Abstract:
The one-loop effective action corresponding the general model of dilaton gravity given by the Lagrangian $L=-\sqrt{g} \left[ \frac{1}{2}Z(\Phi ) g^{\mu\nu} \partial_\mu \Phi \partial_\nu \Phi + C(\Phi ) R + V (\Phi )\right]$, where $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are arbitrary functions of the dilaton field, is found. The question of the quantum equivalence of classically equivalent dilaton gravities is studied. By specific calculation of explicit examples it is shown that classically equivalent quantum gravities are also perturbatively equivalent at the quantum level, but only on-shell. The renormalization group equations for the generalized effective couplings $Z(\Phi )$, $ C(\Phi )$ and $V (\Phi )$ are written. An analysis of the equations shows, in particular, that the Callan-Giddings-Harvey-Strominger model is not a fixed point of these equations.

Abstract:
The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate system is chosen. We carefully carry out the canonical formulation of 2D dilaton gravity theories (classical, CGHS and RST). As in 4D general relativity one must add a boundary term to the bulk Hamiltonian to obtain a well-defined variational problem. This boundary term coincides with the numerical value of the Hamiltonian and gives the correct mass which obviously is time-independent.

Abstract:
All 1+1 dimensional dipheomorphism-invariant models can be viewed in a unified manner. This includes also general dilaton theories and especially spherically symmetric gravity (SSG) and Witten's dilatonic black hole (DBH). A common feature --- also in the presence of matter fields of any type --- is the appearance of an absolutely conserved quantity C which is determined by the influx of matter. Only for a subclass of generalized dilaton theories the singularity structure vanishes together with C. Such `physical' theories include, of course, SSG and DBH. It seems to have been overlooked until recently that the (classical) 'black hole' singularity of the DBH deviates from SSG in a physically nontrivial manner. At the quantum level for all generalized dilaton theories --- in the absence of matter --- the local quantum effects are shown to disappear. This enables us to compute e.g. the second loop order correction to the Polyakov term. For non-minimal scalar coupling we also believe to have settled the controversial issue of Hawking radiation to infinity with a somewhat puzzling result for the case of SSG.

Abstract:
We consider the 2D Poincar\'e gravity and show its exact integrability. The choice of the gauge is discussed. The Euclidean solutions on compact closed differential manifolds are studied.

Abstract:
We extend the classical integrability of the CGHS model of 2d dilaton gravity [1] to a larger class of models, allowing the gravitational part of the action to depend more generally on the dilaton field and, simultaneously, adding fermion- and U(1)-gauge-fields to the scalar matter. On the other hand we provide the complete solution of the most general dilaton-dependent 2d gravity action coupled to chiral fermions. The latter analysis is generalized to a chiral fermion multiplet with a non-abelian gauge symmetry as well as to the (anti-)self-dual sector df = *df (df = -*df) of a scalar field f.

Abstract:
In this work, we have considered dilaton dark energy model in Weyl-scaled induced gravitational theory in presence of barotropic fluid. It is to be noted that the dilaton field behaves as a quintessence. Here we have discussed the role of dilaton dark energy in modified gravity theories namely, f(R); f(T) and Horava-Lifshitz gravities and analyzed the behaviour of the dilaton field and the corresponding potential in respect to these modified gravity theories instead of Einstein's gravity. In f(R) and f(T) gravities, we have considered some particular forms of f(R) and f(T) and we have shown that the potentials always increase with the dilaton fields. But in Horava-Lifshitz gravity, it has been seen that the potential always decreases as dilation field increases.

Abstract:
We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of some parameters the obtained cosmological models can be generically divided into three classes, leading to both singular and nonsingular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that a Bianchi type I Universe isotropizes only in the presence of a dilaton field potential or a central deficit charge.

Abstract:
We present arguments for the existence of a new type of solutions of the Euclidean Einstein-Yang-Mills-dilaton theory in $d=4$ dimensions. Possesing nonvanishing nonabelian charges, these nonselfdual configurations have no counterparts on the Lorentzian section. They provide, however, new saddle points in the Euclidean path integral.

Abstract:
We study two dimensional dilaton gravity and supergravity following hamiltonian methods. Firstly, we consider the structure of constraints of 2D dilaton gravity and then the 2D dilaton supergravity is obtained taking the squere root of the bosonic constraints. We integrate exactly the equations of motion in both cases and we show that the solutions of the equation of motion of 2D dilaton supergravity differs from the solutions of 2D dilaton gravity only by boundary conditions on the fermionic variables, i.e. the black holes of 2D dilaton supergravity theory are exactly the same black holes of 2D bosonic dilaton gravity modulo supersymmetry transformations. This result is the bidimensional analogue of the no-hair theorem for supergravity.