Related papers: Averaging in LRS class II spacetimes
Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an…
Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R)…
In our companion paper we identified a complete set of manifestly gauge-invariant observables for general relativity. This was possible by coupling the system of gravity and matter to pressureless dust which plays the role of a dynamically…
The subject of cosmological backreaction in General Relativity is often approached by coordinate-dependent and metric-based analyses. We present in this letter an averaging formalism for the scalar parts of Einstein's equations that is…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…
The paper is an introduction into General Ether Theory (GET). We start with few assumptions about an universal ``ether'' in a Newtonian space-time which fulfils \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) +…
We construct generalized symmetries for linearized Einstein gravity in arbitrary dimensions. First-principle considerations in QFT force generalized symmetries to appear in dual pairs. Verifying this prediction helps us find the full set of…
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 consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which…
In this paper, it is shown that the cosmological model that was introduced in a sequence of three earlier papers under the title, A Dust Universe Solution to the Dark Energy Problem can be used to analyse and solve the Cosmological…
We present and analyze new exact gyraton solutions of algebraic type II on generalized Melvin universe of type D which admit non-vanishing cosmological constant $\Lambda$. We show that it generalizes both, gyraton solutions on Melvin and on…
We consider the linearised vacuum Einstein equations around a Kerr exterior solution and present a scheme to prove elliptic $L^2(\mathbb{S}^2)$-estimates for the linearised curvature quantities in the equations. The scheme employs the…
A regularization procedure, that allows one to relate singularities of curvature to those of the Einstein tensor without some of the shortcomings of previous approaches, is proposed. This regularization is obtained by requiring that (i) the…
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…
This is the second in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the class of solutions to the…
Beals, Gaveau and Greiner (1996) find the fundamental solution to a 2-Laplace-type equation in a class of sub-Riemannian spaces. This solution is related to the well-known fundamental solution to the p-Laplace equation in Grushin-type…
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold…
We consider a description of the stochastic oscillations of the general relativistic accretion disks around compact astrophysical objects based on the generalized Langevin equation, which accounts for the general retarded effects of the…
This paper treats iterative solution methods to the generalized Lyapunov equation. Specifically it expands the existing theoretical justification for the alternating linear scheme (ALS) from the stable Lyapunov equation to the stable…