On Born-Infeld Gravity in Weitzenbock spacetime

Using the Teleparallel Equivalent of General Relativity formulated in Weitzenb\"{o}ck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended BTZ black hole, which results to exist even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor results to be well behaved, giving so a singularity-free solution.Comment: 8 pages, 1 figure. Accepted for publication in Phys. Rev.

Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory

An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters ``$$the gravitational mass $M$, the charge parameter $Q$ and the rotation parameter $a$" and its associated metric gives Kerr-Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then, calculate the total energy using the gravitational energy-momentum. The energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no energy is shared by the exterior of the Kerr-Newman black hole.Comment: 11 pages, Latex. Will appear in Mod. Phys. Lett.

Teleparallel Killing Vectors of the Einstein Universe

In this short paper we establish the definition of the Lie derivative of a second rank tensor in the context of teleparallel theory of gravity and also extend it for a general tensor of rank $p+q$. This definition is then used to find Killing vectors of the Einstein universe. It turns out that Killing vectors of the Einstein universe in the teleparallel theory are the same as in General Relativity.Comment: 9 pages, accepted for publication in Mod. Phys. Lett.

Cosmological perturbations in f(T) gravity

We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) ansatzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.Comment: 11 pages, 4 figures. Analysis of the vector and tensor sectors adde

Teleparallel Killing Vectors of Spherically Symmetric Spacetimes

In this paper, Killing vectors of spherically spacetimes have been evaluated in the context of teleparallel theory of gravitation. Further, we investigate the Killing vectors of the Friedmann metrics. It is found that for static spherically spacetimes the number of Killing vectors turn out to be \emph{seven} while for the Friedmann models, we obtain \emph{six} teleparallel Killing vectors. The results are then compared with those of General Relativity. We conclude that both of these descriptions of gravity do not provide the consistent results in general. However, these results may coincide under certain conditions for a particular spacetime.Comment: 14 pages, accepted for publication in Communications in Theoretical Physic

Mori Dream Spaces

This article is based on the 7th Takagi Lectures that the author delivered at the University of Tokyo on November 21-23, 2009.We explore the circle of ideas connecting finite generation of the Cox ring, Mori dream spaces and invariant theory

Spherically Symmetric Solutions on a Non-Trivial Frame in f(T) Theories of Gravity

A new solution with constant torsion is derived using the field equations of f(T). Asymptotic forms of energy density, radial and transversal pressures are shown to meet the standard energy conditions, i.e., weak and null energy conditions according to some restrictions on T0, f(T0) and fT(T0). Other solutions are obtained for vanishing radial pressure and for specific choices of f(T). The physics relevant to the resulting models is discussed.Comment: 6 pages, 4 figures, published versio

Gravitation and Duality Symmetry

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than teleparallel gravity or general relativity.Comment: 7 pages, no figures. Version 2: minor presentation changes, references added. Accepted for publication in Int. J. Mod. Phys.

Riemannian and Teleparallel Descriptions of the Scalar Field Gravitational Interaction

A comparative study between the metric and the teleparallel descriptions of gravitation is made for the case of a scalar field. In contrast to the current belief that only spin matter could detect the teleparallel geometry, scalar matter being able to feel the metric geometry only, we show that a scalar field is able not only to feel anyone of these geometries, but also to produce torsion. Furthermore, both descriptions are found to be completely equivalent, which means that in fact, besides coupling to curvature, a scalar field couples also to torsion.Comment: Minor corrections made, and a paragraph added to the last section. Version to appear in Gen. Rel. Gra

Fourth order gravity: equations, history, and applications to cosmology

The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e., the details how within fourth order gravity with L= R + R^2 the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.Comment: 51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School 6.-11.2.06, references 99-109 and related comments are adde