Related papers: Ehlers-Kundt Conjecture about Gravitational Waves …
Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved…
The Kerr-Schild-Kundt (KSK) metrics are known to be one of the universal metrics in general relativity, which means that they solve the vacuum field equations of any gravity theory constructed from the curvature tensor and its higher-order…
A family of exact vacuum solutions, representing generalized plane waves propagating on the (anti-)de Sitter background, is constructed in the framework of Poincar\'e gauge theory. The wave dynamics is defined by the general Lagrangian that…
One of the most profound questions of mathematical physics is that of establishing from first principles the hydrodynamic equations in large, isolated, strongly interacting many-body systems. This involves understanding relaxation at long…
We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant $\lambda$ are…
A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…
We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where…
Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the…
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic…
According to general relativity, trapping surfaces and horizons are classical causal structures that arise in systems with sharply defined energy and corresponding gravitational radius. The latter concept can be extended to a quantum…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
We present a formulation of Einstein--Maxwell vacuum fields due to plane fronted electromagnetic waves sharing their wave fronts with gravitational waves. This is based on a recent geometrical reconstruction of plane fronted wave fields by…
The metric for plane gravitational waves is quantized using the Ashtekar field variables. The z axis (direction of travel of the waves) is taken to be the entire real line. Solutions to the constraints are proposed; they involve open-ended…
We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert-Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency…
Gravitational waves provide a unique window into gravity, cosmology, and high-energy physics, enabling the exploration of fundamental phenomena across a wide range of scales. This review presents a coherent and pedagogical framework that…
A system of equations, describing the evolution of electromagnetic fields, is introduced and discussed. The model is strictly related to Maxwell's equations. As a matter of fact, the Lagrangian is the same, but the variations are subjected…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
Euler's interpretation of Newton's gravity (NG) as Archimedes' thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler's, is recalled and compared with the latter. None of these two…
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…
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…