Related papers: Static self-gravitating many-body systems in Einst…
Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $ f(R,T,R_{\mu\nu}T^{\mu\nu})$ type. We prove this statement by constructing exact and approximate…
We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the…
We prove existence of solutions for an elastic body interacting with itself through its Newtonian gravitational field. Our construction works for configurations near one given by a self-gravitating ball of perfect fluid. We use an implicit…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
Extended objects in GR are often modelled using distributional solutions of the Einstein equations with point-like sources, or as the limit of infinitesimally small "test" objects. In this note, I will consider models of finite…
A general framework for the solutions of the constraints of pure gravity is constructed. It provides with well defined mathematical criteria to classify their solutions in four classes. Complete families of solutions are obtained in some…
We study equilibrium states in relativistic galactic dynamics which are described by solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling…
The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.
Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian…
The static n-body problem of General Relativity states that there are, under a reasonable energy condition, no static $n$-body configurations for $n > 1$, provided the configuration of the bodies satisfies a suitable separation condition.…
Einstein Gravity in 2+1 dimensions arises as a consequence of the equations of motion of a gauge model in an external metric. Newton's constant appears as an order parameter of a spontaneously broken discrete symmetry. Matter is coupled in…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
The purpose of this paper is to analyze the existence of static stable Einstein universe using inhomogeneous linear perturbations in the context of $f(R,T)$ gravity ($R$ and $T$ denote the scalar curvature and trace of the stress-energy…
Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The…
The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
A deformation of Einstein Gravity is constructed based on gauging the noncommutative ISO(3,1) group using the Seiberg-Witten map. The transformation of the star product under diffeomorphism is given, and the action is determined to second…
In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…