Quantization of black holes in the Wheeler-DeWitt approach

Abstract

We discuss black hole quantization in the Wheeler-DeWitt approach. Our consideration is based on a detailed investigation of the canonical formulation of gravity with special considerations of surface terms. Since the phase space of gravity for noncompact spacetimes or spacetimes with boundaries is ill-defined unless one takes boundary degrees of freedom into account, we give a Hamiltonian formulation of the Einstein-Hilbert action as well as a Hamiltonian formulation of the surface terms. It then is shown how application to black hole spacetimes connects the boundary degrees of freedom with thermodynamical properties of black hole physics. Our treatment of the surface terms thereby naturally leads to the Nernst theorem. Moreover, it will produce insights into correlations between the Lorentzian and the Euclidean theory. Next we discuss quantization, which we perform in a standard manner. It is shown how the thermodynamical properties can be rediscovered from the quantum equations by a WKB-like approximation scheme. Back reaction is treated by going beyond the first order approximation. We end our discussion by a rigorous investigation of the so-called BTZ solution in (2ϩ1)-dimensional gravity. ͓S0556-2821͑98͒01504-5͔

Discreteness of time in the evolution of the universe

“…It would be interesting to investigate the effect this deformation of the Wheeler-DeWitt equation will have on the covariant formalism of quantum gravity. The Wheeler-DeWitt equation has also been used for analyzing the quantization of black holes [115]. It is known that the phase space of gravity for non-compact spacetimes cannot be properly defined without taking the boundary degrees of freedom into consideration.…”

Probing Foamy Space–time With Variational Methods

“…When asymptotically flat boundary terms are present we have to take account of such contributions in the WKB expansion such as in Ref. [11]. However in this paper only gravitational transverse-traceless modes are considered on the fixed curved background and Ψ ⊥ is substituted by a trial wave functional.…”

Quantum scalar field on the massless(2+1)-dimensional black hole background

“…A pure gravitational quantum correction to the BTZ entropy has been presented in [19], making use of Chern-Simons representation of the 3-dimensional gravity [22]. Very recently in [23] the first quantum correction to the entropy and the back reaction of the BTZ black hole also have been studied. Here, for the sake of simplicity, we assume that the quantum degrees of freedom of the massive black hole are represented by the quantum scalar field (described as usual by the action (3.5)) propagating outside the black hole [3], and we shall make use of the results of [19] as well as the ones obtained in Sect.…”