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This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
The vibrating string is a source of gravitational waves which requires novel computational techniques, based on the explicit construction of a conserved and renormalized (in a classical sense) energy-momentum tensor. The renormalization is…
A new class of solutions to Einstein's classical field equations of general relativity is presented. The solutions describe a non-rotating, spherically symmetric, compact self gravitating object, residing in a static electro-vacuum space…
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is…
In principle, global properties of solution of Einstein equations need to be addressed using the conformal Einstein equations, because this conformal compactification allows a clean definition of the `infinities' (spacelike, timelike and…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study…
It is pointed out that at present we only prove that inertial static mass and gravitational static mass are equivalent. We have not proved that inertial moving mass and gravitational moving mass are also equivalent. It is proved by the…
We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of the response solutions (i.e., periodic…
We study massless solutions to the Einstein equations coupled to different matter models with a magnetic field and a conformal gauge singularity assuming spatial homogeneity with three commuting spatial translations. We show that there are…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
Using an effective one body approach we describe in detail gravitational waves from classical three body problem on a non-rotating straight line and derive their basic physical characteristics. Special attention is paid to the irregular…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using…
Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to…
A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess a perfect fluid energy momentum tensor, and the…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…