Probing strong gravity 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 spacetime 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 second 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 general relativity? • 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 gravitational wave 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 graviton mass: • Dispersion relation: 2 2 2 2 4 E = p c + mgc λg = h/(mgc) • Group velocity:λg = h/(mgc) 2 4 2 vg/c =1 mgc /2E 1 2 h h (t) 1 i'0 i(2⇡fts(f) Φ(ts(−f))) 2 42 2 ix + A(ts(f)) e− e v−g/c =1 mgc /E dx e− ⇥ 2 − Φ¨(ts(f)) • Modification to gravitational2✓ ◆ waveZ1 phase: δ = ⇡Dc/[λg(1 + z) f] − 2 1δ = ⇡Dc/[λg(11 + z) f] λg = h/(mgc) int 1− 1 L = QLQL = QL L − 2`!λ` 2`! E Ø Bound onλ`=1 graviton> 1.6 10mass:13 km`=1 Xg ⇥ X 23 2 dxµm=(g dx10.76,dx1,dx10−2,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) Φ(tsdoubly(f))) special2 relativity ix A(ts(f)) e− e − dx e− 2 § ↵ =4 higher-dimensionalΦ¨(ts(f)) theories ✓ ◆ Z1 1 1 int 1 1 L = QLQL = QL L − 2`!λ` 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 speed of light? Ø The binary neutron star coalescence GW170817 came with gamma ray burst, 1.74 seconds 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 energy 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 • Wormholes • 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 =theλ other:(EOS; m ) ij − Eij Qij = λ(EOS; m) ij − Q = λE(EOS; m) where λ (EOS; ij m ) λdepends0 λ > on0 λ ij < 0 − ⌘ E λ(EOS; m) λ 0 λ > 0 λQ<ij 0= λ(EOS; m) ij internal structure⌘ (equation− of state) E 4 Qij =• λ(EOS;Blackλ(EOS; holes:mm) )ij λ 0 λ > 0 λ < 0 − E ⌘ • Boson stars,λ (EOS;dark matterm) λ stars:0 λ > 0 λ < 0 ⌘ λ(EOS; m)• λ Gravastars0 λ > 0: λ < 0 × 1000 ⌘ 500 Ø Enters inspiral phase at 5PN order, through 5 5 |[%] λ(m)/m (R/m) 100 / / 50 | 2 3 • O(10 - 10 ) for neutron stars × λ(EOS; m) λ 0 λ > 0 λ < 0 × × ⌘ × • Can also be measurable for black hole 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 σ⇤/⇤ = 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 σ⇤/⇤ σkE /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 − − Wormhole 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(M−f ,af ) • Black holes: =1 >0 20 150 <0 ⇠ −− • Boson stars,A dark∆tγ matter∆φ wstars:=1⌧t>f 0 φ 20 150 <0 0 0 0 ⇠ −− m R =1 >•0 Gravastars20 150: <0 D = !⇠220(M−f ,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 + ) χ 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 + φ ) Almn lmn lmn t/⌧ lmn h(t)= e− lmn cos(! Xt + φ ) Ø Ringdown regime: Kerr metricAlmn