Related papers: Exploring New Physics Frontiers Through Numerical …
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
The acceleration of the cosmic expansion is a fundamental challenge to standard models of particle physics and cosmology. The new physics of dark energy may lie in the nature of gravity, the quantum vacuum, or extra dimensions. I give a…
Throughout the Universe many powerful events are driven by strong gravitational effects that require general relativity to fully describe them. These include compact binary mergers, black hole accretion and stellar collapse, where…
We submit the viewpoint that, perhaps, some of the controversies in gravitation occurred during this century are not due to insufficiencies of Einstein's field equations, but rather to insufficiencies in the mathematics used for their…
We show that Einstein equations are compatible with the presence of massive point particle idealization and find the corresponding two parameter family of solutions. They are complete defined by the bare mechanical mass $M>0$ and the…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
Solving field equations in the context of higher curvature gravity theories is a formidable task. However in many situations, e.g., in the context of $f(R)$ theories the higher curvature gravity action can be written as Einstein-Hilbert…
We quantized the full Einstein equations in a globally hyperbolic spacetime $N=N^{n+1}$, $n\ge 3$, and found solutions of the resulting hyperbolic equation in a fiber bundle $E$ which can be expressed as a product of spatial eigenfunctions…
New theorems about the existence of solution for a system of infinite linear equations with a Vandermonde type matrix of coefficients are proved. Some examples and applications of these results are shown. In particular, a kind of these…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…
Numerical solutions to the Einstein constraint equations are constructed on a selection of compact orientable three-dimensional manifolds with non-trivial topologies. A simple constant mean curvature solution and a somewhat more complicated…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
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…
The Dark Energy problem is forcing us to re-examine our models and our understanding of relativity and space-time. Here a novel idea of Fundamental Forces is introduced. This allows us to perceive the General Theory of Relativity and…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
We attempt to study three significant tests of general relativity in higher dimensions both in commutative and non-commutative spaces. In the context of non-commutative geometry, we will consider a solution of the Einstein equation in…
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,…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…