Related papers: Multiparticle solutions to Einstein's equations
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We propose a nonlocal field theory for gravity in presence of matter consistent with perturbative unitarity, quantum finiteness, and other essential classical properties that we are going to list below. First, the theory exactly reproduces…
Schwarzschild's solution of Einstein's field equations in vacuum can be written in many different forms. Unfortunately Schwarzschild's own original form is less nice looking and simple than that latter derived by Droste and Hilbert. We…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
A class of exact solutions of the Einstein-Maxwell equations is presented which contains infinite sets of gravitoelectric, gravitomagnetic and electromagnetic multipole moments. The multipolar structure of the solutions indicates that they…
We obtain the perturbed components of affine connection and Ricci tensor using algebraic computation. Naturally, the perturbed Einstein field equations for the vacuum can be written. The method can be used to obtain perturbed equations of…
Exact solutions to the Einstein field equations may be generated from already existing ones (seed solutions), that admit at least one Killing vector. In this framework, a space of potentials is introduced. By the use of symmetries in this…
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…
Spacetimes generated by a lightlike particle source for topologically massive gravity and its limits - Einstein gravity and the pure gravitational Chern-Simons model - are obtained both by solving the field equations and by infinite boosts…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
We develop a method for solving the field equations of a quadratic gravitational theory coupled to matter. The quadratic terms are written as a function of the matter stress tensor and its derivatives in such a way to have, order by order,…
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
A solution of the Einstein vacuum field equations is constructed within the contex of perturbation theory. The solution possesses a graphical representation in terms of diagrams.
We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic…
Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…