Valeri P. Frolov

Black Hole Physics: Basic Concepts and New Developments

Preface. I. Basic Concepts. 1. Introduction: Brief History of Black Hole Physics. 2. Spherically Symmetric Black Holes. 3. Rotating Black Holes. 4. Black Hole Perturbations (with N. Andersson). 5. General Properties of Black Holes. 6. Stationary Black Holes. 7. Physical Effects in the Gravitational Field of a Black Hole. 8. Black Hole Electrodynamics. 9. Astrophysics of Black Holes. II. Further Developments. 10. Quantum Particle Creation by Black Holes. 11. Quantum Physics of Black Holes. 12. Thermodynamics of Black Holes. 13. Black Holes in Unified Theories. 14. The Interior of a Black Hole. 15. Ultimate Fate of Black and White Holes. 16. Black Holes, Wormholes, and Time Machines. Conclusions. Appendices: A: Mathematical Formulas. B: Spherically Symmetric Spacetimes. C: Rindler Frame in Minkowski Spacetime. D: Kerr-Newman Geometry. E: Newman-Penrose Formalism. F: Wave Fields in a Curved Spacetime. G: Wave Fields in the Kerr Metric. H: Quantum Fields in Kerr Spacetime. I: Quantum Oscillator. Bibliography. Index.

Black Hole Entropy

According to the thermodynamical analogy in black hole physics, the BekensteinHawking entropy of a black hole in the Einstein theory of gravity is S BH = A H /(4l P 2 ), where A H is the area of a black hole surface and l P=(ћG/c 3)1/2 is the Planck length.

Quantum radiation from a5-dimensional rotating black hole

We study a massless scalar field propagating in the background of a five-dimensional rotating black hole. We show that in the Myers-Perry metric describing such a black hole the massless field equation allows the separation of variables. The obtained angular equation is a generalization of the equation for spheroidal functions. The radial equation is similar to the radial Teukolsky equation for the 4-dimensional Kerr metric. We use these results to quantize the massless scalar field in the space-time of the 5-dimensional rotating black hole and to derive expressions for energy and angular momentum fluxes from such a black hole.

Astrophysics of Black Holes

The black hole phenomenon is undoubtedly one of the most striking and intriguing of those predicted by theorists. However, a paramount question is: “Do black holes exist in the Universe, or are they only an abstract concept of the human mind?” In principle, a black hole could be built artificially. However, this meets such grandiose technical difficulties that it looks impossible, at least in the immediate future. In fact, the artificial construction of a black hole looks even more problematic than an artificial creation of a star. Thus, we have to conclude that the physics of black holes, as well as the physics of stars, is the physics of celestial bodies. Stars definitely exist, but what may one say about the existence of astrophysical black holes?

Particle and light motion in a space-time of a five-dimensional rotating black hole

We study motion of particles and light in a space-time of a 5-dimensional rotating black hole. We demonstrate that the Myers-Perry metric describing such a black hole in addition to three Killing vectors possesses also a Killing tensor. As a result, the Hamilton-Jacobi equations of motion allow a separation of variables. Using first integrals we present the equations of motion in the first-order form. We describe different types of motion of particles and light and study some interesting special cases. We proved that there are no stable circular orbits in equatorial planes in the background of this metric.

Spherically Symmetric Collapse in Quantum Gravity

Abstract The problem of classical singularities is revised on the basis of the quantum-gravity effective equations. We find a simple rule for establishing the Birkhoff theorem in spherically symmetric problems. All exact solutions of the lagrangian with C 2 αβγσ are obtained. Spherically symmetric collapse of the thin null shell of mass M is considered in the framework of a local theory describing vacuum polarization effects. The boundary-value problem is set and the asymptotic solution is obtained. It is found that the shell collapses to r = 0 without the rise of a singularity, and begins expanding. The global behaviour of the solution is obtained for small M . For large M it is conjectured that the event horizon does not form, and the apparent horizon is closed. An object forms, possessing the observable properties of a black hole, but living a finite time.

Through a black hole into a new universe

Abstract The internal structure of spacetime inside a black hole is investigated on the assumption that some limiting curvature exists. It is shown that the Schwarzchild metric inside a black hole can be attached to the de Sitter one at some spacelike junction surface which may represent a short transition layer. The possible fate of the de Sitter space which arises in the interior of a black hole in this model is discussed.

Statistical Origin of Black Hole Entropy in Induced Gravity

The statistical-mechanical origin of the Bekenstein-Hawking entropy SBH in the induced gravity is discussed. In the framework of the induced gravity models the Einstein action arises as the low energy limit of the effective action of quantum fields. The induced gravitational constant is determined by the masses of the heavy constituents. We established the explicit relation between the statistical entropy of the constituent fields and the black hole entropy SBH.

Hidden Symmetries of Higher Dimensional Black Holes and Uniqueness of the Kerr-NUT-(A)dS spacetime

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

Hidden symmetries of higher-dimensional rotating black holes.

We demonstrate that the rotating black holes in an arbitrary number of dimensions and without any restrictions on their rotation parameters possess the same hidden symmetry as the four-dimensional Kerr metric. Namely, besides the spacetime symmetries generated by the Killing vectors they also admit the (antisymmetric) Killing-Yano and symmetric Killing tensors.