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The Averaging problem in general relativity and cosmology is discussed. The approach of macroscopic gravity to resolve the problem is presented. An exact cosmological solution to the equations of macroscopic gravity is given and its…
The kinetic energy of a local system of objects placed in a curved spacetime is gained by the subsequent acceleration of the object following the more contracted region of spacetime. Normally this happens near massive gravitating stars.…
Einstein's field equations in general relativity admit a variety of solutions with spacetime singularities. Numerical relativity has recently revealed the properties of somewhat generic spacetime singularities. It has been found that in a…
Anisotropic stresses are ubiquitous in nature, but their modeling in General Relativity is poorly understood and frame dependent. We introduce the first study on the dynamical properties of anisotropic self-gravitating fluids in a covariant…
In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
In this paper, we have studied gravitational collapse and expansion of non-static anisotropic fluid in $5D$ Einstein Gauss-Bonnet gravity. For this purpose, the field equations have been modeled and evaluated for the given source and…
We present a spherically symmetric solution of the general relativistic field equations in isotropic coordinates for anisotropic neutral fluid, compatible with a super dense star modeling by considering a specific choice of anisotropy…
In the literature different approaches have been proposed to compute the anisotropies of the astrophysical gravitational wave background. The different expressions derived, although starting from our work Cusin, Pitrou, Uzan, Phys.Rev.D96,…
It is now possible to partially deflect gravitation away from an object so that the gravitational attraction on the object is reduced. That effect makes it possible to extract energy from the gravitational field, which makes the generation…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
We consider equations of modified gravity involving critical accelerations and find its solutions for the point-like source by suggesting the appropriate symmetry of metrics in the empty space-time.
We consider possible resolutions of singularities in a contracting anisotropic universe for a class of higher derivative gravity theories. We give evidence that for our models the big crunch singularity may be replaced by a nearly flat…
The full set of equations governing the structure and the evolution of self--gravitating spherically symmetric dissipative fluids with anisotropic stresses, is written down in terms of five scalar quantities obtained from the orthogonal…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid…
We present a general solution of the Einstein gravitational field equations for the static spherically symmetric gravitational interior spacetime of an isotropic fluid sphere. The solution is obtained by transforming the pressure isotropy…
We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the…
Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…