Related papers: 1+1+2 gravitational perturbations on LRS class II …
The 2+1+1 decomposition of space-time is useful in monitoring the temporal evolution of gravitational perturbations/waves in space-times with a spatial direction singled-out by symmetries. Such an approach based on a perpendicular double…
We consider the "kinematics" of spacelike congruences and apply them to a family of self-gravitating magnetic forcelines. Our aim is to investigate the convergence and the possible focusing of these lines, as well as their rotation and…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the varieties of associative, commutative, Leibniz, and Lie algebra…
The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk…
We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…
We consider gravitationally induced perturbations of relativistic Dirac--Goto--Nambu membranes and strings (or {\it p}-branes). The dynamics are described by the first and second fundamental tensors, and related curvature tensors in an {\it…
Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the…
We deal with the gravitational theory relevant to gravito-electromagnetism (GEM) exactly. It is shown that the theory can be decomposed in terms of two sectors of Abelian gauge field theories. The two sectors dominate the whole action in an…
We explore cosmological perturbations in a modified Gauss-Bonnet f(G) gravity, using a 1+3 covariant formalism. In such a formalism, we define gradient variables to get perturbed linear evolution equations. We transform these linear…
One of the main tools for solving linear systems arising from the discretization of the Helmholtz equation is the shifted Laplace preconditioner, which results from the discretization of a perturbed Helmholtz problem $-\Delta u - (k^2 + i…
This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
A new gauge-invariant approach for describing cosmological perturbations is developed. It is based on a physically motivated splitting of the stress-energy tensor of the perturbation into two parts - the bare perturbation and the…
Higher-order perturbations during the ringdown phase are essential for testing gravitational theories. This requires a perturbation framework that extends beyond General Relativity, as well as an appropriate method for reconstructing the…
The equations for the second-order gravitational perturbations produced by a compact-object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill-defined.…
We derive a formalism for solving the Lorenz gauge equations for metric perturbations of Kerr spacetime sourced by an arbitrary stress-energy tensor. The metric perturbation is obtained as a sum of differential operators acting on a set of…
The work describes the method of construction of charges (conserved quantities) for the gravity field in the (3 + 1) decomposition. The presented construction uses tensors of the electrical and magnetic parts of the Weyl tensor and…
We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the "cosmic rulers and clock", which are the building-blocks of any other large-scale-structure…
We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial…
We discuss some perturbative techniques suitable for the gauge-invariant treatment of the scalar and tensor inhomogeneities of an anisotropic and homogeneous background geometry whose spatial section naturally decomposes into the direct…