The Inner Structure of Black Holes

We study the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the r = 0 hypersurface. The inner black hole region is bounded (in the future) by singularities. This resembles the classical inner structure of a Schwarzschild black hole and it is remarkably different from the inner structure of a charged static Reissner-Nordström or a stationary rotating Kerr black holes.     

Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsars

An astrophysically realistic model of wave dynamics in black-hole spacetimes must involve a nonspherical background geometry with angular momentum. We consider the evolution of gravitational (and electromagnetic) perturbations in rotating Kerr spacetimes. We show that a rotating Kerr black hole becomes "bald" slower than the corresponding spherically symmetric Schwarzschild black hole. Moreover, our results turn over the traditional belief (which has been widely accepted during the last three decades) that the late-time tail of gravitational collapse is universal. Our results are also of importance both to the study of the no-hair conjecture and the mass-inflation scenario (stability of Cauchy horizons).     

Black holes in general relativity

It is assumed that the singularities which occur in gravitational collapse are not visible from outside but are hidden behind an event horizon. This means that one can still predict the future outside the event horizon. A black hole on a spacelike surface is defined to be a connected component of the region of the surface bounded by the event horizon. As time increase, black holes may merge together but can never bifurcate. A black hole would be expected to settle down to a stationary state. It is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating. These results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary black hole is a Kerr solution. Using this conjecture and the result that the surface area of black holes can never decrease, one can place certain limits on the amount of energy that can be extracted from black holes.     

Black hole emissions and phase transitions

The nonthermal emission of a rotating black hole is related to the inner horizon of the hole. The transition from the Kerr black hole state to the naked singularity state is considered as a phase transition. An arrangement of the energetics of Kerr black holes into a two-phase thermodynamics is suggested.     

Particle acceleration in Horava–Lifshitz black holes

In this paper we calculate the center-of-mass energy of two colliding test particles near the rotating and non-rotating Horava–Lifshitz black hole. For the case of a slowly rotating KS solution of Horava–Lifshitz black hole we compare our results with the case of Kerr black holes. We confirm the limited value of the center-of-mass energy for static black holes and unlimited value of the center-of-mass energy for rotating black holes. Numerically, we discuss temperature dependence of the center-of-mass energy on the black hole horizon. We obtain the critical angular momentum of particles. In this limit the center-of-mass energy of two colliding particles in the neighborhood of the rotating Horava–Lifshitz black hole could be arbitrarily high. We found appropriate conditions where the critical angular momentum could have an orbit outside the horizon. Finally, we obtain the center-of-mass energy corresponding to this circle orbit.     

Gravitational Collapse in Loop Quantum Gravity

In this paper we study the gravitational collapse applying methods of loop quantum gravity to a minisuperspace model. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust matter) is localized and the other (outside) where the metric is Kantowski–Sachs type. We study the Hamiltonian constraint obtaining a set of three difference equations that give a regular and natural evolution beyond the classical singularity point in “r=0” localized.     

Black holes: a physical route to the Kerr metric

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole. In this paper I discuss the possibility of a quasi–stationary transition from rotating equilibrium configurations of normal matter to rotating bla ck holes.     

Exact solutions for shells collapsing towards a pre-existing black hole

The gravitational collapse of a star is an important issue both for general relativity and astrophysics, which is related to the well-known “frozen star” paradox. This paradox has been discussed intensively and seems to have been solved in the comoving-like coordinates. However, to a real astrophysical observer within a finite time, this problem should be discussed in the point of view of the distant rest-observer, which is the main purpose of this Letter. Following the seminal work of Oppenheimer and Snyder (1939), we present the exact solution for one or two dust shells collapsing towards a pre-existing black hole. We find that the metric of the inner region of the shell is time-dependent and the clock inside the shell becomes slower as the shell collapses towards the pre-existing black hole. This means the inner region of the shell is influenced by the property of the shell, which is contrary to the result in Newtonian theory. It does not contradict the Birkhoff's theorem, since in our case we cannot arbitrarily select the clock inside the shell in order to ensure the continuity of the metric. This result in principle may be tested experimentally if a beam of light travels across the shell, which will take a longer time than without the shell. It can be considered as the generalized Shapiro effect, because this effect is due to the mass outside, but not inside as the case of the standard Shapiro effect. We also found that in real astrophysical settings matter can indeed cross a black hole's horizon according to the clock of an external observer and will not accumulate around the event horizon of a black hole, i.e., no “frozen star” is formed for an external observer as matter falls towards a black hole. Therefore, we predict that only gravitational wave radiation can be produced in the final stage of the merging process of two coalescing black holes. Our results also indicate that for the clock of an external observer, matter, after crossing the event horizon, will never arrive at the “singularity” (i.e. the exact center of the black hole), i.e., for all black holes with finite lifetimes their masses are distributed within their event horizons, rather than concentrated at their centers. We also present a worked-out example of the Hawking's area theorem.     

On the black hole limit of rotating discs and rings

Solutions to Einstein’s field equations describing rotating fluid bodies in equilibrium permit parametric (i.e. quasi-stationary) transitions to the extreme Kerr solution (outside the horizon). This has been shown analytically for discs of dust and numerically for ring solutions with various equations of state. From the exterior point of view, this transition can be interpreted as a (quasi) black hole limit. All gravitational multipole moments assume precisely the values of an extremal Kerr black hole in the limit. In the present paper, the way in which the black hole limit is approached is investigated in more detail by means of a parametric Taylor series expansion of the exact solution describing a rigidly rotating disc of dust. Combined with numerical calculations for ring solutions our results indicate an interesting universal behaviour of the multipole moments near the black hole limit.     

Weak cosmic censorship: as strong as ever

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.     

Pulsation of black holes

The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.     

Formation of black hole and emission of gravitational waves

Numerical simulations were performed for the formation process of rotating black holes. It is suggested that Kerr black holes are formed for wide ranges of initial parameters. The nature of gravitational waves from a test particle falling into a Kerr black hole as well as the development of 3D numerical relativity for the coalescing binary neutron stars are discussed.     

Superradiance resonance cavity outside rapidly rotating black holes

We discuss the late-time behavior of a dynamically perturbed Kerr black hole. We present analytic results for near-extreme Kerr black holes that show that the large number of virtually undamped quasinormal modes that exist for nonzero values of the azimuthal eigenvalue m combine in such a way that the field oscillates with an amplitude that decays as 1/t at late times. This prediction is verified using numerical time evolutions of the Teukolsky equation. We argue that the observed behavior can be understood in terms of the presence of a "superradiance resonance cavity" immediately outside the black hole, and discuss whether it may be relevant for astrophysical black holes.     

Energy and angular momentum flow into a black hole

The area of the event horizon round a rotating black hole will increase in the presence of a non-axisymmetric or time dependent perturbation. If the perturbation is a matter field, the area increase is related to the fluxes of energy and of angular momentum into the black hole in such a way as to maintain the formula for the area in the Kerr solution. For purely gravitational perturbations one cannot define angular momentum locally but one can use the area increase and the expression for area in terms of mass and angular momentum to calculate the slowing down of a black hole caused by a non-axisymmetric distribution of matter at a distance. It seems that the coupling between the rotation of a black hole and the orbit of a particle going round it can be significant if the angular momentum of the black hole is close to its maximum possible value and if the angular velocity of the particle is nearly equal to that of the black hole.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

ROTATING RINDLER SPACE TIME WITH CONSTANT ANGULAR VELOCITY

A new space time metric is derived from Kerr metric if its mass and location approach to infinite in an appropriate way. The new space-time is an infinitesimal neighborhood nearby one of the two horizon poles of an infinite Kerr black hole. In other words, it is the second order infinitesimal neighborhood nearby one of the two horizon poles of a Kerr black hole. It is flat and has event horizon and infinite red shift surface. We prove that it is a rotating Rindler space time with constant angular velocity.     

Minisuperspace model of Machian resolution of Problem of Time. I. Isotropic case

It is well known that the three parameters that characterize the Kerr black hole (mass, angular momentum and horizon area) satisfy several important inequalities. Remarkably, some of these inequalities remain valid also for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this article recent results in this subject are reviewed.     

Gravitational collapse of dark energy field configurations and supermassive black hole formation

Dark energy is the dominant component of the total energy density of our Universe. The primary interaction of dark energy with the rest of the Universe is gravitational. It is therefore important to understand the gravitational dynamics of dark energy. Since dark energy is a low-energy phenomenon from the perspective of particle physics and field theory, a fundamental approach based on fields in curved space should be sufficient to understand the current dynamics of dark energy. Here, we take a field theory approach to dark energy. We discuss the evolution equations for a generic dark energy field in curved space-time and then discuss the gravitational collapse for dark energy field configurations. We describe the 3 + 1 BSSN formalism to study the gravitational collapse of fields for any general potential for the fields and apply this formalism to models of dark energy motivated by particle physics considerations. We solve the resulting equations for the time evolution of field configurations and the dynamics of space-time. Our results show that gravitational collapse of dark energy field configurations occurs and must be considered in any complete picture of our Universe. We also demonstrate the black hole formation as a result of the gravitational collapse of the dark energy field configurations. The black holes produced by the collapse of dark energy fields are in the supermassive black hole category with the masses of these black holes being comparable to the masses of black holes at the centers of galaxies.     

Exact solutions of the Klein–Gordon equation in the Kerr–Newman background and Hawking radiation

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein–Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

Kerr Black Hole in the Background of the Einstein Universe

The Vaidya-Einstein-Kerr (VEK) black hole which represents the spacetime of the Kerr black hole in a non-vacuum, asymptotically non-flat background is investigated. The energy-momentum tensor corresponding to this spacetime satisfies reasonable energy conditions. We study several properties of this black hole and compare and contrast them with those of the Kerr black hole. We investigate the effect of the background on the geometry of the event horizon by computing the equatorial and polar circumferences and determining the oblateness of the horizon. We find that the surface area of the VEK black hole gets nontrivially coupled to rotation in sharp contrast to the Kerr case. We show that the angular velocity of the VEK horizon goes up significantly as the background influence increases. By using the `equatorial tangential velocity' of the VEK horizon we classify the horizon and define the `limiting black hole' a generalization that contains the extreme Kerr black hole as a special case. Finally we investigate the Gaussian curvature and establish conditions for global embedding of the VEK black hole in Euclidean space.