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

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

Velocity of particles in Doubly Special Relativity

Doubly Special Relativity (DSR) is a class of theories of relativistic motion with two observer-independent scales. We investigate the velocity of particles in DSR, defining velocity as the Poisson bracket of position with the appropriate hamiltonian, taking care of the non-trivial structure of the DSR phase space. We find the general expression for four-velocity, and we show further that the three-velocity of massless particles equals 1 for all DSR theories. The relation between the boost parameter and velocity is also clarified.Comment: 12 page

Effective particle kinematics from Quantum Gravity

Particles propagating in de Sitter spacetime can be described by the topological BF \SO(4,1) theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which reduces the local gauge symmetry down to \SO(3,1), and which can be treated as a perturbation. In this paper we focus solely on topological interactions which corresponds to zeroth order in this perturbative expansion. We show that in this approximation the system is effectively described by the \SO(4,1) Chern-Simons theory coupled to particles and living on the 3 dimensional boundary of space-time. Then, using Alekseev--Malkin construction we find the effective theory of particles kinematics. We show that the particles action contains standard kinetic terms and the deformation shows up in the presence of interaction terms. The strength of the interactions is proportional to deformation parameter, identified with Planck mass scale.Comment: 19 pages, 2 figure

Quantum Potential Approach to Quantum Cosmology

In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of the universe. Following Ashtekar et.\ al., we make use of quantum canonical transformation to cast a class of quantum cosmological models to a simple form in which they can be solved explicitly, and then we use the solutions to recover the time evolution.Comment: 17 pages,LaTeX. A newer version of this paper appears as gr-qc/9509040 since the author didn't use the replace command

The Time Evolution of Quantum Universe in The Quantum Potential Picture

We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.Comment: 9 pages, LaTe