Quasi-local black hole horizons: recent advances

There is a possibility that the event horizon of a Kerr-like black hole with perfect fluid dark matter (DM) can be destroyed, providing a potential opportunity for understanding the weak cosmic censorship conjecture of black holes. In this study, we analyze the influence of the strength parameter of perfect fluid DM on the destruction of the event horizon of a Kerr-like black hole with spinning after injecting a test particle and a scalar field. We find that, when a test particle is incident on the black hole, the event horizon is destroyed by perfect fluid dark matter for extremal black holes. For nearly extremal black holes, when the dark matter parameter satisfies α∈-rh,0∪rh,k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in \\left( -r_{h} , 0\\right) \\cup \\left( r_{h} ,k_2\\right) $$\\end{document} i.e. (A<0),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(A<0),$$\\end{document} the event horizon of the black hole will not be destroyed; when the dark matter parameter satisfies α∈k1,-rh∪0,rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\in \\left( k_1 ,-r_{h} \\right] \\cup \\left[ 0,r_{h}\\right] $$\\end{document} i.e. (A≥0),\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(A\\ge 0),$$\\end{document} the event horizon of the black hole will be destroyed. When a classical scalar field is incident into the black hole in the extremal black hole case, we find that the range of mode patterns of the scalar field that can disrupt the black hole event horizon is different for different values of the perfect fluid dark matter strength parameter. In the nearly extremal black hole case, through our analysis, we have found when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0 $$\\end{document} and α≠±rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e \\pm \\ r_h$$\\end{document} i.e. A≠0,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A\ e 0,$$\\end{document} the event horizon of the black hole can be disrupted. Our research results indicate that dark matter might be capable of breaking the black hole horizon, thus potentially violating the weak cosmic censorship conjecture.

It is well known that quasi-local black hole horizons depend on the choice of a time coordinate in a spacetime. This has implications for notions such as the surface of the black hole and also on quasi-local physical quantities such as horizon measures of mass and angular momentum. In this paper, we compare different horizons on non-spherically symmetric slicings of Vaidya spacetimes. The spacetimes we investigate include both accreting and evaporating black holes. For some simple choices of the Vaidya mass function function corresponding to collapse of a hollow shell, we compare the area for the numerically found axisymmetric trapping horizons with the area of the spherically symmetric trapping horizon and event horizon. We find that as expected, both the location and area are dependent on the choice of foliation. However, the area variation is not large, of order $0.035\%$ for a slowly evolving horizon with $\dot{m}=0.02$. We also calculate analytically the difference in area between the spherically symmetric quasi-local horizon and event horizon for a slowly accreting black hole. We find that the difference can be many orders of magnitude larger than the Planck area for sufficiently large black holes.

In classical General Relativity (GR), an observer falling into an astrophysical black hole is not expected to experience anything dramatic as she crosses the event horizon. However, tentative resolutions to problems in quantum gravity, such as the cosmological constant problem, or the black hole information paradox, invoke significant departures from classicality in the vicinity of the horizon. It was recently pointed out that such near-horizon structures can lead to late-time echoes in the black hole merger gravitational wave signals that are otherwise indistinguishable from GR. We search for observational signatures of these echoes in the gravitational wave data released by advanced Laser Interferometer Gravitational-Wave Observatory (LIGO), following the three black hole merger events GW150914, GW151226, and LVT151012. In particular, we look for repeating damped echoes with time-delays of $8 M \log M$ (+spin corrections, in Planck units), corresponding to Planck-scale departures from GR near their respective horizons. Accounting for the "look elsewhere" effect due to uncertainty in the echo template, we find tentative evidence for Planck-scale structure near black hole horizons at false detection probability of $1\%$ (corresponding to $2.5\sigma$ significance level). Future observations from interferometric detectors at higher sensitivity, along with more physical echo templates, will be able to confirm (or rule out) this finding, providing possible empirical evidence for alternatives to classical black holes, such as in ${\it firewall}$ or ${\it fuzzball}$ paradigms.

Black Holes and the Supermassive Compact Object at the Galactic Center: Multi-arts of Thought and Nature

This paper compares the population of binary black hole (BBH) mergers detected by LIGO/Virgo with selected long gamma-ray burst (GRB) world models convolved with a delay function (LGRBs are used as a tracer of stellar-mass BH formation). The comparison involves the redshift distribution and the fraction of LGRBs required to produce the local rate of BBH mergers. We find that BBH mergers and LGRBs cannot have the same formation history, unless BBH mergers have a long coalescence time of several Gyr. This would imply that BHs born during the peak of long GRB formation at redshift z ≈ 2−3 merge within the horizon of current GW interferometers. We also show that LGRBs are more numerous than BBH mergers, meaning that most of them do not end their lives in BBH mergers. We interpret these results as an indication that BBH mergers and LGRBs constitute two distinct populations of stellar-mass BHs, with LGRBs being more frequent than BBH mergers. We speculate that the descendants of LGRBs may resemble galactic high-mass X-ray binaries more than BBH mergers. Finally, we discuss the possible existence of a subpopulation of fast-spinning LGRB descendants among BBH mergers, showing that this population, if it exists, is expected to become dominant beyond redshift z ≈ 1, leading to a change in the observed properties of BBH mergers.

The behavior of quasi-local black hole horizons in a binary black hole merger is studied numerically. We compute the horizon multipole moments, fluxes and other quantities on black hole horizons throughout the merger. These lead to a better qualitative and quantitative understanding of the coalescence of two black holes; how the final black hole is formed, initially grows and then settles down to a Kerr black hole. We calculate the rate at which the final black hole approaches equilibrium in a fully non-perturbative situation and identify a time at which the linear ringdown phase begins. Finally, we provide additional support for the conjecture that fields at the horizon are correlated with fields in the wave-zone by comparing the in-falling gravitational wave flux at the horizon to the outgoing flux as estimated from the gravitational waveform.

In a binary black hole merger, it is known that the inspiral portion of the waveform corresponds to two distinct horizons orbiting each other and that the merger and ringdown signals correspond to the final horizon being formed and settling down to equilibrium. However, we still lack a detailed understanding of the relation between the horizon geometry in these three regimes and the observed waveform. Here we show that the well-known inspiral chirp waveform has a clear counterpart on black hole horizons, namely, the shear of the outgoing null rays at the horizon. We demonstrate that the shear behaves very much like a compact binary coalescence waveform with increasing frequency and amplitude. Furthermore, the parameters of the system estimated from the horizon agree with those estimated from the waveform. This implies that even though black hole horizons are causally disconnected from us, assuming general relativity to be true, we can potentially infer some of their detailed properties from gravitational wave observations.

We find the first binary black hole event horizon with a toroidal topology. It had been predicted that generically the event horizons of merging black holes should briefly have a toroidal topology, but such a phase has never been seen prior to this work. In all previous binary black hole simulations, in the coordinate slicing used to evolve the black holes, the topology of the event horizon transitions directly from two spheres during the inspiral to a single sphere as the black holes merge. We present a coordinate transformation to a foliation of spacelike hypersurfaces that "cut a hole" through the event horizon surface, resulting in a toroidal event horizon. A torus could potentially provide a mechanism for violating topological censorship. However, these toroidal event horizons satisfy topological censorship by construction, because we can always trivially apply the inverse coordinate transformation to remove the topological feature.

I present a set of long-term, direct, relativistic many-body computations of model dense stellar clusters with up-to-date stellar-evolutionary, supernova (SN), and remnant natal-kick models, including pair instability and pulsation pair instability supernova (PSN and PPSN), using an updated version of ${\rm{\small NBODY7}}$ N-body simulation program. The N-body model also includes stellar evolution-based natal spins of black holes (BHs) and treatments of binary black hole (BBH) mergers based on numerical relativity. These, for the first time in a direct N-body simulation, allow for second-generation BBH mergers. The set of 65 evolutionary models have initial masses $10^4{\!-\!}10^5\, \mathrm{M}_{\odot }$, sizes 1–3 pc, metallicity 0.0001–0.02, with the massive stars in primordial binaries and they represent young massive clusters (YMC) and moderately massive open clusters (OC). Such models produce dynamically paired BBH mergers that agree well with the observed masses, mass ratios, effective spin parameters, and final spins of the LVC O1/O2 merger events, provided BHs are born with low or no spin but spin-up after undergoing a BBH merger or matter accretion on to it. In particular, the distinctly higher mass, effective spin parameter, and final spin of GW170729 merger event is naturally reproduced, as also the mass asymmetry of the O3 event GW190412. The computed models produce intermediate-mass, $\sim 100\, \mathrm{M}_{\odot }$ BBH mergers with primary mass within the ‘PSN gap’ and also yield mergers involving remnants in the ‘mass gap’. They also suggest that YMCs and OCs produce persistent, Local-Universe GW sources detectable by LISA. Such clusters are also capable of producing eccentric LIGO-Virgo mergers.

This thesis covers various aspects of the numerical simulation of black-hole spacetimes according to Einstein's general theory of relativity, using the Spectral Einstein Code developed by the Caltech-Cornell-CITA collaboration. The first topic is improvement of binary-black-hole initial data. One such issue is the construction of binary-black-hole initial data with nearly extremal spins that remain nearly constant during the initial relaxation in an evolution. Another concern is the inclusion of physically realistic tidal deformations of the black holes to reduce the high-frequency components of the spurious gravitational radiation content, and represents a first step in incorporating post-Newtonian results in constraint-satisfying initial data. The next topic is the evolution of black-hole binaries and the gravitational waves they emit. The first spectral simulation of two inspiralling black holes through merger and ringdown is presented, in which the black holes are nonspinning and have equal masses. This work is extended to perform the first spectral simulations of two inspiralling black holes with moderate spins and equal masses, including the merger and ringdown. Two configurations are considered, in which both spins are either anti-aligned or aligned with the orbital angular momentum. Highly accurate gravitational waveforms are computed for all these cases, and are used to calibrate waveforms in the effective-one-body model. The final topic is the behavior of quasilocal black-hole horizons in highly dynamical situations. Simulations of a rotating black hole that is distorted by a pulse of ingoing gravitational radiation are performed. Multiple marginally outer trapped surfaces are seen to appear and annihilate with each other during the evolution, and the world tubes they trace out are all dynamical horizons. The dynamical horizon and angular momentum flux laws are evaluated in this context, and the dynamical horizons are contrasted with the event horizon. The formation of multiple marginally outer trapped surfaces in the Vaidya spacetime is also treated.

We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that $(i)$ in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, $(ii)$ in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, $(iii)$ at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

Context. The recent discovery of the binary black hole (BBH) merger event GW190521, between two black holes (BHs) of ≈100 Msamp, in addition to other massive BBH merger events involving BHs within the pair-instability supernova (PSN) mass gap have sparked widespread debate on the origin of such extreme gravitational-wave (GW) events. GW190521 simultaneously triggers two critical questions: how BHs can appear within the ‘forbidden’ PSN gap and, if they do, how they get to participate in general-relativistic (GR) mergers. Aims. In this study, I investigate whether dynamical interactions in young massive clusters (YMCs) serve as a viable scenario for assembling PSN-gap BBH mergers. Methods. To that end, I explore a grid of 40 new evolutionary models of a representative YMC of initial mass and size Mcl = 7.5 × 104 Msamp (N ≈ 1.28 × 105) and rh = 2 pc, respectively. The model grid ranges over metallicity 0.0002 ≤ Z ≤ 0.02 and comprises initial cluster configurations of King central concentration parameters W0 = 7 and 9. In each model, all BH progenitor stars are initially in primordial binaries following observationally motivated distributions. All cluster models are evolved with the direct, relativistic N-body code NBODY7, incorporating up-to-date remnant formation, BH natal spin, and GR merger recoil schemes. Results. Binary black hole mergers from these model cluster computations agree well with the masses and effective spin parameters, χeff, of the events from the latest gravitational-wave transient catalogue (GWTC). In particular, GW190521-like, that is to say ≈200 Msamp, low χeff events are produced via a dynamical merger among BHs derived from star-star merger products. GW190403_051519-like, that is PSN-gap, highly asymmetric, high χeff events result from mergers involving BHs that are spun up via matter accretion or a binary interaction. The resulting present-day, differential intrinsic merger rate density, within the PSN gap, accommodates that from GWTC well. Conclusions. This study demonstrates that, subject to model uncertainties, the tandem of massive binary evolution and dynamical interactions in ≲100 Myr-old, low metallicity YMCs in the Universe can plausibly produce GR mergers involving PSN-gap BHs and in rates consistent with that from up-to-date GW observations. Such clusters can produce extreme events similar to GW190521 and GW190403_051519. The upper limit of the models’ GW190521-type event rate is within the corresponding LIGO-Virgo-KAGRA (LVK)-estimated rate limits, although the typical model rate lies below LVK’s lower limit. The present YMC models yield a merger rate density of 0−3.8 × 10−2 yr−1 Gpc−3 for GW190521-type events. They produce GW190403_051519-like events at a rate within 0−1.6 × 10−1 yr−1 Gpc−3 and their total BBH-merger yield within the PSN gap is 0−8.4 × 10−1 yr−1 Gpc−3.

Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of the universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression has the advantages of being of quasilocal nature and independent of specific spacetime symmetries in order to be well defined. Therefore, we propose it as a definition for general quasilocal universal horizons. Using the new formalism we show that there are no universal analog of cosmological horizons for FLRW models for any scale factor function, and we also state that quasilocal universal horizons are restricted to trapped regions of the spacetime. Using the evolution equation, we analyze the formation of universal horizons under a truncated Horava-Lifshitz theory, in spherical symmetry, showing the existence of regions in parameter space where the universal horizon formation cannot be smooth from the center, under some physically reasonable assumptions. We conclude with our view on the next steps for the understanding of black holes in nonrelativistic gravity theories.

It is known that certain types of particle motion near black hole horizons are chaotic while it has been proposed the existence of a universal bound for their Lyapunov exponent. We discuss the relation between chaos and inaffinity in presence of black hole and cosmological horizons. We argue that although a relation between the Lyapunov exponent and the generalized surface gravity appears naturally, in general there is no reason for the Lyapunov exponent of classical trajectories to be bounded in generic spacetimes with horizon. Moreover, we show that the de Sitter spacetime and cosmological horizons act as a nest of chaos in holography and we find that the Lyapunov exponent of the trajectories is related to the inaffinity in the same way for both cosmological and black hole horizons. This suggests that there is no distinction by the Lyapunov exponent between maximal chaos of black hole and cosmological horizons.

The understanding of strong-field dynamics near black-hole horizons is a long-standing and challenging prob- lem in general relativity. Recent advances in numerical relativity and in the geometric characterization of black- hole horizons open new avenues into the problem. In this first paper in a series of two, we focus on the analysis of the recoil occurring in the merger of binary black holes, extending the analysis initiated in [1] with Robinson- Trautman spacetimes. More specifically, we probe spacetime dynamics through the correlation of quantities defined at the black-hole horizon and at null infinity. The geometry of these hypersurfaces responds to bulk gravitational fields acting as test screens in a scattering perspective of spacetime dynamics. Within a 3 + 1 approach we build an effective-curvature vector from the intrinsic geometry of dynamical-horizon sections and correlate its evolution with the flux of Bondi linear momentum at large distances. We employ this setup to study numerically the head-on collision of nonspinning black holes and demonstrate its validity to track the qualita- tive aspects of recoil dynamics at infinity. We also make contact with the suggestion that the antikick can be described in terms of a "slowness parameter" and how this can be computed from the local properties of the horizon. In a companion paper [2] we will further elaborate on the geometric aspects of this approach and on its relation with other approaches to characterize dynamical properties of black-hole horizons.