On the topology of black holes

We establish from local hypotheses some results concerning the final state topology of black holes. We show that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple.Dedicated to Ted FrankelThis work has been partially supported by NSF grants DMS-8802877 and DMS-9006678     

Superradiant instability for black holes immersed in a magnetic field

We consider the bound states of the massive scalar field around a rotating black hole immersed in the asymptotically uniform magnetic field. In the regime of slow black hole rotation, the Klein–Gordon equation allows separation of variables. We show that the growth rate of the instability can be amplified a few times by the magnetic field. The effect occurs because the magnetic field adds the “effective mass” term B|m|$B|m|$ to the scalar field potential for a Kerr black hole. In addition, and as a by-product, we discuss the behavior of the quasinormal modes for the magnetized rotating black holes.     

On the static Lovelock black holes

We consider static spherically symmetric Lovelock black holes and generalize the dimensionally continued black holes in such a way that they asymptotically for large $r$ go over to the d-dimensional Schwarzschild black hole in dS/AdS spacetime. This means that the master algebraic polynomial is not degenerate but instead its derivative is degenerate. This family of solutions contains an interesting class of pure Lovelock black holes which are the $N$ th order Lovelock $\Lambda $ -vacuum solutions having the remarkable property that their thermodynamical parameters have the universal character in terms of the event horizon radius. This is in fact a characterizing property of pure Lovelock theories. We also demonstrate the universality of the asymptotic Einstein limit for the Lovelock black holes in general.     

On singularities in non-Abelian black holes

Singularities in spherically symmetric black holes in the Einstein-Yang-Mills and the Einstein-Yang-Mills with dilaton theories for the SU(2) group are investigated. Analytical formulas describing the exponentially oscillating and power-law behavior of the metric near a space-like singularity in a solution of the general form are presented. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 855–860 (25 June 1997)     

On the outside of cold black holes

Some general features of the behaviour of fields and particles around extreme (or nearly extreme) black holes are outlined, with an emphasis on their simplicity. In particular, simple solutions representing interacting electromagnetic and gravitational perturbations of an extreme Reissner-Nordström black hole are presented. As an application, the motion of the hole in an asymptotically uniform weak electric field is examined and Newton's second law is so explicitly verified for a geometrodynamical object.An essay for the Gravity Research Foundation, Gloucester, Mass. (selected for Honorable Mention in 1977).     

Finite motion of electrons in the field of microscopic black holes

In the single-particle approximation of the Dirac equation, a study is made of the finite motion of electrons in the field of small black holes (M < 10¹⁷ g) under the assumption that the black hole has rotation (a < M) and charge much less than the critical value (Z < 137). In this case, the motion of the particle is nonrelativistic, and the energy spectrum is hydrogen-like. The influence of rotation of the hole on the binding energy of the particle is small and unimportant for determining the damping of the levels due to capture by the hole. In contrast to a scalar particle, the damping of the electron states is not replaced by excitation for < m_jH + eV_H. The gravitational spin-orbit interaction has a strong influence on the damping. The probability of capture of an electron with spin anti-parallel to the orbital angular momentum is much greater than the probability of capture for a particle with spin parallel to it. In the Schwarzschild field, the damping of the S state of an electron is eight times less than the damping of the ground state of a scalar particle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 56–62, August, 1980.     

Gravitational field in a collision of two Schwarzschild black holes

This paper presents an analysis of the linearized Einstein equations in vacuum for the problem of head-on collision of two Schwarzschild black holes, of which one is much smaller than the other. Based on the decomposition of the metric perturbations into spherical harmonics, introduced by Regge and Wheeler, we give some time-symmetric initial data and calculate the subsequent time-evolution of gravitational field. It is found that the small hole, initially at rest, begins to move like a freely falling particle. A wave-like disturbance generated near the small hole grows up and propagates in the direction opposite to the hole's motion. We investigate the area of the large Schwarzschild horizon distorted by the small hole to obtain the rate of increase with time.     

Abundant stable gauge field hair for black holes in anti-de Sitter space

We present new hairy black hole solutions of SU(N) Einstein-Yang-Mills (EYM) theory in asymptotically anti-de Sitter (AdS) space. These black holes are described by N+1 independent parameters and have N-1 independent gauge field degrees of freedom. Solutions in which all gauge field functions have no zeros exist for all N, and for a sufficiently large (and negative) cosmological constant. At least some of these solutions are shown to be stable under classical, linear, spherically symmetric perturbations. Therefore there is no upper bound on the amount of stable gauge field hair with which a black hole in AdS can be endowed.     

On the possibility of binding of two holes in an antiferromagnetic state

The energy of a pair of holes in a half-filled 2—d Hubbard model is studied assuming an antiferromagnetic spin configuration. By comparing with the energy of a single hole, we discuss the possibility of pairing of holes in connection with the recently discovered highT _c superconductivity.     

On the thermodynamical stability of black holes in nonlinear electrodynamics

We analyze the thermodynamical stability of static and spherically symmetric black hole solutions with nonlinear electromagnetism as a source, and show that any sequence of such black holes in isolation that includes the Schwarzschild black hole is stable in the (β_M,M)$({\beta }_M,M)$ plane for any nonlinear Lagrangian describing the electromagnetic field. The study of three exact solutions (which include the Schwarzschild solution in some limit) in the (β_Q,Q)$({\beta }_Q,Q)$ plane show that they are stable in the microcanonical ensemble, and unstable or less unstable (due to the existence of a turning point) in the canonical ensemble. If the less unstable configurations are stable, our results indicate that they would be in equilibrium with a reservoir at a higher temperature than the corresponding Reissner–Nordstrom configuration. An expression for the heat capacity at constant charge valid for any Lagrangian describing nonlinear electromagnetism is also presented. It displays a divergence with a change of sign that occurs precisely at the turning point obtained by the Poincarè method.     

On the collisions between particles in the vicinity of rotating black holes

Scattering of particles in the gravitational field of rotating black holes is considered. It is shown that scattering energy of particles in the centre of mass system can obtain very large values not only for extremal black holes but also for nonextremal ones. Extraction of energy after the collision is investigated. It is shown that due to the Penrose process the energy of the particle escaping the hole at infinity can be large. Contradictions in the problem of getting high energetic particles escaping the black hole are resolved.     

Weighing black holes in the universe

The determination of the mass of black holes in our universe is crucial to understand their physics nature but is a great challenge to scientists. In this paper I briefly review some methods that are currently used to estimate the mass of black holes, especially those in X-ray binary systems and in galactic nuclei. Our recent progress in improving the mass estimates of supermassive black holes in active galactic nuclei by involving some empirical relations is presented. Finally I point out the similarities and common physics in Galactic black hole X-ray binaries and active galactic nuclei, and demonstrate that the black hole mass estimation is very much helpful to understand the accretion physics around black holes.