ⌧lmn = ⌧lmn(Mf ,af ) tan ✓ R • Look for deviations from theD expressions= for frequencies, damping365000 times: km R tan ✓ ' ! (M ,a ) D(1= + !ˆ ) ! (M ,a ) lmn f f ! tanlmn✓ lmn f365000f km ⌧/lmn0(M=(f ,aff) (10) +/ 365000⌧0ˆlmn)0⌧ kmlmn('Mf ,af ) A A A !A ' A

Carulllo et al., PRD 98, 104020 (2018) Brito et al., PRD 98, 084038 (2018) R D = tan ✓ 365000 km '

1 1

1 1

1 1

1 Ringdown of newly formed black hole Ø Look for deviations from the expressions for frequencies, damping times: ! (M ,a ) (1 + !ˆ ) ! (M ,a ) lmn f f ! lmn lmn f f ⌧ (M ,a ) (1 + ⌧ˆ ) ⌧ (M ,a ) lmn f f ! lmn lmn f f 21 Ø First measurements:

TABLE IX. The median value and symmetric 90% credible interval of the redshifted frequency and damping time estimated using the 1.5 full IMR analysis (IMR), the pyRing analysis with a single damped GW190519 153544 sinusoid (DS), and the pSEOBNRv4HM analysis (pSEOB). GW190521 074359 Event Redshifted Redshifted GW190910 112807 frequency [Hz] damping time [ms] 1.0 hierarchically IMR DS pSEOB IMR DS pSEOB combined +8 +14 +0.3 +3.7 GW150914 248 7 247 16 4.2 0.2 4.8 1.9 +15 +71 +0.4 +36.2 GW170104 287 25 228 102 3.5 0.3 3.6 2.1

+11 +340 +0.3 +22.2 220

. . ˆ 0.5 GW170814 293 14 527 332 3 7 0.2 25 1 19.0 +17 +664 +1.0 +31.8 GW170823 197 17 222 62 5.5 0.8 13.4 9.8 +11 +479 +0.3 +32.5 GW190408 181802 319 20 504 459 3.2 0.3 10.0 8.9 GW190421 213856 162+13 171+50 6.3+1.2 8.5+5.3 14 16 0.8 4.2 +17 +501 +0.8 +3.4 0.0 GW190503 185404 190 15 265 79 5.3 0.8 3.5 1.8 +32 +686 +0.2 +21.3 GW190512 180714 382 42 220 42 2.6 0.2 26.1 22.9 +25 +493 +1.2 +19 .2 GW190513 205428 242 27 250 88 4.3 0.4 5.3 3.8 +10 +11 +12 +1.7 +9.0 +3.6 GW190519 153544 127 9 123 19 124 13 9.7 1.6 9.7 3.8 10.3 3.1 LIGO + Virgo, arXiv:2010.14529 +3 +3 +2 +4.0 +12.4 +7.7 0.5 GW190521 68 4 65 3 67 2 16.0 2.5 22.1 7.4 30.7 7.4 0.5 0.0 0.5 1.0 1.5 GW190521 074359 198+7 197+15 205+15 5.4+0.4 7.7+6.4 5.3+1.5 8 15 12 0.4 3.3 1.2 ˆ +10 +13 +15 +2.0 +17.2 +5.4 f220 GW190602 175927 105 9 93 22 99 15 10.2 1.5 10.0 4.5 8.8 3.6 +11 +7 +7 +2.3 +25.2 +7.2 GW190706 222641 109 10 109 12 112 8 11.3 2.3 20.4 12.9 19.4 8.9 +10 +279 +0.2 +23.0 FIG. 14. The 90% credible region of the joint posterior distribution GW190708 232457 497 46 642 596 2.1 0.1 24.6 22.6 +17 +587 +11 +1.1 +25.6 +5.3 of the fractional deviations of the frequency fˆ220 and the damping GW190727 060333 178 16 345 267 201 21 6.2 0.8 21.1 17.9 15.4 6.1 +10 +350 +0.6 +25.3 time ⌧ˆ220, and their marginalized posterior distributions, for the GW190828 063405 239 11 247 15 4.8 0.5 17.3 10.4 +8 +9 +12 +0.9 +17.1 +3.1 ` = m = 2, n = 0 mode from the pSEOBNRv4HM analysis. We only GW190910 112807 177 8 166 8 174 8 5.9 0.5 13.2 6.2 9.5 2.7 | | +13 +371 +0.7 +30.1 include events that have SNR > 8 in both the inspiral and postinspiral GW190915 235702 232 18 534 493 4.6 0.6 15.0 13.1 stage in this plot where we have sucient information to break the degeneracy between the binary total mass and the fractional deviation parameters in the absence of measurable HMs. The measurements of the fractional deviations for individual events, and as a set of set of simulated numerical relativity signals with parameters measurements, both show consistency with GR. consistent with GW190521 into real data immediately adja- cent to the event, and ran the pSEOB analysis on them. For 3 out of 5 injections around the event we recover posteriors GW190910 112807 it shows excellent agreement with GR that overestimate the damping time and for which the injected for fˆ but the GR prediction has only little support in the GR value lies outside the 90% credible interval, suggesting 220 marginalized posterior distribution of ⌧ˆ . that the overestimation of the damping time for GW190521 is 220 a possible artifact of noise fluctuations. A similar study was In spite of the low number of events, we also apply the conducted with pyRing using the damped sinusoid model for hierarchical framework to the marginal distributions in Fig. 14. The population-marginalized constraints are fˆ = 0.03+0.38 GW190828 063405 and we also observed overestimations of 220 0.35 ⌧ . +0.98 the damping time. This suggests that the overestimation of and ˆ220 = 0 16 0.98, which are consistent with GR for both the damping time is a common systematic error for low-SNR parameters. The ⌧ˆ220 measurement is uninformative, which signals. is not surprising given the spread of the GW190910 112807 result and the low number of events. The hyperparameters also In Fig. 14, we show the 90% credible region of the joint reflect this, since they are constrained for fˆ (µ = 0.03+0.17, posterior distribution of the frequency and damping time devia- 220 0.18 < 0.37) but uninformative for ⌧ˆ (µ = 0.16+0.47, < tions, as well as their respective marginalized distributions. We 220 0.46 . only include events that have SNR > 8 in both the inspiral and 0 88). The bounds for the fractional deviation in frequency p postinspiral regimes, with cuto↵ frequencies as in Table IV. for the 220 mode, from the SEOB analysis, and for the 221 py ing This is because, in order to make meaningful inferences about mode, from the R analysis, can be used to cast constraints ˆ on specific theories of modified gravity that predict non-zero f220 and ⌧ˆ220 with pSEOB in the absence of measurable HMs, 1 the signal must contain sucient information in the inspiral values of these deviations [234, 235], as well as to bound and merger stages to break the degeneracy between the binary possible deviations in the ringdown spectrum caused by a non- total mass and the GR deviations. The fractional deviations Kerr-BH remnant object (see, e.g., [236]). obtained this way quantify the agreement between the pre- and postmerger portions of the waveform, and are thus not fully analogous to the pyRing quantities. B. Echoes From Fig. 14, the frequency and the damping time of the 220 mode are consistent with the GR prediction ( fˆ220 = ⌧ˆ220 = 0) It is hypothesized that there may be compact objects having for GW190519 153544 and GW190521 074359, while for a light ring and a reflective surface located between the light = (m , )+ (m , ) (m, )=8⇡m2(1 + 1 2) A0 A 1 1 A 2 2 A p

2 2 0 = (m1,1)+ (m2,2) (m, )=8⇡m (1 + 1 ) A A A✓ 1 A ' 1 p = ⇡ rad First tests of Hawking’s area increase theorem 180 ✓ 1 Ø ' During binary black hole merger, horizon area should not decrease 1 = ⇡ rad m1 m2 ~ 1 ~ 2 180 mf ~ f

m1 m2 1 2 2 2 0 = (m1,1)+m1 m(2m2~,12~)2 (m, )=8⇡m (1 + 1 ) A A = (mA , )+ (mA, ) (m, )=8⇡m2(1 + 1 2) A0 A 1 1 A 2 2 A R ✓ 1 p D = ' p tan ✓mf ~ f 1 m1 m2 1 2 = ⇡ rad 2 2 365000 km 0 = (m1,1)+ (m2,1802) (m, )=8⇡m (1 + 1 ) A A A ✓ ✓ 11 A ' '' 11✓ 1 p 2 2 Ø ==⇡⇡ radrad' 0 = ✓ (m11,1)+ (m2,2) (m, )=8⇡m (1 + 1 ) “Ingoing” blackA holesA ' consideredA Kerr A R 180180 1 1 D = § Measure masses= ⇡ m m 11 rad, m m 2 2 and1m1 initialm1 21 2 m mspins22 1 1 , 22 from inspiralpsignal tan ✓ ✓ =1 ⇡ rad 180 180 365000 km § Total✓ initial1 horizon' area: DSun 150, 000, 000 km 1 ' ' ' = ⇡ rad 2 2 2 2 0 = (m101,=1)+(m1(,m12)+,2) (mwhere(2m,, 2))=8⇡(m,m (1)=8 + ⇡1m (1) + 1 ) A = A⇡ A radA A 180 A A A 180 ✓ 1 DSun 150, 000, 000 km ' p p DSun '150, 000, 000 km 1 Ø Final' blackR hole also✓ ✓Kerr11 D = '' ✓✓ =11⇡ rad 1 ' 180 § Obtaintan ✓ mass m f andf spinm= f⇡ f 1 fromrad 'ringdown1 frequencies and damping times = ⇡ rad 1 365000R km ✓ 1801 = ⇡ rad § Final horizon area: '180 ✓ = ⇡1 rad 'D = R DSun 150, 000, 000 km 180 tan ✓ ' 1 ' 180 D =f = (mf ,f ) = ⇡ rad 1 A tan365000A✓ km 180 = ⇡ rad ' 365000 km R R 180 ' D = D = Ø According to the theorem:tan ✓ / 0 =( f 0)/ 0 0 tan ✓ R A A A A A R DDSun= 150365000, 000, km000 km D = 365000DSun''tan km150✓ , 000, 000 km tan ✓ ' ' 365000 kmDSun 150, 000, 000 km DSun 150D , 000,'000150 km, 000, 000 km 365000 km ' ' ' D ' 150, 000R, 000 km R Sun 'D = D = R tan ✓ D = tan ✓ R 365000R km D365000tan= ✓ km ' ' D = R 365000tanD✓ km= tanR ✓ ' 365000D = kmtan365000✓ km ' ' tan ✓ 365000365000 km km '' 1

1

1 1

1

1 1 1 1

1 1 1 1

11

1 = (m , )+ (m , ) (m, )=8⇡m2(1 + 1 2) A0 A 1 1 A 2 2 A p

✓ 1 ' 1 = ⇡ rad 180 First tests of Hawking’s area increase theorem

Ø According to the theorem: / =( )/ 0 A A0 Af A0 A0 Ø Measurement on GW150914: R D = tan ✓ 365000 km '

Isi et al., arXiv:2012.04486

§ Agreement at > 95% probability

1 3

0.15 servable imprint in the GW signal at late times. From black hole 3 Eq. (6), a typical time delay reads 0.10 0.15 servable imprint in the GW signal at late times. From black hole Eq. (6), a typical time delay reads`/LP 0.05 outgoing at infinity t 54(n/4) M30 1 0.01 log ms , (7) ingoing at horizon0.10 ⇠ M  ✓ 30 ◆ 0.00 `/LP 0.15 0.05 outgoing at infinity t 54(n/4) M30 1 0.01 log ms , (7) ingoing at horizon wormhole where M30 :=⇠M/(30M ). M30  ✓ ◆ 2 0.00 0.10 The picture of GW signal scattered o↵ the potential 0.15 wormhole ) M where M30 := M/(30M ). * barrier is also supported by two further features shown 2 0.05 outgoing at infinity0.10 The picture of GW signal scattered o↵ the potential V(r trapped outgoing at infinity in Fig. 2, namely the modulation and the distortion of ) M

* barrier is also supported by two further features shown 0.05 outgoing at infinity the echo signal. In general, modulation is due to the 0.00 V(r outgoing at infinity in Fig. 2, namely the modulation and the distortion of 0.15 trapped slow leaking of the echo modes, which contain less en- 0.00 centrifugal barrier star-like ECO the echo signal. In general, modulation is due to the 0.15 ergy thanslow the leaking initial of the one. echo In modes, the wormhole which contain case, less this en- 0.10 centrifugal barrier star-like ECO e↵ect isergy stronger than due the toinitial the one.fact that In the modes wormhole can also case, leak this 0.10 0.05 outgoing at infinity to the “othere↵ect is universe” stronger due through to the fact tunneling that modes at the can second also leak regular at the center 0.05 trapped outgoing at infinitypeak ofto the the potential. “other universe” While the through amplitude tunneling of the at the echoes second regular at the center 0.00 trapped is model-dependent,peak of the potential. for a given While model the amplitude it depends of the only echoes -50 -400.00 -30 -20 -10 0 10 20 30 40 50 is model-dependent, for a given model it depends only -50 -40 -30r /M -20 -10 0 10 20 30 40mildly 50 on `. Distortion is also due to the potential bar- * r /M mildly on `. Distortion is also due to the potential bar- * rier, which acts as a low-pass filter and reflects only the rier, which acts as a low-pass filter and reflects only the low-frequency, quasibound echo modes. This implies that FIG. 1. QualitativeFIG. 1. features Qualitative of the features e↵ective of the potential e↵ective potential felt by felt by low-frequency, quasibound echo modes. This implies that perturbationsperturbations of a Schwarzschild of a Schwarzschild BH compared BH compared to the case to the caseeach echoeach is echo a low-frequency is a low-frequency filtered filtered version version of the of the previ- previ- of wormholesof [12] wormholes and of star-like [12] and of ECOs star-like with ECOs a regular with a cen- regular cen-ous oneous and one the and original the original shape shape of the of mode the mode gets gets quickly quickly ter [22]. The preciseter [22]. location The precise of the location center of of the the center star of is the model- star is model-washedwashed out after out a after few a echoes few echoes1. 1. dependent and4dependent was chosen and for was visual chosen clarity. for visual The clarity. maximum The maximum and minimumand of the minimum potential of the corresponds potential corresponds approximately approximately to to 6 0.4 the location of the unstable and stable PS, and the correspon- B. Waves generated by infalling or scattered 4 wormhole the locationwormhole of the unstable and stable PS, and the correspon- B. Waves generated by infalling or scattered 0.2 dence is exact in the eikonal limit of large angular number l. 2 dence is exact in the eikonal limit of large angular number l. particles 0 0.0 In the wormhole case, modes can be trapped between the particles -2 -0.2 In the wormhole case, modes can be trapped between the -4 -0.4 PSs in the two “universes”. In the star-like case, modes are PSs in the two “universes”. In the star-like case, modes are The features above are observed in a simple scattering 4 empty shell 0.5 empty shell trapped between the PS and the centrifugal barrier near the 2 The features above are observed in a simple scattering (t) (t) Gravitationaltrapped between thewave PS and echoes the centrifugal barrier near the process, but are also evident in the GW signal produced 10 10 0 0.0 center of the star [28–30]. In3 all cases the potential is of fi- Ψ Ψ process, but are also evident in the GW signal produced -2 -0.5 center of thenite star height, [28–30]. and In the all modes cases leak the away, potential with is higher-frequency of fi- by head-on collisions or close encounters, in the test- 0.15 servable imprint in the GW signal at late times. From -4 black hole nite height,Eq. (6), andmodes a typical the time leaking modes delay reads on leak shorter away, timescales. with higher-frequency by head-onparticle collisions limit. The or latterclose diencounters,↵er from the in radial the test- plunge gravastar 0.10 gravastar 4 0.5 • Exotic objects with corrections near 2 `/LP particlestudied limit. in The Ref. latter [12] in di that↵er their from pericenter the radialr plunge> 3M, 0.05 modesoutgoing at infinity leaking on shorter timescales. min 0.0 t 54(n/4) M30 1 0.01 log ms , (7) 0 ingoing at horizon ⇠ horizon: M inner30 potential barrier for 0.00  ✓ ◆ i.e. the particle does not cross the radius of the PS -2 0.15-0.5 studied in Ref. [12] in that their pericenter rmin > 3M, wormhole where M30 := M/(30M ). -4 2 The picture of GWradial signal scattered motion o↵ the potential (in fact, scattered particles in the Schwarzschild geom- -100 0 100 200 300 400 0.10 100 200 300 400 i.e. the particle does not cross the radius of the PS ) M t/M * t/M barrierwhere is also supported• rmin byis two the further location features shown of the minimum of the potential 0.05 outgoing at infinity etry can never get inside the r =4M surface). In V(r outgoing at infinity in Fig. 2, namely theAftermodulation formation/ringdown:and the distortion of continuing trapped (in fact, scattered particles in the Schwarzschild geom- the echo signal. In general, modulation is due to the 0.00 shown in Fig. 1. If we consider a microscopic correction order to compute the GW signal, we use the Regge- FIG. 2. Left: A dipolar (l =1,m = 0) scalar wavepacket scattered0.15 o↵ a Schwarzschild BH and o↵wheredi↵erent ECOsrminslow withis leaking the of thelocation echobursts modes, of whichof the radiation contain minimum less en- called of theechoes potential 6 centrifugal barrier star-like ECO etry can never get inside the r =4M surface). In ` =10 M (r0 =2.000001M). The right panel shows the late-time behavior of the waveform. The result for a wormhole,ergy than aat the the initial horizon one. In the scale wormhole (` case, thisM), then the main contribution Wheeler-Zerilli decomposition reviewed in Appendix B 0.10 e↵ect is stronger• due to the fact that modes can also leak gravastar, and a simple empty shell of matter are qualitatively similar and display a series of “echoes”shown which are modulated in Fig.to 1. the If timeIf we microscopic consider delay comes a⌧ horizon microscopic near the modification radius correction of the star order and to compute the GW signal, we use the Regge- in amplitude and distorted in frequency. For this compactness, the0.05 delay time in Eq. (6) reads t 110outgoingM at infinityfor wormholes,to the “other universe” through tunneling at the second (cf. Ref. [31] for details). regular at the center ⇡ t 82M for gravastars, and t 55M for empty shells, respectively. trapped at the horizonpeak of the scale potential. ( While` the amplitudeM),then then of the echoestime the mainbetween contribution ⇡ ⇡ 0.00 is model-dependent,therefore, for a given model it depends only Wheeler-Zerilli decomposition reviewed in Appendix B -50 -40 -30 -20 -10 0 10 20 30 40 50 ⌧ We have studied the GW emitted during collisions or r /M mildly on `. Distortion is also due to the potential bar- * to the time delay comessuccessive near echoes the radius of the star and rier, which acts as a low-pass filter and reflects only the (cf. Ref.scatters [31] for between details). point particles and ECOs; again the FIG. 1. Qualitative features of the e↵ective potentialtherefore, felt by low-frequency, quasibound echo modes. This implies that ` perturbations of a Schwarzschild BH compared to the case each echo is a low-frequency filteredt versionnM of thelog previ- , ` M, (6)We havegeneral studied qualitative the GW features emitted are duringthe same collisions as those or dis- Infall of wormholes [12] and of star-likeScattering ECOs with a regular cen- ous one and the original shape of the mode gets quickly 1.0 1 ⇠ M ⌧ cussed in Section II A and independent of the nature ter [22].0.2 The precise location of the center of the star is model- washed out after a few echoes . ✓ ◆ scatters between point particles and ECOs; again the dependent and was chosen for visual clarity. The maximum ` and minimum of the potential corresponds approximately to where n set by nature of object: generalof qualitative the ECO. To features be specific, are the we show same in as Fig. those 3 the dis- Zer- the location of the unstable and stable PS, and the correspon- B.where Wavest generatednnMis by alog infalling factor or of scattered order, ` unityM, that takes into(6) account dence is exact in the eikonal limit of large angular number l. illi wavefunction for a point particle plunging into (left 0.5 0.0 ⇠ particles• n = 8 Mfor wormholes⌧ cussed in Section II A and independent of the nature 0.7 In the wormhole case, modes can be trapped between the (t)] the structure of✓ the◆ objects. For wormholes, n =8to 6 (t) PSs22 in the two “universes”.0.1 In the star-like case, modes are panel) or scattering o↵ a wormhole with ` = 10 M,with 22 Ψ The features above are• observed in a simple scattering of the ECO. To be specific, we show in Fig. 3 the Zer- Ψ trapped between the PS and the centrifugal barrier near the account forn the = 6 fact for thatthin-shell the signal gravastars is reflected by the

centerRe[ of the star [28–30]. In all cases the potential is of fi- process, but are also evident in the GW signal produced initial Lorentz boost E =1.5. The coordinate system we -0.2 where n is a factor of order unity that takes into account nite height, and the modes leak away, with higher-frequency by head-on collisions or close encounters, in the test- 0.0 0.6 two maxima• n in = Fig.4 for 1, empty whereas shell for our thin-shell gravas-illi wavefunction for a point particle plunging into (left modes leaking on shorter0.0 timescales. the structureparticle limit. of The the latter objects. di↵er from the radial For plunge wormholes, n =8to use is such that the particles are moving along6 the equa- studiedtar in Ref. model [12] in that and their pericenter the empty-shellrmin > 3M, model it is easy to checkpanel) or scattering o↵ a wormhole with ` = 10 M,with i.e. the particle• doesFor not crossGW150914 the radius of the (M PS = 65 Msun), tor, and it di↵ers - by a ⇡/2 rotation - from the coordinate -0.4 account(in for fact, the scattered fact particles that in the Schwarzschild the signal geom- is reflected by the 0.5 -0.1 that n = 6 and n = 4, respectively. The results showninitial in Lorentz boost E =1.5. The coordinate system we -0.5 0 200 400 600 where rmin is the location of the200 minimum 400 of the 600 potential 800 etry can never get insidetaking the r ℓ=4=Mℓ6surface).Planck, Inand n = 4: axis used in Ref. [12]. As such, the l = 2 Zerilli-Moncrief shown in Fig. 1. If we consider a microscopictwo correction maxima in Fig. 1, whereas for our thin-shell gravas- -200 0 200 400 600 800 -200 0 200 400 600 800order toFig. compute 2 the for GW` signal,= 10 we useM the Regge-are perfectly consistent with this at the horizon scale (` M), then the main contribution use is suchwavefunction, that the particles for example, are moving has contributions along the from equa- az- t/M ⌧ t/M Wheeler-Zerilli decomposition�t = 117 reviewed ms in Appendix B to the time delay comes near the radius oftar the star model and (cf. and Ref.picture, [31] the for details). empty-shell with the wormhole model it case is easy displaying to check longer echo imuthal numbers m =0, 2. Note also that it is easy to therefore, We have studied the GW emitted during collisions or tor, and it di↵ers - by a ⇡/2 rotation - from the coordinate FIG. 3. Left panel: The waveform for the radial infall of a particle with specific energy E =1.5 into a wormhole withdelays than the other cases with the same compactness. ± 6 that n =scatters 6 and betweenn = point 4, particles respectively. and ECOs; again the The results shown in ` =10 M, compared to the BH case. The BH ringdown, causedCardoso by oscillations et al., ofPRL the 116 outer,` 171101 PS as the (2016) particle crosses through, axis used in Ref. [12]. As such, the l = 2 Zerilli-Moncrief t nM log , ` M, (6) general qualitative6 features are the same as those dis- are also present in the wormhole waveform. A part of this pulse travels inwards⇠ and is absorbedM by the⌧ eventFig. horizon 2 for (forcussed BHs)` = inOur Section 10 results II AM andare independent show perfectly that of the the nature dependenceconsistent with on ` is this indeed log- Cardoso et al., PRD 94✓, 084031◆ (2016) wavefunction, for example, has contributions from az- or then bounces o↵ the inner (centrifugal or PS) barrier for ECOs, giving rise to echoes of the initial pulse. This is a low-passof the ECO.arithmically To be specific, we for show all in Fig. the 3 the ECOs Zer- we studied. cavity which cleans the pulse of high-frequency components. Atwhere late times,n is a factoronly a of lower order frequency, unity that takeslong-livedpicture, into account signal is present, withilli wavefunction the for wormhole a point particle plunging case into displaying (left longer echo the structure of the objects. For wormholes, n =8to 6 imuthal numbers m =0, 2. Note also that it is easy to well described by the QNMs of the ECO. Right panel: the same for a scattering trajectory, with pericenter rmin =4.3panel)M,o↵ or scattering o↵ a wormhole with ` = 10 M,with 1 6 account for the fact that the signal is reflected by the As argued in Ref. [12], the logarithmic dependence dis- a wormhole with ` =10 M. The main pulse is generated now through the bremsstrahlung radiationdelays emitted as the than particleinitial Lorentz the boost otherE =1. cases5. The coordinate with system the we same compactness. Incidentally, we note± that all these features (namely time delay, approaches the pericenter. The remaining main features are astwo before. maxima We in Fig. show 1, whereas only the for real our part thin-shell of the gravas- waveform,use isthe such that the particles are moving along the equa- tar model and the empty-shell model it is easy to check played in Eq. (6) implies that even Planckian corrections echoes, modulation, and high-frequency filtering) are precisely imaginary part displays the same qualitative behavior. Our resultstor, and show it di↵ers - that by a ⇡/2 rotation the dependence - from the coordinate on ` is indeed log- that n = 6 and n = 4, respectively. The results shown in 33 what one would expect by the scattering of sound waves in a 6 axis used(` in Ref. [12].LP As such,=2 the l = 210 Zerilli-Moncrief cm) appear relatively soon after Fig. 2 for ` = 10 M are perfectly consistentarithmically with this wavefunction, for⇡ for all example, the has ECOs contributions⇥ we from studied. az- finite-size cavity. picture, with the wormhole case displaying longer echo imuthalthe numbers mainm =0, burst2. Note also of that radiation, it is easy to so they might leave an ob- express these results in a rotated frame [32, 33], and we delayswith than our theprevious other cases study with [12] the2. same compactness. ± 1 checked that the waveforms agree up to numerical errors Our results show that the dependence on ` is indeedAs log- argued in Ref. [12], the logarithmic dependence dis- Incidentally, we note that all these features (namely time delay, arithmically for all the ECOs we studied. As argued in Ref. [12], the logarithmic dependenceplayed dis- in1 Eq.Incidentally, (6) we note implies that all these features that (namely even time delay, Planckian corrections echoes, modulation, and high-frequency filtering) are precisely played in Eq. (6) implies that even Planckian corrections echoes, modulation, and high-frequency33 filtering) are precisely 33 what one would expect by the scattering of sound waves in a (`2 LP =2 10 cm) appear relatively(` soon afterLP what=2 one would expect10 by thecm) scattering ofappear sound waves in relatively a soon after ⇡Note however⇥ the following typo in the original publication: the the main burst of radiation, so they mightthe leave⇡ an main ob- finite-size burst cavity.⇥ of radiation, so they might leave an ob- finite-size cavity. Gravitational wave echoes Ø Theoretical predictions still in early stages

Ø Numerical waveforms for specific black hole mimickers + smaller object: § “Straw man” exotic object § Much higher mass ratio than the systems we currently see with LIGO/Virgo

Ø When searching for echoes, in practice one often assumes that echoes will be damped and widened copies of (part of) the merger/ringdown signal

Abedi et al., PRD 96, 082004 (2017) Westerweck et al., PRD 97, 124037 (2018) Lo et al., PRD 99, 084052 (2019) Ø Alternatively: morphology-independent search for echoes Gravitational wave echoes Ø Morphology-independent search for echoes:

§ Decompose data into generalized wavelets: succession of sine-Gaussians

Characterized by 9 intrinsic parameters: A overallt amplitudew⌧t0 f0 0

A ttime betweenw⌧t0 sinef0 -0Gaussians A tdampingw⌧ factort0 f0 0

A tphasew⌧t0 differencef0 0 A twwidening⌧t0 f0 factor0 !220(Mf ,af ) A tw⌧t0 ftime0 !0 220of( firstMf ,a echof ) A tw⌧t0 f0 0 ⌧ (M ,a ) central!220(M frequencyf220,af ) f f ⌧220(Mf ,af ) A tw⌧t0 f0 !2200 reference(Mf ,af ) phase ⌧220(Mf ,af ) § Compare 3 hypotheses for data from⌧220 a(Mnetworkf ,af ) of detectors: !220(!M220f ,a(Mf ) f ,af ) signal : dataglitch consistsnoise of signal + noise =1 >0  20 150 <0 H H H ! (M =1,a ) >0  20 150 <0 signal glitch : datanoise consists of instrumental220⌧220f(M fglitchesf,af ) + noise⇠ ⇠ H H H ⌧220(Mf ,af ) ! (M =1,a ) >0  20 150 <0 signal glitch noise⌧: =datafpn consistsR only 220of⌧ noise=1(fM f,a>)0  20 150 <0 H H H 220 f f ⇠ ⇠ ⌧§ A= signalfpnR is by definition coherent between detectors, and consistent with a ⌧220(Mf ,af ) R R ⌧ = fpnR v 1 =1 >0  20 150 D<=0 tobsparticular= 1 sky tposition tand source⇠ orientation D = v c 1 ' 22 =1 >0  20 tan150✓tan✓<0 • If a signal is present, signal hasglitch less degreesnoiseR R of freedomsignal than glitch noise tobs = 1 t t ⇠ v c ⇣1 ' 2⌘2  =1 >H0  H20D =150DH=<3650000 365000 kmH km H H t = 1 t • Bayesiant analysisv willt then favor⇠ signal tansignal over✓'tanglitch '✓ glitch noise noise obs ⇣ ⌘ 2 em H H H H H H c tobs '= 2tem 1 =1 >0  20 R150 365000<0 km ⇣ ⌘ v tcem ' 2 D⇠⌧==fpn'R 365000 km ⌧ = fpnR tobs = temv 1 t ⇣ ⌘ tan ✓ ' t = t 1 cem ' 2 R⌧ =⌧fp=nfpRnR obs em ⇣ t ⌘ 2t R365000 km c ' 2 D = 'D v= 1 v 1 ⇣ ⌘ ! tobs = 1 tant ✓ t tobs = 1 t t t 2t Rtan ✓c ' 22v v 1 1 c ' 22 t 2t! t t= =1 1 t t t t ⌧ ⌧/2+2↵ D = ⇣365000⌘obs km365000obs km 2 ⇣2 ⌘ ! 'tan ✓ ' v ct c ' 2' 2 v t 2+2!↵ ⇣ ⇣ ⌘em ⌘ em ⌧ ⌧/ tobs =365000tem km1 tobs = tem 1 ⌧ ⌧/2+2!↵ ' c ' 2 v v temtem c ' 2 ! f f /2↵ t⇣obst=obs=⌘temtem1 1 ⇣ ⌘ p ! p c'c 2' 2 f f /2↵ t 2t ⇣ ⇣ ⌘ ⌘ t 2t f f /p 2!↵ p ! ! p ! p d 2 10 ms 2 t t22tt 13 ! ! ⌧ 10 fp 18F 2 2 2 2+2↵ 2+2↵ ' 10 J/2 md 3Gpc210 ms ⌧t ⌧/ ⌧ ⌧/ 13 ✓ d 10◆✓ ms ◆ ✓ ◆ ! ⌧13 10 fp 18F 2 ! 2+2↵2+2↵ ⌧ 10 f'p 18F 102 J/m 3Gpc t ⌧ ⌧⌧/⌧/ ' 10 J✓/m 3Gpc◆✓ 3 E◆t ✓T ◆ ! ! ✓ ◆✓ ⌧ =◆ ✓fp ◆ 2↵ 2↵ ¯ 2 f f / fp fp/ 3 E 4⇡T E R p p ! 3⌧ =E Tfp ! 2↵ 2↵ 2 f fpf /fp/ ⌧ = fp 4⇡2 E¯ R p p 4⇡ E¯ R ! !2 2 2 2 ✏⌦ = ⌦F/⌦H 13 d 1013 ms d 10 ms ⌧ 10 fp F ⌧ 10 fp 2 F2 2 2 ✏⌦ = ⌦F/⌦H 18 2 18 2 ✏⌦ = ⌦F/⌦H ' 10 J13/m13 3Gpc ' td 10d 10J/ msm10 ms 3Gpc t 2 ✓ ◆✓ ◆ ✓ ◆ 15 ⌧✓ ⌧10 10fp ◆✓fp 18F 18F◆2 ✓2 ◆ EBZ 10 G 10 M' ' 1010J/mJ/m 3Gpc3Gpc t t 3 E T ⌧BZ 2 2 2 157.6 2 s 3 ✓ E✓T ◆✓◆✓ ◆ ✓◆ ✓ ◆ ◆ E ⇠ B 15R c 102' G B10 M M ⌧ = f ⌧ = fp EBZ BZ 10 G 10 M p ¯ 2 ¯ 2 ⌧ ⌧BZ 7.6 7.6 ✓ s ◆✓ s ◆ 4⇡ E R 3 3E ET T 4⇡ E R BZ 2 2 2 B2R2c2 B M ⌧ =⌧ =f f ⇠ B R ⇠c ' ' B M p ¯ p ¯2 2 ✓ ✓◆ ✓ ◆ ✓◆ ◆ 4⇡ 4⇡E RE R ✏⌦ = ⌦F/⌦H ✏⌦ = ⌦F/⌦H ✏⌦ =✏⌦⌦=F/⌦FH/⌦H 15 2 15 2 EBZ 10 G 10 M EBZ 10 G 10 M ⌧BZ 7.6 s ⌧BZ 2 2 2 7.6 15 152s2 2 22 ⇠ B R c ' EBZEBBZ 10M⇠10GB RG c10'M10 M B M ⌧ ⌧BZ ✓ ◆7.6✓7.6 ◆ ✓s s ◆ ✓ ◆ BZ ⇠ B⇠2RB22cR2 2'c2 ' B B M M ✓ ✓ ◆ ✓◆ ✓ ◆ ◆

1 1

1 1 1

1

1 1 1 1 1

1 1 1 1 Prob(d ) B = |Hsignal S/N Prob(d ) Gravitational wave echoes |Hnoise Prob(d signal) Ø Ratio of evidences for signal versus glitch: Bayes factor BS/G = |H Prob(d ) |Hglitch st Ø Analysis of data following the detections of binary coalescences⌧ = infp then R1 and 2nd observing runs of Advanced LIGO/Virgo: v 1 t = 1 t t obs c ' 22 ⇣ ⌘ v t t = t 1 em obs em c ' 2 ⇣ ⌘ t 2t !

⌧ ⌧/2+2↵ !

2↵ fp fp/ 2-detector events 3-detector events! 2 2 Prob(d signal) d 10 ms Ø Similarly for Bayes factor signal versus noise,⌧ BS/N10=13 f |H F ' Prob(p 10d 18noiseJ/)m2 3Gpc t ✓ |H ◆✓ ◆ ✓ ◆ Ø No statistically significant evidence for echoes following these events3 E T ⌧ = fp 2 4⇡ E¯ R ✓ 1Tsang et al., PRD 98, 024023 (2018) ' Tsang1 et al., PRD 101, 064012 (2020) = ⇡ rad✏⌦ = ⌦F/⌦H 180

15 2 EBZ 10 G 10 M ⌧ 7.6 s BZ ⇠ B2R2c2 ' B M ✓ ◆ ✓ ◆ / =( )/ 0 A A0 Af A0 A0

R D = tan ✓ 365000 km '

1

1 Gravitational wave echoes • Signal reconstructions:

Tsang et al., PRD 101, 064012 (2020) LISA: A gravitational wave detector in space (2034)

Ø Laser Interferometer Space Antenna Ø Three probes in orbit around the Sun, exchanging laser beams § Triangle with sides of a few million kilometers § Sensitive to low frequencies (10-4 Hz - 0.1 Hz) § Approved by ESA for launch in 2034 Ø Different kinds of sources: § Merging supermassive binary 5 10 black holes (10 – 10 Msun) § Smaller objects in complicated orbits around supermassive black hole Einstein Telescope and Cosmic Explorer (2035?) Ø Next-generation ground- based facilities § Factor 10 improvement in sensitivity over LIGO/Virgo design sensitivity § Merging binary black holes 4 (3 – 10 Msun) and neutron stars throughout the visible Universe § 105 detections per year!

Cosmological reach of 3G Credit: Evan Hall & John Miller Hall & Evan John Credit:

Stefan Hild LVC Maastricht, Sep 2018 Slide 8 Summary

Ø The first direct detection of gravitational waves has enabled unprecedented tests of general relativity: § First access to genuinely strong-field dynamics of vacuum spacetime § Propagation of gravitational waves over large distances § Probing the nature of compact objects

Ø Some highlights: § Higher post-Newtonian coefficients constrained at ~10% level -23 2 § Graviton mass mg < 1.76 x 10 eV/c § Speed of gravity = speed of light to 1 part in 1015 § Spin-induced quadrupole moment during inspiral: Access to expected values for boson stars § No-hair test consistent with no deviations at 25% level § Area increase theorem passes at > 95% probability

Ø Ultra-high precision tests with next-generation observatories: LISA, Einstein Telescope, Cosmic Explorer § Higher accuracy § Larger number of sources § Propagation of gravitational waves over cosmological distances