Trapping Horizon Research Articles

Mass Inflation without Cauchy Horizons.

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are present for dynamical geometries describing accreting black holes with slowly evolving inner trapping horizons, even in the absence of Cauchy horizons. The explicit evaluation of the adiabatic conditions behind these exponential buildups shows that this phenomenon is universally present for physically reasonable accreting conditions. This noneternal mass inflation does not require the introduction of global spacetime concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with nonextremal inner horizons, including the Kerr geometry in general relativity, and nonextremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived end point of gravitational collapse.

Surface gravity in spherically symmetric collapsing stars

Here we consider the generalized Oppenheimer–Snyder collapse of a star into a four-dimensional Einstein-Gauss–Bonnet black hole as well as a class of regular black holes labeled by the polytropic index of the stellar matter. We then analyze the nature of the horizon and the corresponding surface gravity outside and inside the star. The Hayward and Nielsen–Visser dynamical surface gravity are in agreement with the one resulting from the Killing vector of the outer static metric. However, these two definitions inside the star do not coincide with the Killing surface gravity outside the star when the star crosses the event horizon. This motivates us to study the surface gravity using Fodor’s approach to have a unique surface gravity at the mentioned moment. Then the extremality condition and the first law of thermodynamics are discussed at the trapping horizon of the star.

Cosmology of Tsallis and Kaniadakis holographic dark energy in Saez–Ballester theory and consideration of viscous van der Waals fluid

In the framework of Saez–Ballester (SB) theory, the current study proposes a reconstruction scheme for Tsallis and Kaniadakis holographic dark energy, particular cases of a more generalised Nojiri–Odintsov holographic dark energy (Nojiri and Odintsov, 2006; The European Physical Journal C, 2017, 77, pp.1-8.), with Hubble horizon and future event horizons serving as the universe’s respective trapping horizons. The Hubble parameter was rebuilt by placing a constraint on the metric potential inside the conservation equation. As a result, the holographic dark energy of Tsallis and Kaniadakis are recreated, and the cosmology and thermodynamics are examined. Lastly, an interacting van der Waals (VDW) coupled fluid model was examined in the context of bulk viscosity, and the behaviour of the equation of state (EoS) parameter was examined.

Evolving black hole with scalar field accretion

We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible by a new parametrization of the metric, in which the displacement from the horizon as well as its expansion rate feature explicitly. Our results are valid in a neighbourhood of the horizon and hold for any scalar field potential and spacetime asymptotics. An exact equation for the accretion rate is also obtained, which generalizes the standard Bondi formula. We also develop a dynamical system approach to study near-equilibrium black holes; using this formalism, we focus on a simple model to show that the near-equilibrium dynamics is characterised by scaling relations among dynamical variables. Moreover, we show that solutions with purely ingoing energy-momentum flux never reach equilibrium.

Constraints on horizonless objects after the EHT observation of Sagittarius A*

The images of Sagittarius A* recently released by the Event Horizon Telescope collaboration have been accompanied [ Astrophys. J. Lett. 930 (2022) L17]by an analysis of the constraints on the possible absence of a trapping horizon, i.e. on the possibility that the object at the center of our galaxy is an ultra-compact object with a surface re-emitting incident radiation. Using the observed image size and the broadband spectrum of Sgr A*, it is claimed that the radius of any surface, in which incident radiation is re-emitted thermally, is strongly bounded from above by these latest observations. Herein, we discuss how the reported constraint relies on the extremely strong assumption of perfect balance in the energy exchange between the accretion disk and the central object, and show that this is violated whenever the surface is endowed with any non-zero absorption coefficient. We derive the upper-bound constraints that can be cast on the radius and dimensionless absorption coefficient of the surface. We show that the conclusions of the analysis presented by the EHT collaboration hold only for unnaturally small values of the absorption coefficient (i.e. much lower than 10-14), and thus have to be significantly revised in scenarios with physical significance.

Thakurta metric does not describe a cosmological black hole

Recently, the Thakurta metric has been adopted as a model of primordial black holes. We show that the spacetime described by this metric has neither black-hole event horizon nor black-hole trapping horizon and involves the violation of all the standard energy conditions as a solution of the Einstein equation. Therefore, this metric does not describe a cosmological black hole in the early universe. It is pointed out that a contradictory claim by the other group stems from an incorrect choice of sign.

Black to white transition of a charged black hole

We present an exact solution of the Maxwell-Einstein equations, which describes the exterior of a charged spherical mass collapsing into its own trapping horizon and then bouncing back from an anti-trapping horizon at the same space location of the same asymptotic region. The solution is locally but not globally isometric to the maximally extended Reissner-Nordstr\"{o}m metric and depends on seven parameters. It is regular, and defined everywhere except for a small region, where quantum tunnelling is expected. This region lies outside the mass: the mass-bounce and its near exterior are governed by classical general relativity. We discuss the relevance of this result for the fate of realistic black holes. We comment on possible effects of the classical instabilities and the Hawking radiation.

Apparent horizons of the Thakurta spacetime and the description of cosmological black holes

We discuss the validity of the Thakurta metric to describe cosmological black holes by analysing the nature of its horizon. By adopting the preferred foliation of the Thakurta spacetime associated with the Kodama time, we demonstrate that the Thakurta horizon is indeed a future outer trapping horizon. Therefore, the respective observers see it as a cosmological black hole, contrary to some claims in the literature.

On the Inner Horizon Instability of Non-Singular Black Holes

Regular black holes represent a conservative model in which the classical singularity is replaced by a non-singular core without necessarily modifying the spacetime outside the trapping horizon. Given the possible lack of phenomenological signatures, it is crucial to study the consistency of the model. In this short work, we review the physical mechanism leading to the instability of the central core, arguing that that non-perturbative backreation is non-negligible and must be taken into account to provide a meaningful description of physical black holes.

Marginal tubes and foliations by marginal surfaces

In this paper, we introduce the notion of a marginal tube, which is a hypersurface foliated by marginal surfaces. It generalises the notion of a marginally trapped tube and several notions of black hole horizons, for example trapping horizons, isolated horizons, dynamical horizons, etc. We prove that if every spacelike section of a marginal tube is a marginal surface, then the marginal tube is null. There is no assumption on the topology of the marginal tube. To prove it, we study the geometry of spacelike surfaces in a four-dimensional spacetime with the help of double null coordinate systems. The result is valid for arbitrary four-dimensional spacetimes, regardless of any energy condition.

Geodesically complete black holes in Lorentz-violating gravity

We present a systematic study of the geometric structure of non-singular spacetimes describing black holes in Lorentz-violating gravity. We start with a review of the definition of trapping horizons, and the associated notions of trapped and marginally trapped surfaces, and then study their significance in frameworks with modified dispersion relations. This leads us to introduce the notion of universally marginally trapped surfaces, as the direct generalization of marginally trapped surfaces for frameworks with infinite signal velocities (Hořava-like frameworks), which then allows us to define universal trapping horizons. We find that trapped surfaces cannot be generalized in the same way, and discuss in detail why this does not prevent using universal trapping horizons to define black holes in Hořava-like frameworks. We then explore the interplay between the kinematical part of Penrose’s singularity theorem, which implies the existence of incomplete null geodesics in the presence of a focusing point, and the existence of multiple different metrics. This allows us to present a complete classification of all possible geometries that neither display incomplete physical trajectories nor curvature singularities. Our main result is that not all classes that exist in frameworks in which all signal velocities are realized in Hořava-like frameworks. However, the taxonomy of geodesically complete black holes in Hořava-like frameworks includes diverse scenarios such as evaporating regular black holes, regular black holes bouncing into regular white holes, and hidden wormholes.

Trapping horizons of the evolving charged wormhole and black bounce

We obtain one family of dynamic solutions in the Einstein-Maxwell-scalar(EMS) theory. Our solutions could describe the evolving charged black(white) hole or wormhole and its transition, including the case of black bounce/wormhole transition. We compare different wormhole throat definitions and suggest that the usage of trapping horizons is the most suitable choice for tracking the evolution of the dynamic black(white) hole and wormhole, and their conversion in a unified framework. Then we research several evolving processes in the appropriate parameters region, including the charge, the initial condition for the scalar hair, and parameters in our EMS Lagrangian. The results show that the appearance of a degenerate marginal trapped surface is the crucial event for the conversion or transition, particularly in these cases: i) when the evolving wormhole converts to a black hole, the surface emerges and splits into two trapping horizons; ii) if the metric would become a black hole but finally fails, two trapping horizons combine as the surface and then vanish; iii) if the black bounce/wormhole transition happens, one single trapping horizon changes its type.

Temperature and entropy\u2013area relation of quantum matter near spherically symmetric outer trapping horizons

We consider spherically symmetric spacetimes with an outer trapping horizon. Such spacetimes are generalizations of spherically symmetric black hole spacetimes where the central mass can vary with time, like in black hole collapse or black hole evaporation. While these spacetimes possess in general no timelike Killing vector field, they admit a Kodama vector field which in some ways provides a replacement. The Kodama vector field allows the definition of a surface gravity of the outer trapping horizon. Spherically symmetric spacelike cross sections of the outer trapping horizon define in- and outgoing lightlike congruences. We investigate a scaling limit of Hadamard 2-point functions of a quantum field on the spacetime onto the ingoing lightlike congruence. The scaling limit 2-point function has a universal form and a thermal spectrum with respect to the time parameter of the Kodama flow, where the inverse temperature beta = 2pi /kappa is related to the surface gravity kappa of the horizon cross section in the same way as in the Hawking effect for an asymptotically static black hole. Similarly, the tunnelling probability that can be obtained in the scaling limit between in- and outgoing Fourier modes with respect to the time parameter of the Kodama flow shows a thermal distribution with the same inverse temperature, determined by the surface gravity. This can be seen as a local counterpart of the Hawking effect for a dynamical horizon in the scaling limit. Moreover, the scaling limit 2-point function allows it to define a scaling limit theory, a quantum field theory on the ingoing lightlike congruence emanating from a horizon cross section. The scaling limit 2-point function as well as the 2-point functions of coherent states of the scaling limit theory is correlation-free with respect to separation along the horizon cross section; therefore, their relative entropies behave proportional to the cross-sectional area. We thus obtain a proportionality of the relative entropy of coherent states of the scaling limit theory and the area of the horizon cross section with respect to which the scaling limit is defined. Thereby, we establish a local counterpart, and microscopic interpretation in the setting of quantum field theory on curved spacetimes, of the dynamical laws of outer trapping horizons, derived by Hayward and others in generalizing the laws of black hole dynamics originally shown for stationary black holes by Bardeen, Carter and Hawking.

Thermodynamics of traversable wormholes in f(R,T) gravity

In this paper, we discuss thermodynamics for spherically symmetric and static traversable wormholes which include Morris–Thorne wormholes and charged wormholes in the background of [Formula: see text] gravity. The local coordinates have been used to find trapping horizons of these objects and generalized surface gravity has been worked out on the trapping horizons. The expression for the unified first law has also been derived from the gradient of Misner–Sharp energy with the help of gravitational field equations and from this law the first law of wormhole dynamics has been obtained. We have done this analysis for the simplest case of [Formula: see text] gravity where [Formula: see text], [Formula: see text] and [Formula: see text] being the traces of the Ricci and stress–energy tensors. Also, we have extended these thermodynamic results to non-minimal curvature-matter coupling.

From uneventful Horizon to firewall in D-dimensional effective theory

Assuming the standard effective-field-theoretic formulation of Hawking radiation, we show explicitly how a generic effective theory predicts a firewall from an initially uneventful horizon for a spherically symmetric, uncharged black hole in [Formula: see text] dimensions for [Formula: see text]. The firewall is created via higher-derivative interactions within the scrambling time after the collapsing matter enters the trapping horizon. This result manifests the trans-Planckian problem of Hawking radiation and demonstrates the incompatibility between Hawking radiation and the uneventful horizon.

Thermodynamics of dynamical wormholes

We study thermodynamics of dynamical traversable wormholes. The surface gravity is evaluated on the trapping horizon and the unified first law of thermodynamics is set up. The thermodynamic stability of these wormholes has been investigated. We have also extended these results to charged dynamical wormholes. Our results generalize those that exist for static Morris-Thorne wormholes.

Dynamical black hole in a bouncing universe

We analyze the causal structure of McVittie spacetime for a classical bouncing cosmological model. In particular, we compute the trapping horizons of the metric and integrate the trajectories of radial null geodesics before, during, and after the bounce takes place. In the contracting phase up to the occurrence of the bounce, a dynamical black hole is present. When the universe reaches a certain minimum scale, the trapping horizons disappear and the black hole ceases to exist. After the bounce, the central weak singularity becomes naked. In the expanding phase, for large positive values of the cosmic time, the behaviour of null geodesics indicates that the solution contains a black hole. These results suggest that neither a contracting nor an expanding universe can accommodate a black hole at all times.

Black holes in a type-II minimally modified gravity

In the context of the recently proposed type-II minimally modified gravity theory, i.e. a metric theory of gravity with two local physical degrees of freedom that does not possess an Einstein frame, we study spherically symmetric vacuum solutions to explore the strong gravity regime. Despite the absence of extra degrees of freedom in the gravity sector, the vacuum solutions are locally different from the Schwarzschild or Schwarzschild-(A)dS metric in general and thus the Birkhoff theorem does not hold. The general solutions are parameterized by several free functions of time and admit regular trapping and event horizons. Depending on the choice of the free functions of time, the null convergence condition may be violated in vacuum. Even in the static limit, while the solutions in this limit reduce to the Schwarzschild or Schwarzschild-(A)dS solutions, the effective cosmological constant deduced from the solutions is in general different from the cosmological value that is determined by the action. Nonetheless, once a set of suitable asymptotic conditions is imposed so that the solutions represent compact objects in the corresponding cosmological setup, the standard Schwarzschild or Schwarzschild-(A)dS metric is recovered and the effective cosmological constant agrees with the value inferred from the action.

Black hole in asymmetric cosmological bounce

AbstractWe determine the causal structure of the McVittie spacetime for a cosmological model with an asymmetric bounce. The analysis includes the computation of trapping horizons; regular, trapped, and antitrapped regions; and the integration of the trajectories of radial null geodesics before, during, and after the bounce. We find a trapped region since the beginning of the contracting phase up to shortly before the bounce, thus showing the existence of a black hole. When the universe reaches a certain minimum scale in the contracting phase, the trapping horizons disappear, and the central singularity becomes naked. These results suggest that neither a contracting nor an expanding universe can accommodate a black hole at all times.

Quantum effects across dynamical horizons

We present a generalization of the Hawking effect for dynamical trapping horizons by calculating the tunneling rate in the Hamilton–Jacobi formalism. It turns out that all horizons classified by Hayward are subjected to thermal quantum effects. While the Hawking effect for future outer and past inner trapping horizons is given as a particle emission, we show that the Hawking effect for future inner and past outer trapping horizons translates to an absorption. The universality of the treatment allows a natural transfer to the static case.