A Class of Exact Solutions of the Wheeler -- De Witt Equation

In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information about solutions and their interpretation. In particular, strong evidence is presented that Wheeler-DeWitt quantization is not equivalent to reduced phase space quantization.

We consider the Wheeler-De Witt equation for canonical quantum gravity coupled to massless scalar field. After regularizing and renormalizing this equation, we find a one-parameter class of its solutions.

We can solve the Wheeler-DeWitt equation of the small universe enough to metric becomes diagonal and take a Gaussian normal coordinate. Our previous works are concerning to this paper. In this paper, we only write how to solve the Wheeler-DeWitt equation of such universe. Our motivation is simple, that is to solve the Wheeler-DeWitt equation. Even if the Wheeler-DeWitt equation is solved, quantum gravity does not complete yet. However, this work may be one of the first step t...

We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic solutions to satisfy both the energy and momentum constraints.

We construct the regularized Wheeler--De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for only a small subset of all wavefunctions being integrals of scalar densities this condition can be satisfied. It turns out that the resulting operator is much simpler than the one used in \cite{JK} to find exact solutions of Wheeler--De Witt equation. We proceed to finding exact solutions of quantum gravity and we discuss their ...

The Wheeler-DeWitt equation is based on the use of canonical quantization rules that may be inconsistent for constrained dynamical systems, such as minisuperspaces subject to Einstein's equations. The resulting quantum dynamics has no classical limit and it suffers from the infamous ``problem of time.'' In this article, it is shown how a dynamical time (an internal clock) can be constructed by means of a Hamilton-Jacobi formalism, and then used for a consistent canonical quan...

We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born-Oppenheimer sch...

We discuss the implications of a wave function for quantum gravity, which involves nothing but 3-dimensional geometries as arguments and is invariant under general coordinate transformations. We derive an analytic wave function from the Wheeler-DeWitt equation for spherically symmetric space-time with the coordinate system arbitrary. The de Broglie-Bohm interpretation of quantum mechanics is applied to the wave function. In this interpretation, deterministic dynamics can be y...

We construct the regularised Wheeler-De Witt operator demanding that the algebra of constraints of quantum gravity is anomaly free. We find that for a subset of all wavefunctions being integrals of scalar densities this condition can be satisfied. We proceed to finding exact solutions of quantum gravity being of the form of functionals of volume and average curvature of compact three-manifold.

In this article, I present a volume average regularization for the second functional derivative operator that appears in the metric-basis Wheeler-DeWitt equation. Naively, the second functional derivative operator in the Wheeler-DeWitt equation is infinite, since it contains terms with a factor of a delta function or derivatives of the delta function. More precisely, the second functional derivative contains terms that are only well defined as a distribution---these terms onl...