Apparent horizons in D-dimensional Robinson-Trautman spacetime

We derive the higher dimensional generalization of Penrose-Tod equation describing apparent horizons in Robinson-Trautman spacetimes. New results concerning the existence and uniqueness of its solutions in four dimensions are proven. Namely, previous results of Tod are generalized to nonvanishing cosmological constant.Comment: 4 pages, 1 figure, to appear in ERE 2008 conference proceedings, to be published by AI

The wave equation on axisymmetric stationary black hole backgrounds

Understanding the behaviour of linear waves on black hole backgrounds is a central problem in general relativity, intimately connected with the nonlinear stability of the black hole spacetimes themselves as solutions to the Einstein equations--a major open question in the subject. Nonetheless, it is only very recently that even the most basic boundedness and quantitative decay properties of linear waves have been proven in a suitably general class of black hole exterior spacetimes. This talk will review our current mathematical understanding of waves on black hole backgrounds, beginning with the classical boundedness theorem of Kay and Wald on exactly Schwarzschild exteriors and ending with very recent boundedness and decay theorems (proven in collaboration with Igor Rodnianski) on a wider class of spacetimes. This class of spacetimes includes in particular slowly rotating Kerr spacetimes, but in the case of the boundedness theorem is in fact much larger, encompassing general axisymmetric stationary spacetimes whose geometry is sufficiently close to Schwarzschild and whose Killing fields span the null generator of the horizon.Comment: 20 pages, 6 pages, to appear in the proceedings of the Spanish Relativity Meeting, Salamanca 200

Accelerated expansion through interaction

Interactions between dark matter and dark energy with a given equation of state are known to modify the cosmic dynamics. On the other hand, the strength of these interactions is subject to strong observational constraints. Here we discuss a model in which the transition from decelerated to accelerated expansion of the Universe arises as a pure interaction phenomenon. Various cosmological scenarios that describe a present stage of accelerated expansion, like the LCDM model or a (generalized) Chaplygin gas, follow as special cases for different interaction rates. This unifying view on the homogeneous and isotropic background level is accompanied by a non-adiabatic perturbation dynamics which can be seen as a consequence of a fluctuating interaction rate.Comment: 4 pages, to appear in the Proceedings of the Spanish Relativity Meeting ERE2008 in Salamanca, September 200

The Interaction Rate in Holographic Models of Dark Energy

Observational data from supernovae type Ia, baryon acoustic oscillations, gas mass fraction in galaxy clusters, and the growth factor are used to reconstruct the the interaction rate of the holographic dark energy model recently proposed by Zimdahl and Pav\'{o}n [1] in the redshift interval $0 < z < 1.8$. It shows a reasonable behavior as it increases with expansion from a small or vanishing value in the far past and begins decreasing at recent times. This suggests that the equation of state parameter of dark energy does not cross the phantom divide line.Comment: 8 pages, 2 figures. Key words: cosmology, holography, late accelerated expansion, dark energy. To appear in the Proceedings of the Spanish Relativity Meeting held in Salamanca (Spain) in September 2008. Uses AIP styl

F-Term Hybrid Inflation Followed by Modular Inflation

We consider the well motivated model of the (standard) supersymmetric F-term hybrid inflation (FHI) which can be realized close to the grand unification scale. The predicted scalar spectral index $n_s$ cannot be smaller than 0.98 and can exceed unity including corrections from minimal supergravity, if the number of e-foldings corresponding to the pivot scale $k_*=0.002/{\rm Mpc}$ is around 50. These results are marginally consistent with the fitting of the Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. However, $n_s$ can be reduced by restricting the number of e-foldings that $k_*$ suffered during FHI. The additional e-foldings required for solving the horizon and flatness problems can be generated by a subsequent stage of fast-roll [slow-roll] modular inflation realized by a string modulus which does [does not] acquire effective mass before the onset of modular inflation.Comment: To appear in the proceedings of the Spanish Relativity Meeting (ERE 2008) 15-20 September 2008, Salamanca, Spai

On the dark energy rest frame and the CMB

Dark energy is usually parametrized as a perfect fluid with negative pressure and a certain equation of state. Besides, it is supposed to interact very weakly with the rest of the components of the universe and, as a consequence, there is no reason to expect it to have the same large-scale rest frame as matter and radiation. Thus, apart from its equation of state $w$ and its energy density $\Omega_{DE}$ one should also consider its velocity as a free parameter to be determined by observations. This velocity defines a cosmological preferred frame, so the universe becomes anisotropic and, therefore, the CMB temperature fluctuations will be affected, modifying mainly the dipole and the quadrupole.Comment: 4 pages. Contribution to the proceedings of Spanish Relativity Meeting 2008, Salamanca, Spain, 15-19 September 200

Exact f(R)f(R)-cosmological model coming from the request of the existence of a Noether symmetry

We present an $f(R)$-cosmological model with an exact analytic solution, coming from the request of the existence of a Noether symmetry, which is able to describe a dust-dominated decelerated phase before the current accelerated phase of the universe.Comment: 4 pages, 2 figures, Contribution to the proceedings of Spanish Relativity Meeting 2008, Salamanca, Sapin, 15-19 September 200

Application of initial data sequences to the study of Black Hole dynamical trapping horizons

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes.Comment: Contribution to the proceedings volume of the Spanish Relativity Meeting 2008: Physics and Mathematics of Gravitation, Salamanca, Spain, 15-19 Sep 200

Information geometry of asymptotically AdS black holes

We investigate thermodynamic geometries of two families of asymptotically Anti-de Sitter black holes, i.e. the Reissner-Nordstr\"om Anti-de Sitter in four dimensions and the BTZ black hole. It is found that the Anti-de Sitter space renders the geometry nontrivial (c.f. the Reissner-Nordstr\"om black hole in asymptotically flat background). The BTZ black hole's thermodynamic geometry is trivial despite the fact that it is characterized by the (negative) cosmological constant. As a matter of curiosity we compute thermodynamic geometry of these black holes regarding the cosmological constant as a true parameter but no physically significant results can be derived.Comment: Contribution to proceedings of ERE2008, 4 page

New results for Petrov type D pure radiation fields

We present a new family of Petrov type D pure radiation spacetimes with a shear-free, non-diverging geodesic principal null congruence.Comment: 4 pages; changed the appearance of some v's and nu'