Effective Geometry

We introduce the concept of effective geometry by studying several systems in which it arises naturally. As an example of the power and conciseness of the method, it is shown that a flowing dielectric medium with a linear response to an external electric field can be used to generate an analog geometry that has many of the formal properties of a \Sch black hole for light rays, in spite of birefringence. The surface gravity of this analog black hole has a contribution that depends only on the dielectric properties of the fluid (in addition to the usual term dependent on the acceleration). This term may be give a hint to a new mechanism to increase the temperature of Hawking radiation.Comment: 13 pages, RevTex4, Contribution to the Proceedings of the Xth Brazilian School of Gravitation and Cosmology, to be published by AI

Evolution of Vacuum Bubbles Embeded in Inhomogeneous Spacetimes

We study the propagation of bubbles of new vacuum in a radially inhomogeneous background filled with dust or radiation, and including a cosmological constant, as a first step in the analysis of the influence of inhomogeneities in the evolution of an inflating region. We also compare the cases with dust and radiation backgrounds and show that the evolution of the bubble in radiation environments is notably different from that in the corresponding dust cases, both for homogeneous and inhomogeneous ambients, leading to appreciable differences in the evolution of the proper radius of the bubble.Comment: 18 pages, 15 figures, accepted for publication in Journal of Cosmology and Astroparticle Physics (new version with a few cosmetic changes w.r.t. the published one

Cosmography and the redshift drift in Palatini f(R)f({\cal R}) theories

We present an application to cosmological models in $f({\cal R})$ theories within the Palatini formalism of a method that combines cosmography and the explicit form of the field equations in the calculation of the redshift drift. The method yields a sequence of constraint equations which lead to limits on the parameter space of a given $f({\cal R})$-model. Two particular families of $f({\cal R})$-cosmologies capable of describing the current dynamics of the universe are explored here: (i) power law theories of the type $f({\cal R})={\cal R}-\beta /{\cal R}^n$, and (ii) theories of the form $f({\cal R})={\cal R}+\alpha \ln{{\cal R}} -\beta$. The constraints on $(n,\beta)$ and $(\alpha,\beta)$, respectively, limit the values to intervals that are narrower than the ones previously obtained. As a byproduct, we show that when applied to General Relativity, the method yields values of the kinematic parameters with much smaller errors that those obtained directly from observations.Comment: 7 pages, 2 figure

Cylindrically symmetric spinning Brans-Dicke spacetimes with closed timelike curves

We present here three new solutions of Brans-Dicke theory for a stationary geometry with cylindrical symmetry in the presence of matter in rigid rotation with $T^\mu_\mu\neq 0$. All the solutions have eternal closed timelike curves in some region of the spacetime, the size of which depends on $\omega$. Moreover, two of them do not go over a solution of general relativity in the limit $\omega \to \infty$.Comment: revtex, 10 pages, 1 figure in p

A Born-Infeld-like f(R) gravity

Several features of an $f(R)$ theory in which there is a maximum value for the curvature are analyzed. The theory admits the vaccuum solutions of GR, and also the radiation evolution for the scale factor of the standard cosmological model. Working in the Jordan frame, a complete analysis of the phase space is performed, and its results supported with examples obtainted by numerical integration. In particular, we showed that theory has nonsingular cosmological solutions which after the bounce enter a phase of de Sitter expansion and subsequently relax to a GR-like radiation-dominated evolution.Comment: Latex file, 14 pages, 7 figures (jpg format), including more detailed discussions than previous version, accepted for publication in Physical Review