Andrei Zelnikov

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.

The wave function of a black hole and the dynamical origin of entropy.

Recently it was proposed to explain the dynamical origin of the entropy of a black hole by identifying its dynamical degrees of freedom with states of quantum fields propagating in the black-holes interior. The present paper contains the further development of this approach. The no-boundary proposal (analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is put forward for defining the wave function of a black hole. This wave function is a functional on the configuration space of physical fields (including the gravitational one) on the three-dimensional space with the Einstein-Rosen bridge topology.It is shown that in the limit of small perturbations on the Kruskal background geometry the no-boundary wave function coincides with the Hartle-Hawking vacuum state. The invariant definition of inside and outside modes is proposed. The density matrix describing the internal state of a black hole is obtained by averaging over the outside modes. This density matrix is used to define the entropy of a black hole, which is to be divergent. It is argued that the quantum fluctuations of the horizon which are internally present in the proposed formalism may give the necessary cut-off and provide a black hole with the finite entropy.

Black hole entropy: Off shell versus on shell.

Different methods of calculation of quantum corrections to the thermodynamical characteristics of a black hole are discussed and compared. The relation between on-shell and off-shell approaches is established. The off-shell methods are used to explicitly demonstrate that the thermodynamical entropy

On 4D Hawking radiation from the effective action

S^{TD}

Spherical collapse of small masses in the ghost-free gravity

of a black hole, defined by the first thermodynamical law, differs from the statistical-mechanical entropy

Head-on collision of ultrarelativistic particles in ghost-free theories of gravity

S^{SM}

Relativistic gyratons in asymptotically AdS spacetime

, determined as

Finite temperature nonlocal effective action for quantum fields in curved space

S^{SM}=-\mbox{Tr}(\hat{\rho}^H\ln\hat{\rho}^H)

Gravitational field of relativistic gyratons

for the density matrix

CFT and black hole entropy in induced gravity

\hat{\rho}^H