The collisional Penrose process

Shortly after the discovery of the Kerr metric in 1963, it was realized that a region existed outside of the black hole’s event horizon where no time-like observer could remain stationary. In 1969, Roger Penrose showed that particles within this ergosphere region could possess negative energy, as measured by an observer at infinity. When captured by the horizon, these negative energy particles essentially extract mass and angular momentum from the black hole. While the decay of a single particle within the ergosphere is not a particularly efficient means of energy extraction, the collision of multiple particles can reach arbitrarily high center-of-mass energy in the limit of extremal black hole spin. The resulting particles can escape with high efficiency, potentially serving as a probe of high-energy particle physics as well as general relativity. In this paper, we briefly review the history of the field and highlight a specific astrophysical application of the collisional Penrose process: the potential to enhance annihilation of dark matter particles in the vicinity of a supermassive black hole.     

Exact solutions for spherical gravitational collapse around a black hole:the effect of tangential pressure

Spherical gravitational collapse towards a black hole with non-zero tangential pressure is studied.Exact solutions corresponding to different equations of state are given.We find that when taking the tangential pressure into account,the exact solutions have three qualitatively different outcomes.For positive tangential pressure,the shell around a black hole may eventually collapse onto the black hole,or expand to infinity,or have a static but unstable solution,depending on the combination of black hole mass,mass of the shell and the pressure parameter.For vanishing or negative pressure,the shell will collapse onto the black hole.For all eventually collapsing solutions,the shell will cross the event horizon,instead of accumulating outside theeventhorizon,even if clocked by a distant stationary observer.     

Horizon Entropy

Although the laws of thermodynamics are well established for black hole horizons, much less has been said in the literature to support the extension of these laws to more general settings such as an asymptotic de Sitter horizon or a Rindler horizon (the event horizon of an asymptotic uniformly accelerated observer). In the present paper we review the results that have been previously established and argue that the laws of black hole thermodynamics, as well as their underlying statistical mechanical content, extend quite generally to what we call here causal horizons. The root of this generalization is the local notion of horizon entropy density.     

Radiation Energy Flux and Radiation Power of Schwarzschild Black Hole

Applying the entropy density near the event horizon, we obtained the result that the radiation energy flux of the black hole is always proportional to the quartic of the temperature of its event horizon. That is to say, the thermal radiation of the black hole always satisfies the generalized Stefan–Boltzmann law. The derived generalized Stefan–Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient which is related to the black hole mass, the kinds of radiation particles and space–time metric near the event horizon. In this paper, we have put forward a thermal particle model in curved space–time. By this model, the result has been obtained that when the thin film thickness and the cut-off distance are both fixed, the radiation energy flux received by observer far away from the Schwarzschild black hole is proportional to the average radial effusion velocity of the radiation particles in the thin film, and inversely proportional to the square of the distance between the observer and the black hole.     

A boosted Kerr black hole solution and the structure of a general astrophysical black hole

A solution of Einstein’s vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity—which are the core of the black hole structure—do not alter, being independent of the boost parameter. Possible consequences for astrophysical processes connected with Penrose processes in the asymmetric ergosphere are discussed.     

静态球对称黑洞的热质点模型及辐射功率

利用静态球对称黑洞的热质点模型,研究了黑洞的热辐射规律,得到了当η取固有厚度时,对所有Schwarzschild黑洞,其辐射功率都相同,其视界处的辐射能通量与黑洞的质量的平方成反比,而距黑洞遥远的观察者所接收到的辐射能通量与观测者到黑洞的距离的平方成反比; Reissner-Nordstrm黑洞视界处的辐射能通量和辐射功率不仅与黑洞的质量有关,还与黑洞的电荷有关,而距黑洞遥远的观察者所接收到的辐射能通量,当截断的固有厚度η、黑洞的质量m和电荷Q取定后与观测者到黑洞之间的距离的 关键词： 静态球对称黑洞 热质点模型 辐射功率 辐射能通量     

Rotating dirty black hole and its shadow

In this paper, we examine the effect of dark matter to a Kerr black hole of mass m. The metric is derived using the Newman-Janis algorithm, where the seed metric originates from the Schwarzschild black hole surrounded by a spherical shell of dark matter with mass M and thickness Δr_s. The seed metric is also described in terms of a piecewise mass function with three different conditions. Specializing in the non-trivial case where the observer resides inside the dark matter shell, we analyzed how the effective mass of the black hole environment affects the basic black hole properties. A high concentration of dark matter near the rotating black hole is needed to have considerable deviations on the horizons, ergosphere, and photonsphere radius. The time-like geodesic, however, shows more sensitivity to deviation even at very low dark matter density. Further, the location of energy extraction via the Penrose process is also shown to remain unchanged. With how the dark matter distribution is described in the mass function, and the complexity of how the shadow radius is defined for a Kerr black hole, deriving an analytic expression for Δr_s as a condition for notable dark matter effects to occur remains inconvenient.     

Perturbative Approach to the Inner Structure of a Rotating Black Hole

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an empty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Kerr. We shall discuss the generalization of Price's analysis (regarding the latetime asymptotic decay of perturbations outside the black hole) from Schwarzschild to Kerr, and present preliminary results. We then consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbitrarily) small initial perturbations. This, we argue, justifies the attempt to apply the small-perturbation approach to the black hole's interior. We discuss the physical significance of this late-time region. We shall also outline the strategy we use for evolving the perturbations from the event horizon to the inner horizon.     

Origin of the blackhole information paradox

It is argued that the blackhole information paradox originates from treating the blackhole geometry as strictly classical. It is further argued that the theory of quantum fields in a classical curved space with a horizon is an ill posed problem. If the geometry is allowed to fluctuate quantum mechanically, then the horizon effectively disappears. The sharp horizon emerges only in the classical limit when the ratio of the Compton wavelength of the black hole to its Schwarzschild radius vanishes. The region of strong gravity that develops when matter collapses to form the blackhole remains visible to the whole of spacetime and has to be described by a microscopic theory of strong gravity. The arguments imply that the information paradox is demoted from a paradox involving fundamental principles of physics to the problem of describing how matter at the highest densities gravitates.     

The Thermal Radiation from Static Spherically Symmetric Black Holes

By use of the radiant emittance near the event horizon of static spherically symmetric black hole, the radiation field around the black hole was studied and found the generalized Stefan Boltzmann coefficient σ of thermal radiation near the event horizon is much greater than the flat space-time blackbody radiation. For Schwarzschild black hole, σ will increased as the black hole mass increases. For Reissner-Nordström black hole, σ has some relation with the quality and the charges of the black hole. Thermal particle model was proposed creatively to study the radiation power and radiant energy flux of static spherically symmetric black hole, found when η take the inherent thickness, for all Schwarzschild black hole the radiation power are the same and the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole, for Reissner-Nordström black hole the radiation power is associated with the quality and the charge of the black hole. When given the mass and charges of the black hole, the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole.     

Overcharging a Reissner-Nordstr?m Taub-NUT regular black hole

The destruction of a regular black hole event horizon might provide us the possibility to access regions inside black hole event horizon. This paper investigates the possibility of overcharging a charged Taub-NUT regular black hole via the scattering of a charged field and the absorption of a charged particle. For the charged scalar field scattering, both the near-extremal and extremal charged Taub-NUT regular black holes cannot be overcharged. For the test charged particle absorption, the result shows that the event horizon of the extremal charged Taub-NUT regular black hole still exists while the event horizon of the near-extremal one can be destroyed. However, if the charge and energy cross the event horizon in a continuous path, the near-extremal charged Taub-NUT regular black hole might not be overcharged.     

Fuzzy spaces topology change as a possible solution to the black hole information loss paradox

The black hole information loss paradox is one of the most intricate problems in modern theoretical physics. A proposal to solve this is one related with topology change. However it has found some obstacles related to unitarity and cluster decomposition (locality). In this Letter we argue that modelling the black hole's event horizon as a noncommutative manifold – the fuzzy sphere – we can solve the problems with topology change, getting a possible solution to the black hole information loss paradox.     

The four laws of black hole mechanics

Expressions are derived for the mass of a stationary axisymmetric solution of the Einstein equations containing a black hole surrounded by matter and for the difference in mass between two neighboring such solutions. Two of the quantities which appear in these expressions, namely the area A of the event horizon and the surface gravity of the black hole, have a close analogy with entropy and temperature respectively. This analogy suggests the formulation of four laws of black hole mechanics which correspond to and in some ways transcend the four laws of thermodynamics.Research supported in part by the National Science Foundation.     

The effect of spherical shells of matter on the Schwarzschild black hole

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with aC ⁰ metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational shock waves at the horizon of a Schwarzschild black hole, and (2) a configuration involving onlyone external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the Wheeler wormhole to another universe.Supported in part by the Stichting voor Fundamenteel Onderzoek der Materie     

Unitary dynamics of spherical null gravitating shells

The dynamics of a thin spherically symmetric shell of zero-rest-mass matter in its own gravitational field is studied. A form of action principle is used that enables the reformulation of the dynamics as motion on a fixed background manifold. A self-adjoint extension of the Hamiltonian is obtained via the group quantization method. Operators of position and of direction of motion are constructed. The shell is shown to avoid the singularity, to bounce and to re-expand to that asymptotic region from which it contracted; the dynamics is, therefore, truly unitary. If a wave packet is sufficiently narrow and/or energetic then an essential part of it can be concentrated under its Schwarzschild radius near the bounce point but no black hole forms. The quantum Schwarzschild horizon is a linear combination of a black and white hole apparent horizons rather than an event horizon.     

Three remarks on axisymmetric stationary horizons

In the first remark the catalogue of axisymmetric stationary horizons is completed by a subset of uncharged translation-symmetric horizons, which was ignored in the previous paper [5]. The subset consists of two one-parameter families: extreme Kerr horizon (a=m) and a more symmetric family. In the second remark the surface area, net angular momentum and net charges of a black hole are computed. It turns out that the four invariant functionsA, B, C, D used in [5] to classify the horizons describe, at least formally and up to a constant factor:A the profile of the black hole surface,B the surface density of angular momentum andC cosD, C sinD the surface density of electric and magnetic charge. In the third remark a simplified model of a black hole surrounded by a charged matter shell is found to satisfy a sort of generalized “no-hair-conjecture”. An example of a non-Kerr-Newman field around a horizon is provided; the magnetic field in it is hoped to have some astrophysical importance.     

Tunneling into fuzzball states

String theory suggests that black hole microstates are quantum, horizon sized ‘fuzzballs’, rather than smooth geometries with horizon. Radiation from fuzzballs can carry information and does not lead to information loss. But if we let a shell of matter collapse then it creates a horizon, and it seems that subsequent radiation will lead to information loss. We argue that the resolution to this problem is that the shell can tunnel to the fuzzball configurations. The amplitude for tunneling is small because we are relating two macroscopically different configurations, but the number of states that we can tunnel to, given through the Bekenstein entropy, is very large. These small and large numbers can cancel each other, making it possible for the shell to tunnel into fuzzball states before a significant amount of radiation has been emitted. This offers a way to resolve the information paradox.