A Rotating Charged Black Hole Solution in f(R) Gravity

In the context of f(R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. The new metric is obtained by solving the field equations and we show that the behavior of it is typical of a rotating charged source. In addition, we analyze the thermodynamics of the new black hole. The results ensures that the thermodynamical properties in f(R) gravities are qualitatively similar to those of standard General Relativity.Comment: 9 pages, no figure

A f(R) gravity without cosmological constant

In this work we consider the possibility of describing the current evolution of the universe, without the introduction of any cosmological constant or dark energy (DE), by modifying the Einstein-Hilbert (EH) action. In the context of the f(R) gravities within the metric formalism, we show that it is possible to find an action without cosmological constant which exactly reproduces the behavior of the EH action with cosmological constant. In addition the f(R) action is analytical at the origin having Minkowski and Schwarzschild as vacuum solutions. The found f(R) action is highly non-trivial and must be written in terms of hypergeometric functions but, in spite of looking somewhat artificial, it shows that the cosmological constant, or more generally the DE, is not a logical necessity.Comment: 5 pages, no figure

Some cosmological and astrophysical aspects of modified gravity theories

This thesis will try to contribute to the understanding of open issues in cosmology by considering f(R) and brane-world theories. In Chapter 1, we shall summarize the main features of f(R) gravities in the metric formalism and we shall introduce both the notion of brane excitations, the branons, and the brane-skyrmions. We shall finish the chapter by providing some insight about the possibility of mini black holes detection in the LHC as a signature for the validity of these modified gravity theories. The Chapter 2 will deal with f(R) theories able to mimic Einstein-Hilbert plus cosmological constant solutions and f(R) theories will be shown to be able to mimic the cosmological evolution generated by any perfect fluid with constant equation of state. The Chapter 3 will be devoted to the computation of cosmological perturbations for f(R) theories. Special attention will be paid here to obtain a completely general differential equation for the evolution of perturbations and its particularization for the so-called sub-Hubble scales will be explicitly shown. In the Chapter 4 we shall focus on the study of black holes in f(R) gravities in an arbitrary number of dimensions. With this purpose we shall study constant curvature solutions for f(R) theories as well as perturbative solutions around the standard SAdS geometry. An important part of this chapter will be then devoted to the thermodynamics of SAdS black holes in f(R) theories. In the Chapter 5 we will thoroughly study brane-skyrmions. In this context, the recent claim of detection of an unexpected feature in the CMB, referred to as the cold spot, will be explained as a topological defect on the brane in complete agreement with those calculations in the literature that tried to explain that cold spot as a texture of a NLSM. Main conclusions are summarized all together in Chapter 6 .Comment: PhD. thesis, April 2010, Complutense University of Madrid. 129 pages. Preface, five chapters and conclusions. Two appendice

CMB Tensor Anisotropies in Metric f(R) Gravity

We present a description of CMB anisotropies generated by tensor perturbations in f(R) theories of gravity. The temperature power spectrum in the special case of $f(R)=R^n$ is computed using a modified version of CAMB package.Comment: 4 pages, 1 figure. Contribution submitted to the proceedings of the Spanish Relativity Meeting ERE2011, September 2011, Madrid, Spai

On the consistency of universally non-minimally coupled f(R,T,RμνTμν)f(R,T,R_{\mu\nu}T^{\mu\nu}) theories

We discuss the consistency of a recently proposed class of theories described by an arbitrary function of the Ricci scalar, the trace of the energy-momentum tensor and the contraction of the Ricci tensor with the energy-momentum tensor. We briefly discuss the limitations of including the energy-momentum tensor in the action, as it is a non fundamental quantity, but a quantity that should be derived from the action. The fact that theories containing non-linear contractions of the Ricci tensor usually leads to the presence of pathologies associated with higher-order equations of motion will be shown to constrain the stability of this class of theories. We provide a general framework and show that the conformal mode for these theories generally has higher-order equations of motion and that non-minimal couplings to the matter fields usually lead to higher-order equations of motion. In order to illustrate such limitations we explicitly study the cases of a canonical scalar field, a K-essence field and a massive vector field. Whereas for the scalar field cases it is possible to find healthy theories, for the vector field case the presence of instabilities is unavoidable.Comment: Minor changes, version published matching Phys. Rev. D 91 (2015) 104003. 15 pages, no figure