Related papers: Perturbations of generic Kasner spacetimes and the…
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
We use perturbations in order to study the stability of the Cauchy Horizon in a Reissner-Nordstr\"om space-time. The perturbations are either scalar or gravitational, and indicate some strong instabilities.
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
We investigate the stability of a spatially homogeneous and isotropic non-singular cosmological model. We show that the complete set of independent perturbations (the electric part of the perturbed Weyl tensor and the perturbed shear) are…
In a previous work the authors have solved the Einstein equations of General Relativity for a class of metrics with constant spatial curvature, where it was found a non vanishing Weyl tensor in the presence of a primordial magnetic field…
General Relativity predicts that the spacetime near a cosmological singularity undergoes an infinite number of chaotic oscillations between different Kasner epochs with rapid transitions between them. This so-called BKL behaviour persists…
Generalized Kerr-NUT-de Sitter spacetime is the most general spacetime which admits a rank-2 closed conformal Killing-Yano tensor. It contains the higher-dimensional Kerr-de Sitter black holes with partially equal angular momenta. We study…
The metric perturbation tensor corresponding to a transverse oscillation of spacetime is composed of products of cosines. When averaged over many wavelengths, such a metric may look either Minkowskian or Euclidean at large scales, depending…
Extreme black holes have been argued to be unstable, in the sense that under linearized gravitational perturbations of the extreme Kerr spacetime the Weyl scalar $\psi_4$ blows up along their event horizons at very late advanced times. We…
We determine the leading order fall-off behaviour of the Weyl tensor in higher dimensional Einstein spacetimes (with and without a cosmological constant) as one approaches infinity along a congruence of null geodesics. The null congruence…
We study the evolution of the Weyl curvature invariant in all spatially homogeneous universe models containing a non-tilted gamma-law perfect fluid. We investigate all the Bianchi and Thurston type universe models and calculate the…
The scale invariant Petrov classification of the Weyl tensor is linked to the scale invariant combination of the Kasner index constraints, and the Lifshitz-Khalatnikov Kasner index parametrization scheme turns out to be a natural way of…
We transcribe into the framework of the torsionful version of the {\epsilon}-formalism of Infeld and van der Waerden the world definition of the Weyl tensor for a curved spacetime that occurs in the realm of Einstein-Cartan's theory. The…
In this chapter we consider perturbations and stability of higher dimensional black holes focusing on the static background case. We first review a gauge-invariant formalism for linear perturbations in a fairly generic class of…
We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild-Tangherlini solution. We find a particular gauge invariant component of the Weyl tensor…
After a concise overview of Einstein spacetimes of type II (or more special) in four and five dimensions, we summarize recent results in the six-dimensional case. We assume the optical matrix to be non-degenerate and ``generic'', and the…
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…
Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either…
We study the full linear perturbations of a homogeneous and isotropic spacetime in the Eddington-inspired Born-Infeld gravity. The stability of the perturbations are analyzed in the Eddington regime. We find that, for positive $\kappa$, the…
We study the second-order perturbations in the Einstein-de Sitter Universe in synchronous coordinate. We solve the second-order perturbed Einstein equation with scalar-tensor, and tensor-tensor couplings between 1st order perturbations, and…