Topological Black Holes in Quantum Gravity

We derive the black hole solutions with horizons of non-trivial topology and investigate their properties in the framework of an approach to quantum gravity being an extension of Bohm's formulation of quantum mechanics. The solutions we found tend asymptotically (for large $r$) to topological black holes. We also analyze the thermodynamics of these space-times.Comment: 4pages, no figures, plain LaTe

Quantum Potential and Quantum Gravity

The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.Comment: 12 pages LaTeX, to appear in From Field Theory to Quantum Groups. Birthday volume dedicated to Jerzy Lukierski, World Scientifi

DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis

In this paper we have constructed a coordinate space (or geometric) Lagrangian for a point particle that satisfies the Doubly Special Relativity (DSR) dispersion relation in the Magueijo-Smolin framework. At the same time, the symplectic structure induces a Non-Commutative phase space, which interpolates between $\kappa$-Minkowski and Snyder phase space. Hence this model bridges an existing gap between two conceptually distinct ideas in a natural way. We thoroughly discuss how this type of construction can be carried out from a phase space (or first order) Lagrangian approach. The inclusion of external physical interactions are also briefly outlined. The work serves as a demonstration of how Hamiltonian (and Lagrangian) dynamics can be built around a given non-trivial symplectic structure.Comment: 9 pages, LaTex, Title and abstract changed, Thoroughly revised version, No major change in conclusions, Title modified, sign typos in eq.s corrected, to appear in PL

Black Hole Solution of Quantum Gravity

We present a spherically symmetric and static exact solution of Quantum Einstein Equations. This solution is asymptotically (for large $r$) identical with the black hole solution on the anti--De Sitter background and, for some range of values of the mass possesses two horizons. We investigate thermodynamical properties of this solution.Comment: Plain Latex, 10 page