sign in sign up
<<
Home , Accretion disk, Fuzzball (string theory)

Shadows: Emergent Horizons from Microstructure

Fabio Bacchini∗ Centre for mathematical Astrophysics, Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium

Daniel R. Mayerson† Institut de Physique Th´eorique, Universit´eParis-Saclay, CNRS, CEA, Orme des Merisiers 91191, Gif-sur-Yvette CEDEX, France

Bart Ripperda Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA and Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

Jordy Davelaar Columbia Astrophysics Laboratory, Columbia University, 550 W 120th St, New York, NY 10027, USA Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA and Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

H´ector Olivares Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands

Thomas Hertog and Bert Vercnocke Institute for Theoretical Physics, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium

We study the physical properties of four-dimensional, -theoretical, horizonless “fuzzball” geometries by imaging their shadows. Their microstructure traps light rays straying near the would- be horizon on long-lived, highly redshifted chaotic . In fuzzballs sufficiently near the scaling limit this creates a shadow much like that of a hole, while avoiding the paradoxes associated with an . Observations of the shadow size and residual glow can potentially discriminate between fuzzballs away from the scaling limit and alternative models of black compact objects.

Introduction.— The recent images of the shadow of proposed BH alternatives. Here we concentrate on the the supermassive (BH) at the center of M87 subset of fuzzballs known as “microstate geometries” [15– taken by the Event Horizon Telescope (EHT) [1] open 18]. These are horizonless solutions of low-energy string up the exciting prospect to explore the strong- theory that describe compact objects with an intricate environment near BHs with horizon-scale resolution. geometric and topological inner structure and which can It has long been believed that the vicinity of the hori- be thought of as coherent “microstates” corresponding to zon is well described by BH solutions of classical gen- BHs. Therefore, in contrast to the ECO models usually arXiv:2103.12075v1 [hep-th] 22 Mar 2021 eral relativity. However, many theorists who study the employed in phenomenological studies, fuzzballs admit a quantum evolution of BHs have now concluded that there firm embedding in . Their phenomenology must be modifications to BHs extending to horizon scales has recently begun to be explored; see e.g. [19, 20] and (see e.g. [2]), in order to resolve the information para- also [21–24]. dox that stems from the discovery of We study the behavior of null geodesics (light rays) in and BH evaporation. A variety of proposals have been four-dimensional fuzzball geometries and use this to ob- made, among which exotic compact objects (ECOs) [3–5] tain the first images of fuzzball shadows as they would such as [6] or [7], firewalls signal- be perceived by a distant observer. To this end we first ing a complete breakdown of semiclassical gravity at the construct a novel axisymmetric scaling solution which we horizon [8], new non-local interactions [9], and fuzzball name the “ring fuzzball”. Our analysis of this confirms geometries [10]. Since shadows of compact black ob- that, as far as the behavior of geodesics is concerned, jects are sensitive to the object’s properties in the near- fuzzballs in the scaling limit can resemble BH geometries horizon region (see e.g. [11–14]), their observation offers arbitrarily well. It also reveals the key features and mech- a promising route to differentiate between some of these anisms of fuzzballs through which such phenomenological 2 horizon behavior emerges. Instead of considering a finite number of point singu- Even though the geometries we study here are su- larities on the circle of radius R, we employ a “smeared” persymmetric and have various limitations [20] (such as configuration of uniform charge density on the entire cir- small ), we expect that the overall cle. This yields properties of their shadows presented here qualitatively   −2q0 4rR sin θ capture those of shadows of more general (as yet uncon- MD0 = √ K , π r2 + R2 + 2rR sin θ r2 + R2 + 2rR sin θ structed) fuzzballs which correspond to realistic BHs. (7) Geometry.— We consider a class of four-dimensional where K(·) is the complete elliptic integral of the first multi-center solutions in [25–27] with metric kind and we used standard spherical coordinates (r, θ, φ) 3 ds2 = −Q−1/2(dt + ω)2 + Q1/2 dx2 + dy2 + dz2 , (1) on the flat R base. In this case, (4) determines ω = ωφdφ and note that (1) is now axisymmetric and equatorially which are smooth and horizonless when uplifted to five symmetric (θ ↔ π − θ). This microstate geometry, de- dimensions (and have controlled singularities in four di- termined by (5) and (7), is the “ring fuzzball” which we mensions). These solutions are completely determined will study using ray tracing. I by eight harmonic functions H = (V,K ,LI ,M) (where The ring fuzzball solution allows for the “scaling limit” I = 1, 2, 3) on the flat R3 basis spanned by (x, y, z) λ → 0, in which it approaches the metric of the static, [28, 29]. The metric warp factor is then given by supersymmetric BH given by (1) with 3 J K I 2P 1 P − q0 2 2 K K V = LI = 0,K = 1 + ,M = − + . Q = Z1Z2Z3V − µ V ,ZI = LI + CIJK , (2) r 2 r 2V (8) 1 1 µ = M + KI L + C KI KJ KK , (3) 3 2V I 6V 2 IJK This BH has 2MBH = 3P +q0 −P and a horizon at p 3 3 r = 0 with area ABH = 16π P (q0 − P ). The angular where for the STU model CIJK = |IJK | [30]. Finally, momentum of the (static) BH vanishes while the ring the rotation one-form ω is determined by fuzzball has J = 2P 3(1 − 3P 2)λ. Note that this ring 1 fuzzball represents the first ever explicitly constructed ∗ dω = V dM − MdV + KI dL − L dKI  , (4) (exactly) scaling solution that is also axisymmetric. 3 2 I I Ray Tracing.— We explore the geometry of the ring 3 where ∗3 is the Hodge with respect to the flat R fuzzball by tracing geodesics with the ray-tracing code basis, and demanding that it vanishes at spatial infinity. Raptor [36–38]. Ray tracing allows for visualizing the In this Letter, we consider microstate geometries in- environment of compact objects (see e.g. [39]). The ob- spired by the “black-hole deconstruction” paradigm [31– server is represented by a camera at a specified position 33], which consist of a pair of fluxed D6-D6 centers where 106 incoming geodesics converge. Geodesics are surrounded by a halo of D0 brane centers [31, 34, 35]. The numerically integrated backwards in time from the cam- harmonic functions are then given by era to where they originated. The integration is halted when a geodesic reaches an outer “celestial sphere”, for   3   1 1 1 P 1 1 which we assume a radius equal to the camera’s radial V = − ,M = − + + + MD0, r1 r2 2 2 r1 r2 location. To highlight lensing patterns, each geodesic is     I 1 1 2 1 1 assigned a color according to the quadrant (each of equal K = 1 + P + ,LI = −P − . (5) angular width in φ) of the sphere that it originates from. r1 r2 r1 r2 If a geodesic does not reach the celestial sphere within a The “centers” at ~r1 and ~r2 are fluxed D6 in a ten- predetermined maximum integration time (correspond- dimensional perspective, and we place these on the z-axis ing to an observation window for a physical observer), at z = ±l/2. For MD0, we can choose to distribute any we assign the color black to it. For example, geodesics number of centers on the circle x2 + y2 = R2 at z = 0; if that fall into horizons will appear black. the total charge of all these centers is −q0 (with q0 > 0), In our four-dimensional model, the D6-D6 centers and the so-called bubble equations (i.e. regularity conditions the D0 ring are (naked) singularities; we have explicitly on the metric) [25, 30] relate l and R as checked that no geodesics that we consider ever approach a singularity close enough to require the application of s q2 boundary conditions at the singularities. (Nevertheless, l = 8P 3λ, R = 2λ 0 − 4P 6. (6) (1 − (1 − 3P 2)λ)2 such boundary conditions can be derived from higher- dimensional string-theoretical embedding and will be dis- This is a one-parameter family of solutions entirely deter- cussed in [40].) mined by λ > 0. We will show that λ can be effectively For each geodesic, we track the position on the celestial tuned to obtain a correspondence between microstate ge- sphere (or lack thereof), the total elapsed (coordinate) ometries and classical BHs. time on its trajectory, as well as: 3

• , measured as the minimum value of the combined effect of long-term trapping and strong red- √ −1/4 −gtt = Q that a geodesic encounters on its shift that makes fuzzball microstates exhibit an emerging path. This provides a measure of how much energy horizon behavior and ultimately mimic a classical BH. a geodesic would lose in escaping from the gravity We also note that the geodesics in the ring fuzzball well. metric encode information on the inner structure of the BH it mimics. The curvature plots in the last row of Curvature, measured as the maximum value of the • Figure 1 indicate that one can interpret the microstate Kretschmann scalar K = RµνρσR that the µνρσ geometry as “resolving” the curvature singularity of a BH geodesic encounters on its path. This provides an into constituent pieces. In a higher-dimensional, string- estimate of the amount of (tidal) stress a geodesic theoretical embedding, these pieces would even be com- encounters. pletely smooth without curvature divergences. We have also tracked the tidal stresses and geodesic devi- The geodesic trapping mechanism is further shown ation along geodesics (in the spirit of higher-dimensional explicitly in Figure 2, where we plot a representative studies of tidal forces in microstate geometries [41–44]). geodesic for the λ = 0.01 case (also for P = 2, q0 = 50). However, for the geometries we consider, we found that This shows that the geodesic is trapped in the near-center these quantities provide essentially the same information region and experiences strong redshift as it bounces be- given by K; we will discuss these further in [40]. tween the two on-axis centers and the charge ring. Fur- Results.— Our results are presented in Figure 1 for ther, the chaotic and long-lived nature of these orbits is the ring fuzzball defined by (5) and (7) with the rep- apparent; geodesics may remain trapped far longer than resentative choice P = 2 and q0 = 50, and for values the observation window. λ = 0.19, 0.05, 0.01, 0.001. (The bubble equations require For higher-dimensional microstate geometries, λ ≤ 17/88 ≈ 0.193.) For comparison, we also show re- “chaotic trapping” behavior of geodesics was anticipated sults for the BH defined by (8) (also with P = 2, q0 = 50), in [47, 48], and was shown to be related to the presence which corresponds to the λ → 0 limit of the ring fuzzball. of so-called “evanescent ergosurfaces” (timelike surfaces From top to bottom row, we show the light bending (via of infinite redshift) in [49–52]. There are no evanescent the four-color screen visualization), the total elapsed co- ergosurfaces in four-dimensional microstate geometries; ordinate time, the redshift, and the curvature. In all our results are thus the first explicit indication and cases the camera is located at x0 = (250, 0, 0), pointed exploration of such trapping effects in this context. towards the origin, and oriented such that the z-axis is Note that a chaotic trapping mechanism was observed vertical (using the R3 coordinates of (1)). in lensing in boson star ECO models [53, 54], although As λ decreases to 0, the general expectation is for the without exploring its relation to an emerging horizon. microstate geometry to resemble the BH increasingly well To further make the phenomenological possibilities of [30, 45, 46]. Here we observe the explicit mechanism these microstate geometries explicit, in Figure 3 we com- by which the ring fuzzball, despite possessing no hori- pare the effective shadows of three ring fuzzballs with zon, does so. First, as λ decreases, the four-color screen that of an extremal Kerr-Newman BH. (Note that the pictures reveal that increasingly many geodesics travel- charge of this BH can be interpreted as “dark charge” ing near the would-be horizon scale follow chaotic paths. that only interacts gravitationally with standard-model They are scattered across the celestial sphere and form particles and is not ruled out by current observations fewer coherent geometric structures (as indicated by the [55–57].) The three fuzzballs have P = 1/4, λ = 0.1, larger chaotically colored regions). Second, the elapsed- P = 307/500, λ = 0.3, and P = 7/8, λ = 0.11, and we al- time pictures confirm that these complicated chaotic or- ways choose q0 such that the mass is constant M = 7/4. bits are long-lived; moreover, as λ decreases, an increas- We trace geodesics in all metrics and construct four-color ing amount of geodesics do not escape the near-center pictures, and subsequently darken the received light at region within the observation window (as indicated by the camera by the (maximal) redshift encountered by the presence of more black pixels in the four-color screen each geodesic on its path towards the observer. We as- pictures). sume that light will scatter off the microstructure (due Finally, the redshift and curvature plots show that to e.g. the large tidal stresses encountered) before they geodesics in such long-lived, almost-trapped chaotic or- can escape from the near-center region, making the red- bits also experience extremely strong redshift and en- shift a reasonable proxy for the energy loss of the counter large curvature. When including back- and therefore the darkness of the resulting image. In reaction, on such trajectories will interact with this way, the observed image of the microstate geome- and lose energy to the fuzzball microstructure, leading try can appear as dark as that of a Kerr-Newman BH. to effective scrambling behavior as expected in a BH. Figure 3 clearly shows that, depending on the value of Thus, such photons – even if they escape after their long, P, λ, fuzzballs can mimic BHs to different degrees. In chaotic orbits – will be significantly redshifted and fall particular, fuzzball shadows can appear very dark, but outside any detectable wavelength range. It is therefore with a much smaller area (top left); or, while the shadow 4

FIG. 1: From left to right columns: visualizations of diagnostics for the ring fuzzball (P = 2 and q0 = 50) for decreasing values of λ, compared to the λ → 0 BH in the rightmost column. Rows from top to bottom: four-color screen indicating the portion of the celestial sphere from which geodesics originate; coordinate time t elapsed at the end of the numerical integration (normalized to MBH ); strongest redshift experienced by the geodesic (normalized to the redshift at the camera position); strongest curvature encountered (normalized to K at the BH horizon). size can be within observational uncertainty bounds [1], in Figure 3 is just within this acceptable bound, and a weak redshift may make fuzzballs appear too bright the bottom-left panel is well within this bound (i.e. for (top right). With the appropriate parameters, fuzzballs P = 7/8, all allowed values λ . 0.118 are not excluded). can also appear almost indistinguishable from actual BHs Discussion.— We have studied the physical proper- (bottom left). Quantitatively, if we determine q0 by ties of fuzzballs, both as interesting geometries in their keeping the mass fixed as we vary P , then the values own right and as phenomenological alternatives to BHs, 0.695 . P . 0.912 correspond to solutions with an effec- by numerically calculating and imaging the behavior of tive horizon area within 10% of that of the Kerr-Newman null geodesics in a class of microstate geometries. The im- BH; this is approximately the uncertainty in the shadow ages presented here are the first visualizations of fuzzball size of M87* measured by the EHT [1]. This bound rules geometries. They confirm several physical properties out the top-left panel in Figure 3. Furthermore, for M87* of microstate geometries which had generally been an- the measured upper bound on the brightness at the center ticipated but never verified, such as their trapping be- of the shadow is < 10% of the average image brightness √ havior. As the ring fuzzball approaches the BH limit, [1]. If we assume this implies a redshift of −gtt < 0.1 its microstructure induces increasingly chaotic motion of at the center of the fuzzball shadow, the top-right panel geodesics straying in the near-center region. Infalling 5

FIG. 2: Left panel: three-dimensional visualization of a representative geodesic in the near-center region of the ring fuzzball geometry with P = 2, q0 = 50 and λ = 0.01. The on-axis centers and the charged ring are shown in red. Middle column: a short portion of the same trajectory projected on the φ = π/2 plane, colored by elapsed time (top) and local redshift (bottom). Right column: the full chaotic trajectory shown until the final integration time.

geodesics that reach the microstructure will be heavily blueshifted and subsequently backreact with the struc- ture and/or be heavily scattered. The light that will emanate from this region will then be too redshifted to be detectable. In this way, the microstructure conspires to create a shadow very much like that of a BH, while avoiding the paradoxes associated with an event horizon. Our results indicate that fuzzballs sufficiently near the scaling limit yield a theoretically appealing and phe- nomenologically viable BH alternative. Vice versa, ob- servations of a faint residual glow in the object’s shadow, or of its shadow’s size compared to its mass, have the po- tential to discriminate between BHs and fuzzballs some- what away from the scaling limit. These should therefore be prime targets for current and future imaging missions such as the EHT. This motivates a more detailed investigation of the characteristics that differentiate microstate geometries from BHs through the intricate structure of their shad- ows. This will require not only further advances in the construction of more realistic fuzzballs but also an accu- FIG. 3: Visualization of ring fuzzballs with rate modeling of the plasma in a realistic disk, P = 1/4, λ = 0.1 (top left), P = 307/500, λ = 0.3 (top coupled to full radiative transfer methods. This approach right), P = 7/8, λ = 0.11 (bottom left), compared to an has been employed for BH geometries considered by the extremal Kerr-Newman BH (bottom right) of equal EHT [58], as well as for more exotic objects [13, 59], and mass (and same angular momentum as the bottom left we intend to report on this elsewhere [40, 57]. fuzzball). All images are darkened according to the More broadly, the chaotic behaviour of geodesics on maximal redshift encountered by each geodesic. The the would-be horizon scales also suggests that gravi- two bottom pictures exhibit minimal but non-zero tational waves propagating in this region will similarly differences. be chaotically dispersed. Therefore one expects the 6 resulting gravitational wave signal that leaks out to Holes: Complementarity or Firewalls?, JHEP 02 (2013), be chaotic and dispersed over extended time intervals. 062. This suggests that the post-ringdown phase of gravi- [9] S. B. Giddings, Black hole information, unitarity, and tational waves generated in fuzzball mergers will not nonlocality, Phys. Rev. D 74, 106005 (2006). [10] S. D. Mathur, The Fuzzball proposal for black holes: An exhibit a markedly clear echo structure (see also [20, 60]). Elementary review, Fortsch. Phys. 53, 793 (2005). [11] F. H. Vincent, Z. Meliani, P. Grandclement, E. Gourgoul- We would like to thank Iosif Bena, Vitor Cardoso, hon, and O. Straub, Imaging a boson star at the Galactic Nejc Ceplak, Bogdan Ganchev, Shaun Hampton, Car- center, Class. Quant. Grav. 33, 105015 (2016). los Herdeiro, Tom Lemmens, Yixuan Li, Marina Mar- [12] M. Grould, Z. Meliani, F. H. Vincent, P. Grandcl´ement, tinez, Ben Niehoff, Nicholas Warner for useful discus- and E. Gourgoulhon, Comparing timelike geodesics sions, Tom Lemmens for collaboration and suggestions around a Kerr black hole and a boson star, Class. Quant. Grav. 34, 215007 (2017). from closely related work, and Iosif Bena for comments [13] H. Olivares, Z. Younsi, C. M. Fromm, M. De Laurentis, and suggestions on a preliminary draft of this Letter. O. Porth, Y. Mizuno, H. Falcke, M. Kramer, and L. Rez- The computational resources and services used in this zolla, How to tell an accreting boson star from a black work were provided by the VSC (Flemish Supercom- hole, MNRAS 497, 521 (2020). puter Center), funded by the Research Foundation – [14] S. B. Giddings and D. Psaltis, Event Horizon Telescope Flanders (FWO) and the Flemish Government – de- Observations as Probes for Quantum Structure of Astro- partment EWI. FB is supported by a Junior PostDoc- physical Black Holes, Phys. Rev. D 97, 084035 (2018). [15] I. Bena and N. P. Warner, Resolving the Struc- toral Fellowship (grant number 12ZW220N) from Re- ture of Black Holes: Philosophizing with a Hammer, search Foundation – Flanders (FWO). DRM is sup- arXiv:1311.4538 (2013). ported by ERC Advanced Grant 787320 - QBH Struc- [16] I. Bena, D. R. Mayerson, A. Puhm, and B. Vercnocke, ture and ERC Starting Grant 679278 - Emergent-BH. Tunneling into Microstate Geometries: Quantum Effects BR is supported by a Joint Princeton/Flatiron Postdoc- Stop , JHEP 07 (2016), 031. toral Fellowship. Research at the Flatiron Institute is [17] I. Bena, S. Giusto, E. J. Martinec, R. Russo, M. Shige- supported by the Simons Foundation. JD is supported mori, D. Turton, and N. P. Warner, Asymptotically-flat supergravity solutions deep inside the black-hole regime, by NASA grant NNX17AL82G. HO is supported by a JHEP 02 (2018), 014. Virtual Institute of Accretion (VIA) postdoctoral fel- [18] P. Heidmann, D. R. Mayerson, R. Walker, and N. P. lowship from the Netherlands Research School for As- Warner, Holomorphic Waves of Black Hole Microstruc- tronomy (). TH and BV were supported by ERC- ture, JHEP 02 (2020), 192. CoG HoloQosmos 616732, C16/16/005 KU Leuven re- [19] T. Hertog and J. Hartle, Observational implications of search grant, the FWO research projects GCD-C3714- fuzzball formation, Gen. Rel. Grav. 52,7 (2020). G.0011.12 (Odysseus) and G092617N, and the COST ac- [20] D. R. Mayerson, Fuzzballs and Observations, Gen. Rel. Grav. 52, 115 (2020). tion CA16104 GWVerse CA16104. [21] I. Bena and D. R. Mayerson, Multipole Ratios: A New FB and DRM contributed equally to this work. Window into Black Holes, PRL 125, 221602 (2020). [22] I. Bena and D. R. Mayerson, Black Holes Lessons from Multipole Ratios, arXiv:2007.09152 (2020). [23] M. Bianchi, D. Consoli, A. Grillo, J. F. Morales, P. Pani, and G. Raposo, Distinguishing fuzzballs from black holes ∗ [email protected] through their multipolar structure, PRL 125, 221601 † [email protected] (2020). [1] EHT Collaboration, First M87 Event Horizon Telescope [24] M. Bianchi, D. Consoli, A. Grillo, J. F. Morales, P. Pani, Results. I. The Shadow of the , and G. Raposo, The multipolar structure of fuzzballs, ApJL 875, L1 (2019). JHEP 01 (2021), 003. [2] S. D. Mathur, The Information paradox: A Pedagogical [25] B. Bates and F. Denef, Exact solutions for supersymmet- introduction, Class. Quant. Grav. 26, 224001 (2009). ric stationary black hole composites, JHEP 11 (2011), [3] V. Cardoso and P. Pani, The observational evidence for 127. horizons: from echoes to precision gravitational-wave [26] F. Denef, Supergravity flows and D-brane stability, JHEP physics, arXiv:1707.030211 (2017). 08 (2000), 050. [4] V. Cardoso and P. Pani, Tests for the existence of black [27] P. Berglund, E. G. Gimon, and T. S. Levi, Supergravity holes through gravitational wave echoes, Nature Astron. microstates for BPS black holes and black rings, JHEP 1, 586 (2017). 06 (2006), 007. [5] V. Cardoso and P. Pani, Testing the nature of dark com- [28] J. P. Gauntlett and J. B. Gutowski, General concentric pact objects: a status report, Living Rev. Rel. 22, 4 black rings, PRD 71, 045002 (2005). (2019). [29] I. Bena, P. Kraus, and N. P. Warner, Black rings in Taub- [6] D. J. Kaup, Klein-Gordon Geon, Phys. Rev. 172, 1331 NUT, PRD 72, 084019 (2005). (1968). [30] I. Bena and N. P. Warner, Black holes, black rings and [7] P. O. Mazur and E. Mottola, Gravitational vacuum con- their microstates, Lect. Notes Phys. 755, 1 (2008). densate stars, Proc. Nat. Acad. Sci. 101, 9545 (2004). [31] F. Denef, D. Gaiotto, A. Strominger, D. Van den Bleeken, [8] A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, Black and X. Yin, Black Hole Deconstruction, JHEP 03 (2012), 7

071. Abyss: Black ring microstates, JHEP 07 (2008), 019. [32] T. S. Levi, J. Raeymaekers, D. Van den Bleeken, [47] M. Bianchi, D. Consoli, and J. F. Morales, Probing W. Van Herck, and B. Vercnocke, Godel space from Fuzzballs with Particles, Waves and Strings, JHEP 06 wrapped M2-branes, JHEP 01 (2010), 082. (2018), 157. [33] J. Raeymaekers and D. Van den Bleeken, Microstate so- [48] M. Bianchi, D. Consoli, A. Grillo, and J. F. Morales, The lutions from black hole deconstruction, JHEP 12 (2015), dark side of fuzzball geometries, JHEP 05 (2019), 126. 095. [49] F. C. Eperon, H. S. Reall, and J. E. Santos, Instability of [34] J. M. Maldacena, A. Strominger, and E. Witten, Black supersymmetric microstate geometries, JHEP 10 (2016), hole entropy in M theory, JHEP 12 (1997), 002. 031. [35] D. Gaiotto, A. Strominger, and X. Yin, Superconformal [50] J. Keir, Wave propagation on microstate geometries, An- black hole , JHEP 11 (2005), 017. nales Henri Poincare 21, 705 (2019). [36] T. Bronzwaer, J. Davelaar, Z. Younsi, M. Mo´scibrodzka, [51] D. Marolf, B. Michel, and A. Puhm, A rough end for H. Falcke, M. Kramer, and L. Rezzolla, RAPTOR I: smooth microstate geometries, JHEP 05 (2017), 021. Time-dependent radiative transfer in arbitrary space- [52] F. C. Eperon, Geodesics in supersymmetric microstate times, A&A 613, A2 (2018). geometries, Class. Quant. Grav. 34, 165003 (2017). [37] J. Davelaar, T. Bronzwaer, D. Kok, Z. Younsi, [53] P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. M. Mo´scibrodzka, and H. Falcke, Observing supermas- Runarsson, Shadows of Kerr black holes with scalar hair, sive black holes in virtual reality, Comput. Astrophys. Phys. Rev. Lett. 115, 211102 (2015). Cosm. 5, 1 (2018). [54] P. V. P. Cunha, J. Grover, C. Herdeiro, E. Radu, [38] T. Bronzwaer, Z. Younsi, J. Davelaar, and H. Fal- H. Runarsson, and A. Wittig, Chaotic lensing around cke, RAPTOR II. Polarized radiative transfer in curved boson stars and Kerr black holes with scalar hair, Phys. spacetime, A&A 641, A126 (2020). Rev. D 94, 104023 (2016). [39] F. Bacchini, B. Ripperda, A. Chen, and L. Sironi, Gener- [55] V. Cardoso, C. F. Macedo, P. Pani, and V. Ferrari, Black alized, energy-conserving numerical simulations of parti- holes and gravitational waves in models of minicharged cles in general relativity. I. Time-like and null geodesics, dark matter, Journal of Cosmology and Astroparticle ApJS 237, 6 (2018). Physics 2016 (05), 054–054. [40] D. R. Mayerson, F. Bacchini, B. Ripperda, J. Davelaar, [56] G. Bozzola and V. Paschalidis, General relativistic sim- H. Olivares, B. Vercnocke, and T. Hertog, in preparation ulations of the quasi-circular inspiral and merger of (2021). charged black holes: GW150914 and fundamental physics [41] A. Tyukov, R. Walker, and N. P. Warner, Tidal Stresses implications, PRL 126, 041103 (2021). and Energy Gaps in Microstate Geometries, JHEP 02 [57] B. Ripperda, J. Davelaar, H. Olivares, D. R. Mayerson, (2018), 122. F. Bacchini, B. Vercnocke, and T. Hertog, Can we de- [42] I. Bena, E. J. Martinec, R. Walker, and N. P. Warner, tect signatures of dark matter and hidden dimensions in Early Scrambling and Capped BTZ Geometries, JHEP black-hole shadows? (2021), in preparation. 04 (2019), 126. [58] EHT Collaboration, First M87 Event Horizon Telescope [43] I. Bena, A. Houppe, and N. P. Warner, Delaying the Results. V. Physical Origin of the Asymmetric Ring, Inevitable: Tidal Disruption in Microstate Geometries, ApJL 875, L5 (2019). arXiv:2006.13939 (2020). [59] Y. Mizuno, Z. Younsi, C. Fromm, O. Porth, M. De Lau- [44] E. J. Martinec and N. P. Warner, The Harder They Fall, rentis, H. Olivares, H. Falcke, M. Kramer, and L. Rez- the Bigger They Become: Tidal Trapping of Strings by zolla, The current ability to test theories of gravity with Microstate Geometries, arXiv:2009.07847 (2020). black hole shadows, Nature Astron. 2, 585 (2018). [45] I. Bena, C.-W. Wang, and N. P. Warner, Mergers and [60] V. Dimitrov, T. Lemmens, D. Mayerson, V. Min, and typical black hole microstates, JHEP 11 (2006), 042. B. Vercnocke, Gravitational Waves, Holography, and [46] I. Bena, C.-W. Wang, and N. P. Warner, Plumbing the Black Hole Microstates, arXiv:2007.01879 (2020).