Valery P. Frolov

A Spherically Symmetric Black Hole

We begin the analysis of the physical properties of black holes with the simplest case in which both the black hole and its gravitational field are spherically symmetric.

Primordial Black Holes and the Ultimate Fate of Black and White Holes

We already know that a black hole is created when a mass contracts to a size less than its gravitational radius (Section 2.6). Stars of sufficiently large mass must convert into black holes at the end of their evolution [Zel’dovich and Novikov (1967, 1971)]. The smaller the mass of matter, the greater the density to which it must be compressed in order to create a black hole. Powerful pressure develops at high densities, counteracting the compression. As a result, black holes of mass M ≪ M ⊙ cannot form in the contemporary Universe. However, the density of matter at the beginning of expansion in the Universe was enormously high.

Thermodynamics of Black Holes

The discovery of the thermal radiation of black holes by Hawking was a complete surprise to most specialists, even though quite a few indications of a close relationship between black-hole physics and thermodynamics had crystallized before this discovery.

Quantum Effects in Black Holes. Particle Production

So far, our description has completely ignored quantum specifics of interaction of matter and physical fields with black holes. Quantum effects are, indeed, insignificant for black holes of about solar mass (and greater). However, for a small-mass black hole these effects cannot be ignored; in fact, they qualitatively change the black hole evolution. They are also likely to become important for those regions inside a black hole where the classical theory predicts a spacetime singularity.

Wave Fields Around a Spherical Black Hole

In this chapter we describe the evolution of physical fields in the external field of a spherical black hole. Once this evolution is known, one can successfully study various processes in black hole physics. Among such processes there are, for example, the radiation of gravitational, electromagnetic, and other waves by particles falling on the black hole, nonspherical gravitational collapse giving rise to a black hole, scattering of various types of waves falling on the black hole from the outside, and some others.