Related papers: Stochastic Einstein equations
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
Imposing non-integrable constraints on Ricci flows of (pseudo) Riemannian metrics we model mutual transforms to, and from, non-Riemannian spaces. Such evolutions of geometries and physical theories can be modelled for nonholonomic manifolds…
In this paper, we examine stacky structures in Einstein's theory of gravity. In brief, we first give a construction of the moduli stack of solutions to (vacuum) Einstein field equations on $n$-dimensional spacetimes, with vanishing…
We consider the stochastic quantization method for scalar fields defined in a curved manifold and also in a flat space-time with event horizon. The two-point function associated to a massive self-interacting scalar field is evaluated, up to…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
We introduce a stochastic analysis of Grassmann random variables suitable for the stochastic quantization of Euclidean fermionic quantum field theories. Analysis on Grassmann algebras is developed here from the point of view of quantum…
Einstein's static model is the first relativistic cosmological model. The model is static, finite and of spherical spatial symmetry. I use the solution of Einstein's field equations in a homogeneous and isotropic universe -- Friedmann's…
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton…
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
The Einstein equations of general relativity reduce, when the spacetime metric is of the Friedmann--Lemaitre--Robertson--Walker type governing an isotropic and homogeneous universe, to the Friedmann equations, which is a set of nonlinear…
This paper investigates the Einstein relation; the connection between the volume growth, the resistance growth and the expected time a random walk needs to leave a ball on a weighted graph. The Einstein relation is proved under different…
In the context of Brans-Dicke scalar tensor theory of gravitation, the cosmological Friedmann equation which relates the expansion rate $H$ of the universe to the various fractions of energy density is analyzed rigorously. It is shown that…
A static Friedmann brane in a 5-dimensional bulk (Randall-Sundrum type scenario) can have a very different relation between the density, pressure, curvature and cosmological constant than in the case of the general relativistic Einstein…
The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…