Related papers: Stochastic Gauss Equations
From a minimum of total energy of celestial bodies, their basic parameters are obtained. The steady-state values of the mass, radius, and temperature of stars and white dwarfs, as well as masses of pulsars are calculated. The luminosity and…
We discuss stochastic representations of advection diffusion equations with variable diffusivity, stochastic integrals of motion and generalized relative entropies.
In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
Einstein's field equations with a background source term that induces perturbations and the applications of this new formalism to a compact dense matter relativistic star are presented. We introduce a new response kernel in the field…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
This paper concerns an approximation of the expectation values of the position and momentum of the solution to the semiclassical Schr\"odinger equation with a Gaussian as the initial condition. Of particular interest is the approximation…
The self-gravitating systems are formed by particles interacting through gravity. They describe structure formation in the universe. As a consequence of the long range interaction of gravity, they are inhomogeneous even at thermal…
In most books the Delaunay and Lagrange equations for the orbital elements are derived by the Hamilton-Jacobi method: one begins with the 2-body Hamilton equations, performs a canonical transformation to the orbital elements, and obtains…
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
Stellar pulsations in rotating relativistic stars are reviewed. Slow rotation approximation is applied to solving the Einstein equations. The rotational effects on the non-axisymmetric oscillations are explicitly shown in the polar and…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…
A stochastic gravitational wave background causes the apparent positions of distant sources to fluctuate, with angular deflections of order the characteristic strain amplitude of the gravitational waves. These fluctuations may be detectable…
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 derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave…
A brief introduction to the gauge invariant classical and quantum theory of cosmological perturbations is given. The formalism is applied to inflationary Universe models and yields a consistent and unified description of the generation and…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…