Related papers: Stochastic Einstein equations
Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin…
The Einstein relation connecting the diffusion constant and the mobility is violated beyond the linear response regime. For a colloidal particle driven along a periodic potential imposed by laser traps, we test the recent theoretical…
We consider a proposed alternative to quantum gravity, in which the spacetime metric is treated as classical, even while matter fields remain quantum. Consistency of the theory necessarily requires that the metric evolve stochastically.…
Stochastic differential equations (SDE) are widely used in modeling stochastic dynamics in literature. However, SDE alone is not enough to determine a unique process. A specified interpretation for stochastic integration is needed.…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
Gravitational probes should maintain spatial flatness for Einsten-Infeld-Hoffmann dynamics of relativistic matter-energy. The continuous elementary source/particle in Einstein's gravitational theory is the r^{-4} radial energy density…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
In order to reconcile the wave-function collapse in quantum mechanics with the finiteness of signals' propagation in general relativity, we delve into a stochastic version of the Ricci flow and study its non-relativistic limit in presence…
The Einstein relation describes the response of a diffusing particle to a small constant external force. It states that, as the force tends to zero, the ratio of the limiting velocity to the force magnitude converges to the diffusivity…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
We consider the 3-dimensional formulation of Einstein's theory for spacetimes possessing a non-null Killing field $\xi^a$. It is known that for the vacuum case some of the basic field equations are deducible from the others. It will be…
The manuscript studies a 3+N+1-dimensional space in which the N extra dimensions are dynamically compact. The 3 large dimensions, behaving as the spacial part of the FRW metric, possess a different scale factor in comparison with the N…
The Einstein vacuum equations on an (n+1)-dimensional toroidal manifold $\mathbb{M}^{n+1}=\mathbb{T}^{n}\times\mathbb{R}^{+}$ reduce to a system of n-dimensional nonlinear ODEs in terms of the set of toroidal radii $(a_{i})_{i=1}^{n}$ or…
The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
Recently, Ryu et al. showed that two broadened bands connected by a set of four Einstein-coefficient spectra for stimulated and spontaneous single-photon transitions will obey detailed balance at equilibrium if the spectra satisfy…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…