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

Effective geometry in Astrophysics

The effective metric is introduced by means of two examples (non-linear electromagnetism and hydrodynamics),along with applications in Astrophysics. A sketch of the generality of the effect is also given.Comment: 9 pages, contributions for the proceedings of the First International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2003), Olinda (Brazil