Related papers: Constants of motion for vacuum general relativity
Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action are derived. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still…
A constant homogeneous magnetic field is applied to a composite system made of two scalar particles with opposite charges. Motion is described by a pair of coupled Klein-Gordon equations that are written in closed form with help of a…
In this paper, the metric approach of $f(R)$ theory of gravity is used to investigate the exact vacuum solutions of spatially homogeneous rotating spacetimes. For this purpose, R is replaced by f(R) in the standard Einstein-Hilbert action…
A solution for the Einstein gravity coupled with non linear electrodynamics is introduced in 2+1 dimensions. Especially, in the case with a non-vanishing cosmological constant, we obtain a novel black hole solution. To find fundamental…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural…
The present work considers (4+1)-dimensional spatially homogeneous vacuum cosmological models. Exact solutions -- some already existing in the literature, and others believed to be new -- are exhibited. Some of them are the most general for…
Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
We solve (2+1) noncommutative gravity coupled to point-like sources. We find continuity with Einstein gravity since we recover the classical gravitational field in the $\theta \to 0$ limit or at large distance from the source. It appears a…
A new set of field equations for a space-time dependent Newton's constant $G(x)$ and cosmological constant $\Lambda(x)$ in the presence of matter is presented. We prove that it represents the most general mathematically consistent,…
We show that the tree dimensional Einstein vacuum field equations with cosmological constant are integrable. Using the $sl(2,R)$ valued soliton connections we obtain the metric of the spacetime in terms of the dynamical variables of the…
The computations of numerical relativity make use of (3+1)- decompositions of Einstein field equations. We examine the conceptual characteristics of this method; instances of compact-star binaries are considered. The preeminent role of the…
Geroch's solution-generating method is extended to the case of Einstein spaces, which possess a Killing vector {{}and are thus asymptotically (locally) (anti-)de Sitter}. This includes the reduction to a three-dimensional coset space, the…
We find constrained instantons in Einstein gravity with and without a cosmological constant. These configurations are not saddle points of the Einstein-Hilbert action, yet they contribute to non-perturbative processes in quantum gravity. In…
The equations of motion for a Lagrangian ${\cal L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It…
We show that the asymptotic dynamics of three-dimensional gravity with positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter gravity and conformal…
We study a lattice regularization of the gravitational path integral--causal dynamical triangulations--for (2+1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of…
We revisit the problem of the equations of motion of a system of $N$ self-interacting massive particles (without spins) in the first post-Minkowskian (1PM) approximation of general relativity. We write the equations of motion, gravitational…