Black but Not Dark

Large black holes of millions of solar masses are known to be present in the centre of galaxies. Their mass is negligible compared to the mass of the luminous matter, but their entropy far exceeds the entropy of the latter by 10 orders of magnitude. Strong gravitational fields make them 'black' - but at the same time, they cause them to emit radiation so they are not 'dark'. What is the meaning of their borders that may only be crossed once and that leads to the information paradox and what are the properties of their interiors? In discussing these and related questions (is it possible that the volume of a black hole might be infinite?), we uncover the unexpected meaning of the term 'strong gravity'

The symmetry of the interior and exterior of Schwarzschild and Reissner–Nordstrom black holes : sphere vs. cylinder

One can question the relationship between the symmetries of the exterior and interior of black holes with an isotropic and static exterior. This question is justified by the variety of recent findings indicating substantial or even dramatic differences in the properties of the exterior and interior of isotropic, static black holes. By invoking some of these findings related to a variety of the thought experiments with freely falling or uniformly accelerated test particles, one can establish the dynamic properties of the interior, which turn out to be equivalent to anisotropic cosmology, simultaneously expanding and contracting, albeit in different directions. In order to illustrate the comparison between the symmetry of the exterior vs. the interior, we apply conventional t, r, θ, φ coordinates to both of these ranges, although on the horizon(s) they display singular behavior. Using a simple approach based on co-moving and freely falling observers, the dynamics of the cylindrically shaped interior are explored. That enables us to present schematic snapshots of the interior of a Schwarzschild black hole, expanding along its cylindrical axis and contracting along its spherical base, as well as the interior of a Reissner−Nordström black hole, expanding first and then contracting along the cylindrical axis up to the terminal instant r =r−

On the speed of a test particle inside the Schwarzschild event horizon and other kinds of black holes

We present the results of an investigation of the speed of a radially infalling test particle crossing the event horizon of a black hole within a Schwarzschild spacetime. One finds that the speed as measured by a special class of observers, at rest outside the horizon and static inside the horizon, increases when the test particle approaches the horizon but decreases inside the horizon. The corresponding situation regarding black holes possessing both outer and inner horizons is also briefly discussed

Inside spherically symmetric black holes or how a uniformly accelerated particle may slow down

Three types of phenomena occurring on both sides of the event horizon of spherically symmetric black holes are analyzed and discussed here. These phenomena are: a light ray orbiting a photon sphere and its analogue, the motion of a uniformly accelerated massive particle and a generalized Doppler effect. The results illustrate how the anisotropic dynamics of the interior of black holes, distinct in the cases both with and without an additional internal horizon, affect non-quantum behaviour

Quantum phenomena inside a black hole: quantization of the scalar field iniside horizon in Schwarzschild spacetime

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.Comment: 12 page

Unbounded energy collisions inside and outside black holes

The possibility of on-horizon collisions of unbounded energy in the case of an extreme Kerr black hole is known as the BSW effect. It is also a widely accepted point of view that the energy collision of two identical particles of mass m near the horizon of a Schwarzschild black hole is limited to a value of 25 m. We show that there are two possible scenarios for unbounded energy collisions both for the exterior and for the interior of spherically symmetric black holes. Similar scenarios are found for axially symmetric black holes. It is shown that divergent (infinite) energy on-(inner)horizon collisions are excluded due to the anisotropic character of the dynamics of black hole interiors

Quantum phenomena inside a black hole : quantization of the scalar field inside horizon in Schwarzschild spacetime

International audienceWe discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case