Space-time deformations as extended conformal transformations

A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation theory giving a natural picture by which gravitational waves are described by small deformations of the metric. As further result, deformations can be related to approximate Killing vectors (approximate symmetries) by which it is possible to parameterize the deformed region of a given manifold. The perspectives and some possible physical applications of such an approach are discussed.Comment: 9 page

A CFT description of the BTZ black hole: topology versus geometry (or thermodynamics versus statistical mechanics

In this paper we review the properties of the black hole entropy in the light of a general conformal field theory treatment. We find that the properties of horizons of the BTZ black holes in ADS_{3}, can be described in terms of an effective unitary CFT_{2} with central charge c=1 realized in terms of the Fubini-Veneziano vertex operators. It is found a relationship between the topological properties of the black hole solution and the infinite algebra extension of the conformal group in 2D, SU(2,2), i.e. the Virasoro Algebra, and its subgroup SL(2,Z) which generates the modular symmetry. Such a symmetry induces a duality for the black hole solution with angular momentum J\neq 0. On the light of such a global symmetry we reanalyze the Cardy formula for CFT_{2} and its possible generalization to D>2 proposed by E. Verlinde.Comment: 21 page

Universal Tunnelling Time in photonic Barriers

Tunnelling transit time for a frustrated total internal reflection in a double-prism experiment was measured using microwave radiation. We have found that the transit time is of the same order of magnitude as the corresponding transit time measured either in an undersized waveguide (evanescent modes) or in a photonic lattice. Moreover we have established that in all such experiments the tunnelling transit time is approximately equal to the reciprocal 1/f of the corresponding frequency of radiation.Comment: 8 pages, 4 figures, 1 tabl

f(R) cosmology with torsion

f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard General Relativity. Only for f(R)=R^{2}, torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f'(R), which can be expressed also as a nonlinear function of the trace of the matter energy-momentum tensor. We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f(R) gravity, torsion can be a geometric source for acceleration.Comment: 13 page

The Cardy-Verlinde equation in a spherical symmetric gravitational collapse

The Cardy-Verlinde formula is analyzed in the contest of the gravitational collapse. Starting from the holographic principle, we show how the equations for a homogeneous and isotropic gravitational collapse describe the formation of the black hole entropy. Some comments on the role of the entangled entropy and the connection with the c-theorem are made

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.Comment: 19 page

Inflaton Potential Reconstruction and Generalized Equations of State

We extend a previous analysis concerning cosmological fluids with generalized equations of state in order to study inflationary scenarios. In the framework of the slow-roll approximation we find the expressions for the perturbation parameters $\epsilon$, $\eta$ and the density perturbation spectra in terms of the adiabatic index \ga as a function of the universe scale factor. This connection allows to find straightforwardly \ga corresponding, for example, to the simplest {\it chaotic} model and to the Harrison-Zeldovich potential and shows its capability to be applied to more complicate situations. Finally, we use this description to develop a new approach to the early universe dynamics, based on a $1/N$ expansion, where $N$ is the e-fold number. To this aim, we introduce a set of suitable dimensionless variables and show that at the zero-th order in $1/N$, an improved slow-roll approximation is obtained.Comment: 15 pages, plain Latex, to appear in Mod. Phys. Lett.