Raül Vera

Signature Change on the Brane

We explore the possibility of having a good description of classical signature change in the brane scenario.

Review on exact and perturbative deformations of the Einstein–Straus model: uniqueness and rigidity results

The Einstein–Straus model consists of a Schwarzschild spherical vacuole in a Friedman–Lemaître–Robertson–Walker (FLRW) dust spacetime (with or without

A local characterization for static charged black holes

\Lambda

Junction conditions in quadratic gravity: thin shells and double layers

Λ). It constitutes the most widely accepted model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model is that there is no influence from the cosmic background, since the spherical vacuole is static. Spherical generalizations to other interior matter models are commonly used in the construction of lumpy inhomogeneous cosmological models. On the other hand, the model has proven to be reluctant to admit non-spherical generalizations. In this review, we summarize the known uniqueness results for this model. These seem to indicate that the only reasonable and realistic non-spherical deformations of the Einstein–Straus model require perturbing the FLRW background. We review results about linear perturbations of the Einstein–Straus model, where the perturbations in the vacuole are assumed to be stationary and axially symmetric so as to describe regions (voids in particular) in which the matter has reached an equilibrium regime.

Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.

Axially symmetric equilibrium regions of Friedmann-Lemaitre-Robertson-Walker universes

We obtain a purely local characterization that singles out the Majumdar–Papapetrou class, the near-horizon Bertotti–Robinson geometry and the Reissner–Nordstrom exterior solution, together with its plane and hyperbolic counterparts, among the static electrovacuum spacetimes. These five classes are found to form the whole set of static Einstein–Maxwell fields without sources and conformally flat space of orbits, that is, the conformastat electrovacuum spacetimes. The main part of the proof consists in showing that a functional relationship between the gravitational and electromagnetic potentials must always exist. The classification procedure also provides an improved characterization of Majumdar–Papapetrou, by only requiring a conformally flat space of orbits with a vanishing Ricci scalar of the usual conveniently rescaled 3-metric. A simple global consideration allows us to state that the asymptotically flat subset of the Majumdar–Papapetrou class and the Reissner–Nordstrom exterior solution are the only asymptotically flat conformastat electrovacuum spacetimes.

First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models

We present a critical review about the study of linear perturbations of matched spacetimes including gauge problems. We analyse the freedom introduced in the perturbed matching by the presence of background symmetries and revisit the particular case of spherical symmetry in n-dimensions. This analysis includes settings with boundary layers such as brane world models and shell cosmologies.

On global models for isolated rotating axisymmetric charged bodies: uniqueness of the exterior field

The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.