Related papers: A Matrix Formulation of Einstein's Vacuum Field Eq…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
In many numerical implementations of the Cauchy formulation of Einstein's field equations one encounters artificial boundaries which raises the issue of specifying boundary conditions. Such conditions have to be chosen carefully. In…
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source,…
We construct new classes of modified theories in which the matter sector couples with the Einstein tensor, namely we consider direct couplings of the latter to the energy-momentum tensor, and to the derivatives of its trace. We extract the…
We present new exact inhomogeneous vacuum cosmological solutions of Einstein's equations. They provide new information about the nature of general cosmological solutions to Einstein's equations.
In this paper the macroscopic Einstein and Maxwell equations for system, in which the electromagnetic interactions are dominating (for instance, the cosmological plasma before the moment of recombination), are derived. Ensemble averaging of…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is…
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…
We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…
A Noether-enhanced Legendre transformation from Lagrange densities to energy-momentum tensors is developed into an alternative framework for formulating classical field equations. This approach offers direct access to the Hamiltonian while…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
Quantum field theories and Matrix models have a far richer solution set than is normally considered, due to the many boundary conditions which must be set to specify a solution of the Schwinger-Dyson equations. The complete set of solutions…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
Inflationary spatially homogeneous cosmological models within an Einstein-Aether gravitational framework are investigated. The matter source is assumed to be a scalar field which is coupled to the aether field expansion and shear scalars…
Since the appearance of Einstein's paper {\em"On the Electrodynamics of Moving Bodies"} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell's equations. The celebrated mass-energy…
We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe…
Scalar-Tensor theories of gravity can be formulated in different frames, most notably, the Einstein and the Jordan one. While some debate still persists in the literature on the physical status of the different frames, a frame…