Related papers: Stochastic Gauss Equations
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
High-Reynolds-number turbulence driven by stellar convection in main-sequence stars generates stochastic gravitational radiation. We calculate the wave-strain power spectral density as a function of the zero-age main-sequence mass for an…
In this paper we investigate the gravitational waves emission by stellar dynamical structures as complex systems in the quadrupole approximation considering bounded and unbounded orbits. Precisely, after deriving analytical expressions for…
The general relativistic mass-energy variation formula for axisymmetric equilibrium states of a selfgravitating system is developed in the particular case for which the relevant matter consists of a perfectly conducting multiconstituent…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a…
A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving…
The equations of motion of a secularly precessing ellipse are developed using time as the independent variable. The equations are useful when integrating numerically the perturbations about a reference trajectory which is subject to secular…
This is the fourth paper in a series that attempt to put forward a consistent framework for modelling solid regions in neutron stars. Here we turn our attention to axial perturbations of spherically symmetric spacetimes using a gauge…
We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of…
We study the stochastically forced system of isentropic Euler equations of gas dynamics with a $\gamma$-law for the pressure. We show the existence of martingale weak entropy solutions; we also discuss the existence and characterization of…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a (3+1) slicing of spacetime, a Langevin equation for the dynamical conjugate momentum and a Fokker-Planck equation for…
The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion. Here we explore what geodesic motion can tell us about dynamical scattering in the…
Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour of the solar system or for complex…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
The gravitational wave radiation emitted by all, resolved and unresolved, astrophysical sources in the observable universe generates a stochastic background. This background has a directional dependence inherited from the inhomogeneities of…