Related papers: Expanding universe with nonlinear gravitational wa…
In this paper we study cosmological solutions to the Einstein--Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Gravitational waves provide a novel and independent measurement of cosmological parameters, offering a promising avenue to address the Hubble tension alongside traditional electromagnetic observations. In the absence of electromagnetic…
An exact analytical model of the process of collision and nonlinear interaction of gravitational and/or electromagnetic soliton wave and strong non-soliton electromagnetic traveling wave of arbitrary profile propagating in the expanding…
We consider the propagation of nonlinear sound waves in a perfect fluid at rest. By employing the Riemann wave equation of nonlinear acoustics in one spatial dimension, it is shown that waves carrying a constant density perturbation at…
This work is a follow-up to the paper, "Numerical Relativity as a Tool for Studying the Early Universe". In this article, we determine if cosmological gravitational waves can be accurately extracted from a dynamical spacetime using an…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…
Using the Teukolsky and Sasaki-Nakamura equations for the gravitational perturbation of the Kerr spacetime, we calculate the post-Newtonian expansion of the energy and angular momentum luminosities of gravitational waves from a test…
A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at…
In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of…
We consider quantization of the positive curvature Friedmann cosmology in the unimodular modification of Einstein's theory, in which the spacetime four-volume appears as an explicit time variable. The Hamiltonian admits self-adjoint…
We solve a $1+5$-dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvature singularities can be removed by an extension of the…
Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a…
The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation.…
H.A. Wilson, then R.H. Dicke, proposed to describe gravitation by a spatial change of the refractive index of the vacuum around a gravitational mass. Dicke extended this formalism in order to describe the apparent expansion of the Universe…
The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding…
We prove here that Newtons universal gravitation and momentum conservation laws together reproduce Weinbergs relation. It is shown that the Hubble parameter H must be built in this relation, or equivalently the age of the Universe t. Using…
We consider quantum general relativity in three dimensions with a positive cosmological constant. The Hartle-Hawking wave function is computed as a function of metric data at asymptotic future infinity. The analytic continuation from…
Fully non-linear, plane-symmetric exact solutions of the Einstein equations describing the scattering of gravitational and electromagnetic waves have existed for many years. For these closed-form solutions to be found, idealized wave…
We review recent work on the Einstein equations of general relativity when the curvature is defined in a weak sense. Weakly regular spacetimes are constructed, in which impulsive gravitational waves, as well as shock waves, propagate.