The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative β-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found...

The general relativity theory is redefined equivalently in almost Kähler variables: symplectic form, θ[g], and canonical symplectic connection, D̂[g] (distorted from the Levi–Civita connection by a tensor constructed only from metric coefficients and their derivatives). The fundamental geometric and physical objects are uniquely determined in metric compatible form by a (pseudo) Riemannian metri...

The solutions of two-dimensional gravity following from a non– linear Lagrangian L = f(R)√g are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of twodimensional Einstein-dilaton gravity and vice versa. KEY : Dilaton gravity in 1+1 dimensions, exact solutions, Birkhoff theorem, ...

The statistical origin of the entropy of charged black holes in models of induced Einstein-Maxwell gravity is investigated. The constituents inducing the EinsteinMaxwell action are charged and interact with an external gauge potential. This new feature, however, does not change divergences of the statistical-mechanical entropy of the constituents near the horizon. It is demonstrated that the me...

Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian f (R) where R is the scalar curvature and f is an arbitrary function. It may happen that a singularity in the Einstein frame corresponds to a regular surfac...

We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized two-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributio...

Using the coherent-state representation we show that the classical Einstein equation for the FRW cosmological model with a general minimal scalar field can be derived from the semiclassical quantum Einstein equation. E-Mail: [email protected] E-Mail: [email protected] E-Mail: [email protected] 1 Canonical quantum gravity has been initiated by DeWitt in the seminal paper [1]. As ...

To comply with the equivalence principle in Einstein-Cartan-like theories of gravity we propose a modification of the action principle in affine flat spaces with torsion.

We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.