Related papers: Modifying the Einstein Equations off the Constrain…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
The modified Gauss-Bonnet gravity can be motivated by a number of physical reasons, including: the uniqueness of a gravitational Lagrangian in four and higher dimensions and the leading order $\alpha^\prime$ corrections in superstring…
In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a…
In this paper, we first review Huei's formulation in which it is shown that the linearized Einstein equations can be written in the same form as the Maxwell equations. We eliminate some imperfections like the scalar potential which is ill…
There is now overwhelming observational evidence that our Universe is accelerating in its expansion. I discuss how modified gravitational models can provide an explanation for this observed late-time cosmic acceleration. We consider…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
The nature of gravitational singularities has been questioned by some recent research, challenging the notion that classical determinism breaks down at these points. By allowing for dynamic changes in the orientation of spatial…
We present a simple technique for generating new solutions of Einstein's equations using such function transformations that leave the field equations in the Ernst form. In this context we recover all the known covariant transformations of…
The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…
Inspired by Verlinde's idea, some modified versions of entropic gravity have appeared in the literature. Extending them in a unified formalism, we derive the generalized gravitational equations accordingly. From gravitational equations, the…
We discuss the set of constraints for Einstein-aether theories, comparing the flat background case with what is expected when the gravitational fields are dynamic. We note potential pathologies occurring in the weak gravitational field…
We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\mu\nu}$ in…
This is the second in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper the numerical methods used to solve the system of evolution…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
There is evidence that Newton and Einstein's theories of gravity cannot explain the dynamics of a universe made up solely of baryons and radiation. To be able to understand the properties of galaxies, clusters of galaxies and the universe…
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…
The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant…