Black Hole Dynamics Research Articles

Wavelet spectral timing: X-ray reverberation from a dynamic black hole corona hidden beneath ultrafast outflows

ABSTRACT Spectral timing analyses based upon wavelet transforms provide a new means to study the variability of the X-ray emission from accreting systems, including AGN, stellar mass black holes, and neutron stars, and can be used to trace the time variability of X-ray reverberation from the inner accretion disc. The previously missing iron K reverberation time lags in the AGN IRAS 13224–3809 and MCG–6-30-15 are detected and found to be transitory in nature. Reverberation can be hidden during periods in which variability in the iron K band becomes dominated by ultrafast outflows. Following the time evolution of the reverberation lag between the corona and inner accretion disc, we may observe the short time-scale increase in scale height of the corona as it is accelerated away from the accretion disc during bright X-ray flares in the AGN I Zw 1. Measuring the variation of the reverberation lag that corresponds to the continuous, stochastic variations of the X-ray luminosity sheds new light on the disc–corona connection around accreting black holes. Hysteresis is observed between the X-ray count rate and the scale height of the corona, and a time lag of 10∼40 ks is observed between the rise in luminosity and the increase in reverberation lag. This correlation and lag are consistent with viscous propagation through the inner accretion disc, leading first to an increase in the flux of seed photons that are Comptonized by the corona, before mass accretion rate fluctuations reach the inner disc and are able to modulate the structure of the corona.

Slowly evolving horizons in Einstein gravity and beyond

We study event horizon candidates for slowly evolving dynamical black holes (BHs) in General Relativity and Einstein–Gauss–Bonnet (EGB) gravity. Such a type of horizon candidate has been termed as slowly evolving null surface (SENS). It signifies a near-equilibrium state of a dynamic BH. We demonstrate the time evolution of such surfaces for three different metrics. First, we locate such a surface for a charged Vaidya metric and show that the parameter space of the BH gets constrained to allow a physically admissible SENS. We then consider a supertranslated Vaidya solution that contains a non-spherical horizon and study the properties of the SENS. This spacetime generates a non-vanishing shear at the SENS due to the presence of the supertranslation field. The SENS for a spherically symmetric Vaidya-like solution in EGB gravity yields a bound on the accretion rate that depends on the size of the horizon. We also show that the first and second laws of BH mechanics can be established for these slowly evolving surfaces.

Entropy current and fluid-gravity duality in Gauss-Bonnet theory

Working within the approximation of small amplitude expansion, recently an entropy current has been constructed on the horizons of dynamical black hole solution in any higher derivative theory of gravity. In this note, we have dualized this horizon entropy current to a boundary entropy current in an asymptotically AdS black hole metric with a dual description in terms of dynamical fluids living on the AdS boundary. This boundary entropy current is constructed using a set of mapping functions relating each point on the horizon to a point on the boundary. We have applied our construction to black holes in Einstein-Gauss-Bonnet theory. We have seen that up to the first order in derivative expansion, Gauss-Bonnet terms do not add any extra corrections to fluid entropy as expected. However, at the second order in derivative expansion, the boundary current will non-trivially depend on how we choose our horizon to boundary map, which need not be expressible entirely in terms of fluid variables. So generically, the boundary entropy current generated by dualizing the horizon current will not admit a fluid dynamical description.

Failed supernova simulations beyond black hole formation

ABSTRACT We present an axisymmetric failed supernova simulation beyond black hole formation, for the first time with numerical relativity and two-moment multi-energy neutrino transport. To ensure stable numerical evolution, we use an excision method for neutrino radiation hydrodynamics within the inner part of black hole domain. We demonstrate that our excision method is capable of stably evolving the radiation hydrodynamics in dynamical black hole space–time. As a remarkable signature of the final moment of proto-neutron star (PNS), we find the emergence of high-energy neutrinos. Those high-energy neutrinos are associated with the PNS shock surface being swallowed by the central black hole and could be a possible observable of failed supernovae.

Universality in binary black hole dynamics: An integrability conjecture

The waveform of a binary black hole coalescence appears to be both simple and universal. In this essay we argue that the dynamics should admit a separation into “fast and slow” degrees of freedom, such that the latter are described by an integrable system of equations, accounting for the simplicity and universality of the waveform. Given that Painlevé transcendents are a smoking gun of integrable structures, we propose the Painlevé-II transcendent as the key structural element threading a hierarchy of asymptotic models aiming at capturing different (effective) layers in the dynamics. Ward’s conjecture relating integrable and (anti-)self-dual solutions can provide the avenue to encode background binary black hole data in (nonlocal) twistor structures.

Ketju – resolving small-scale supermassive black hole dynamics in gadget-4

ABSTRACT We present the new public version of the ketju supermassive black hole (SMBH) dynamics module, as implemented into gadget-4. ketju adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularized integrator instead of the leapfrog integrator with gravitational softening used by gadget-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. ketju also includes post-Newtonian (PN) corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the PN equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented ketju SMBH dynamics module can also be straightforwardly incorporated into other codes similar to gadget-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.

De Sitter-Invariant Black Holes

In the de Sitter-invariant approach to gravitation, all solutions to the gravitational field equations are spacetimes that reduce locally to de Sitter. Consequently, besides including a Schwarzschild event horizon, the de Sitter-invariant black hole also has a de Sitter cosmic horizon. Accordingly, it can lodge matter and dark energies. Owing to this additional structure concerning Poincaré-invariant general relativity, such a black hole can establish a link between the black hole dynamics and the universe’s evolution. Possible implications for cosmology are discussed, and a comparison with recent observations indicating the existence of a cosmological coupling of black holes is presented.

Challenging event horizons with spin (3/2) fields

We attempt to destroy the event horizons of Kerr black holes by perturbing them with massless spin (3/2) fields. We carry out a detailed analysis by incorporating the explicit form of the absorption probabilities and backreaction effects due to the self energy of the test fields. For extremal and nearly extremal black holes, backreaction effects dominate for perturbations with large magnitudes. However, small perturbations can destroy the event horizons of extremal black holes and drive nearly extremal black holes closer to extremality. Eventually, nearly extremal black holes reach a certain stage where they can be continuously driven to extremality and beyond. Both the cosmic censorship conjecture and the third law of black hole dynamics can be violated by spin (3/2) fields. This directly follows from the fact that fermionic fields do not satisfy the null energy condition. Therefore this result does not contradict with the fact that cosmic censorship and the laws of black hole mechanics remain valid for perturbations satisfying the null energy condition.

Dynamical Black Hole Entropy in Effective Field Theory

In recent work, Hollands, Kovács and Reall have built on previous work of Wall to provide a definition of dynamical black hole entropy for gravitational effective field theories (EFTs). This entropy satisfies a second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms.

Dain’s invariant for black hole initial data

Dynamical black holes in the non-perturbative regime are not mathematically well understood. Studying approximate symmetries of spacetimes describing dynamical black holes gives an insight into their structure. Utilising the property that approximate symmetries coincide with actual symmetries when they are present allows one to construct geometric invariants characterising the symmetry. In this paper, we extend Dain’s construction of geometric invariants characterising stationarity to the case of initial data sets for the Einstein equations corresponding to black hole spacetimes. We prove the existence and uniqueness of solutions to a boundary value problem showing that one can always find approximate Killing vectors in black hole spacetimes and these coincide with actual Killing vectors when they are present. In the time-symmetric setting we make use of a 2 + 1 decomposition to construct a geometric invariant on a marginally outer trapped surface that vanishes if and only if the Killing initial data equations are locally satisfied.

Dynamics of intermediate mass black holes in globular clusters

Context. We recently introduced a new method for simulating collisional gravitational N-body systems with approximately linear time scaling with N. Our method is based on the multi-particle collision (MPC) scheme, previously applied in fluid dynamics and plasma physics. We were able to simulate globular clusters with a realistic number of stellar particles (at least up to several times 106) on a standard workstation. Aims. We simulated clusters hosting an intermediate mass black hole (IMBH), probing a broad range of BH-cluster and BH–average-star mass ratios, unrestricted by the computational constraints that affect direct N-body codes. Methods. We set up a grid of hybrid particle-in-cell-MPC N-body simulations using our implementation of the MPC method, MPCDSS. We used either single mass models or models with a Salpeter mass function (a single power law with an exponent of −2.35), with the IMBH initially sitting at the centre. The force exerted by and on the IMBH was evaluated with a direct sum scheme with or without softening. For all simulations we measured the evolution of the Lagrangian radii and core density and velocity dispersion over time. In addition, we also measured the evolution of the velocity anisotropy profiles. Results. We find that models with an IMBH undergo core collapse at earlier times, the larger the IMBH mass the shallower they are, with an approximately constant central density at core collapse. The presence of an IMBH tends to lower the central velocity dispersion. These results hold independently of the mass function of the model. For the models with Salpeter MF, we observed that equipartition of kinetic energies is never achieved, even long after core collapse. Orbital anisotropy at large radii appears to be driven by energetic escapers on radial orbits, triggered by strong collisions with the IMBH in the core. We measured the wander radius, that is the distance of the IMBH from the centre of mass of the parent system over time, finding that its distribution has positive kurtosis. Conclusions. Among the results we obtained, which mostly confirm or extend previously known trends that had been established over the range of parameters accessible to direct N-body simulations, we underline that the leptokurtic nature of the IMBH wander radius distribution might lead to IMBHs presenting as off-centre more frequently than expected, with implications on observational IMBH detection.

Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity

We propose a new method to account for quantum-gravitational effects in cosmological and black hole spacetimes. At the core of our construction is the “decoupling mechanism”: when a physical infrared scale overcomes the effect of the regulator implementing the Wilsonian integration of fluctuating modes, the renormalization group flow of the scale-dependent effective action freezes out, so that at the decoupling scale the latter approximates the standard quantum effective action. Identifying the decoupling scale allows to access terms in the effective action that were not part of the original truncation and thus to study leading-order quantum corrections to field equations and their solutions. Starting from the Einstein-Hilbert truncation, we exploit for the first time the decoupling mechanism in quantum gravity to investigate the dynamics of quantum-corrected black holes from formation to evaporation. Our findings are in qualitative agreement with previous results in the context of renormalization group improved black holes, but additionally feature novel properties reminiscent of higher-derivative operators with specific non-local form factors.

Non-linear black hole dynamics and Carrollian fluids

The dynamics of black hole horizons has recently been linked to that of Carrollian fluids. This results in a dictionary between geometrical quantities and those of a fluid with unusual properties due its underlying Carrollian symmetries. In this work we explore this relation in dynamical settings with the interest of shedding light on either side by relevant observations. In particular: we discuss how the null surface where the Carrollian fluid evolves is affected by its behavior; that the fluid’s equilibration properties are tied to teleological considerations; the connection of higher derivative contributions as both source of energy and dissipation for the fluid and the non-linear behavior of black holes. This latter point, connects with discussions of non-linear modes in the relaxation to equilibrium of perturbed black holes.

Complementarity and the unitarity of the black hole S-matrix

Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.

Curvature and dynamical spacetimes: can we peer into the quantum regime?

Stationary compact astrophysical objects such as black holes and neutron stars behave as classical systems from the gravitational point of view. Their (observable) curvature is everywhere ‘small’. Here we investigate whether mergers of such objects, or other strongly dynamical spacetimes such as collapsing configurations, may probe the strong-curvature regime of general relativity. Our results indicate that dynamical black hole spacetimes always result in a modest increase in the Kretschmann scalar, relative to the stationary state. In contrast, we find that the Kretschmann scalar can dynamically increase by orders of magnitude, during the gravitational collapse of scalar fields, and that the (normalized) peak curvature does not correspond to that of the critical solution. Nevertheless, without fine tuning of initial data, this increase lies far below that needed to render quantum-gravity corrections important.

Modeling Quantum Particles Falling into a Black Hole: The Deep Interior Limit

In this paper, we construct a solvable toy model of the quantum dynamics of the interior of a spherical black hole with falling spherical scalar field excitations. We first argue about how some aspects of the quantum gravity dynamics of realistic black holes emitting Hawking radiation can be modeled using Kantowski–Sachs solutions with a massless scalar field when one focuses on the deep interior region r≪M (including the singularity). Further, we show that in the r≪M regime, and in suitable variables, the KS model becomes exactly solvable at both the classical and quantum levels. The quantum dynamics inspired by loop quantum gravity is revisited. We propose a natural polymer quantization where the area a of the orbits of the rotation group is quantized. The polymer (or loop) dynamics is closely related to the Schroedinger dynamics away from the singularity with a form of continuum limit naturally emerging from the polymer treatment. The Dirac observable associated with the mass is quantized and shown to have an infinite degeneracy associated with the so-called ϵ-sectors. Suitable continuum superpositions of these are well-defined distributions in the fundamental Hilbert space and satisfy the continuum Schroedinger dynamics.

Isolated and dynamical black hole mergers withB-POP: the role of star formation and dynamics, star cluster evolution, natal kicks, mass and spins, and hierarchical mergers

ABSTRACTThe current interpretation of LIGO–Virgo–KAGRA data suggests that the primary mass function of merging binary black holes (BBHs) at redshift z ≲ 1 contains multiple structures, while spins are relatively low. Theoretical models of BBH formation in different environments can provide a key to interpreting the population of observed mergers, but they require the simultaneous treatment of stellar evolution and dynamics, galaxy evolution, and general relativity. We present B-POP, a population synthesis tool to model BBH mergers formed in the field or via dynamical interactions in young, globular, and nuclear clusters. Using B-POP, we explore how black hole (BH) formation channels, star cluster evolution, hierarchical mergers, and natal BH properties affect the population of BBH mergers. We find that the primary mass distribution of BBH mergers extends beyond $M_1 \simeq 200\, {}$ M⊙, and the effective spin parameter distribution hints at different natal spins for single and binary BHs. Observed BBHs can be interpreted as members of a mixed population comprised of $\sim 34{{\ \rm per\ cent}} \, {}(66{{\ \rm per\ cent}})$ isolated (dynamical) BBHs, with the latter likely dominating at redshift z > 1. Hierarchical mergers constitute the $4.6\!-\!7.9{{\ \rm per\ cent}}$ of all mergers in the reference model, dominating the primary mass distribution beyond $M_1 \gt 65\, {}$ M⊙. The inclusion of cluster mass-loss and expansion causes an abrupt decrease in the probability for mergers beyond the third generation to occur. Considering observational biases, we find that $2.7\!-\!7.5{{\ \rm per\ cent}}$ of mock mergers involve intermediate-mass black hole (IMBH) seeds formed via stellar collisions. Comparing this percentage to observed values will possibly help us to constrain IMBH formation mechanisms.

Barren plateaus from learning scramblers with local cost functions

The existence of barren plateaus has recently revealed new training challenges in quantum machine learning (QML). Uncovering the mechanisms behind barren plateaus is essential in understanding the scope of problems that QML can efficiently tackle. Barren plateaus have recently been shown to exist when learning global properties of random unitaries, which is relevant when learning black hole dynamics. Establishing whether local cost functions can circumvent these barren plateaus is pertinent if we hope to apply QML to quantum many-body systems. We prove a no-go theorem showing that local cost functions encounter barren plateaus in learning random unitary properties.

Vaidya and Generalized Vaidya Solutions by Gravitational Decoupling

In this paper, we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution that can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and most well known when the mass function is the function only of space coordinate r. The second case is a Vaidya spacetime case when the mass function depends on time v. Finally, the third case represents the generalization of these two cases: the mass function is the function of both r and v. We also calculate the apparent horizon and singularity locations for all three cases.

Dynamics of binary black holes in young star clusters: the impact of cluster mass and long-term evolution

ABSTRACT Dynamical interactions in dense star clusters are considered one of the most effective formation channels of binary black holes (BBHs). Here, we present direct N-body simulations of two different star cluster families: low-mass (∼500–800 M⊙) and relatively high-mass star clusters (≥5000 M⊙). We show that the formation channels of BBHs in low- and high-mass star clusters are extremely different and lead to two completely distinct populations of BBH mergers. Low-mass clusters host mainly low-mass BBHs born from binary evolution, while BBHs in high-mass clusters are relatively massive (chirp mass up to ∼100 M⊙) and driven by dynamical exchanges. Tidal disruption dramatically quenches the formation and dynamical evolution of BBHs in low-mass clusters on a very short time-scale (≲100 Myr), while BBHs in high-mass clusters undergo effective dynamical hardening until the end of our simulations (1.5 Gyr). In high-mass clusters, we find that 8 per cent of BBHs have primary mass in the pair-instability mass gap at metallicity Z = 0.002, all of them born via stellar collisions, while only one BBH with primary mass in the mass gap forms in low-mass clusters. These differences are crucial for the interpretation of the formation channels of gravitational-wave sources.