Related papers: Ehlers-Kundt Conjecture about Gravitational Waves …
The observation of gravitational waves opens up a new window to probe the universe and the nature of the gravitational field itself. As a result, they serve as a new and promising tool to not only test our current theories but to study…
The energy of gravitational waves is a fundamental problem in gravity theory. The existing descriptions for the energy of gravitational waves, such as the well-known Isaacson energy-momentum tensor, suffer from several defects. Due to the…
Plane electromagnetic and gravitational waves interact with particles in such a way as to cause them to oscillate not only in the transverse direction but also along the direction of propagation. The electromagnetic case is usually shown by…
Gravitational waves are excellent tools to probe the foundations of General Relativity in the strongly dynamical and non-linear regime. One such foundation is Lorentz symmetry, which can be broken in the gravitational sector by the…
Time-harmonic electromagnetic waves in vacuum are described by the Helmholtz equation $\Delta u+\omega ^{2}u=0 $ for $ (x,y,z) \in \mathbb{R}^3 $. For the evolution of such waves along the $z$-axis a Schr\"odinger equation can be derived…
As an example of the unification of gravitation and particle physics, an exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in…
Ehlers and Kundt [1] argued in favor of the velocity effect: particles initally at rest hit by a burst of gravitational waves should fly apart with constant velocity after the wave has passed. Zel'dovich and Polnarev [2] suggested instead…
Along the lines of the Einstein-Rosen wave equation of General Relativity (GR), we derive a gravitational wave equation with cylindrical symmetry in the Einstein-aether (EA) theory. We show that the gravitational wave in the EA is periodic…
In geophysical environments, wave motions that are shaped by the action of gravity and global rotation bear the name of gravito-inertial waves. We present a geometrical description of gravito-inertial surface waves, which are low-frequency…
The periodic orbit conjecture states that, on closed manifolds, the set of lengths of the orbits of a non-vanishing vector field all whose orbits are closed admits an upper bound. This conjecture is known to be false in general due to a…
We derive the Euler-Heisenberg solutions that describe electromagnetic waves propagating through very intense uniform magnetic or electric background, with the effective metric approach. We first explore the case of a magnetic background:…
We describe the properties of evanescent gravitational waves (EGWs)---wave solutions of Einstein equations which decay exponentially in some direction while propagating in another. Evanescent waves are well-known in acoustics and optics and…
In this paper, we systematically study spacetimes of gravitational plane waves in Einstein-aether theory. Due to the presence of the timelike aether vector field, now the problem in general becomes overdetermined. In particular, for the…
The Quantum Ergodic Conjecture equates the Wigner function for a typical eigenstate of a classically chaotic Hamiltonian with a delta-function on the energy shell. This ensures the evaluation of classical ergodic expectations of simple…
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. Exact solution with own angular momentum in form of a…
We derive a new formulation of the compressible Euler equations exhibiting remarkable structures, including surprisingly good null structures. The new formulation comprises covariant wave equations for the Cartesian components of the…
Gravitational waves provide a novel and powerful way to test astrophysical models of compact objects, early universe processes, beyond the Standard Model particle physics, dark matter candidates, Einstein's theory of General Relativity and…
Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e g compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i e the…
We construct a general relativity formula for the law of gravity for material bodies. The formula contains three numeric parameters that are to be determined experimentally. If they are chosen from symmetry considerations, then the theory…
We show that, given any static spacetime whose spatial slices are asymptotically Euclidean (or, more generally, asymptotically conic) manifolds modeled on the large end of the Schwarzschild exterior, there exist stationary solutions to the…