Related papers: A Matrix Formulation of Einstein's Vacuum Field Eq…
We determine exact and analytic solutions of the gravitational field equations in Einstein-aether scalar model field with a Bianchi I background space. In particular, we consider nonlinear interactions of the scalar field with the aether…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
We derive linear scalar perturbation equations for Einstein-Cartan field equations of Weyssenhoff fluid, as well as for the corresponding perturbations of Bianchi identity and geodesic equations. The equations are given in both conformal…
A consistent variational derivation of the Majorana 4-spinor field equations coupled to Einstein's theory of gravitation is given. The equivalence of the first and the second order variational field equations is explicitly demonstrated. The…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric…
The Einstein-scalar field theory can be used to model gravitational physics with scalar field matter sources. We discuss the initial value formulation of this field theory, and show that the ideas of Leray can be used to show that the…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
The Einstein vacuum equations in the formulation developed by Newman, Penrose [NP] and Friedrich [Fr] are expressed in terms of a Lie superbracket. Differential identities are derived from the super Jacobi identity. This perspective…
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries…
The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter,…
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…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
A system of field equations for an Einstein-Maxwell model with $RF^2$-type nonminimal coupling in a non-Riemannian space-time with a non-vanishing torsion is derived and the resulting field equations are expressed in terms of the Riemannian…
This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and $f(R,T)$-modifications. The constructions are possible in terms of…
The in-in effective action formalism is used to derive the semiclassical correction to Einstein's equations due to a massless scalar quantum field conformally coupled to small gravitational perturbations in spatially flat cosmological…
The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order…
A novel tensor-based formula for solving the linear systems involving Kronecker sum is proposed. Such systems are directly related to the matrix and tensor forms of Sylvester equation. The new tensor-based formula demonstrates the…