Related papers: A mathematical comment on gravitational waves
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
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…
The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a…
This dissertation consists of four parts. In Part I, we briefly review fundamental theories of gravity, performed experimental tests, and gravitational waves. The framework and the methods that we use in our calculations are discussed in…
We develop a theoretical frame for the study of classical and quantum gravitational waves based on the properties of a nonlinear ordinary differential equation for a function $\sigma(\eta)$ of the conformal time $\eta$, called the auxiliary…
In a recent paper we have deduced the basic equations that predict the emission of gravitational waves (GW) according to the Einstein gravitation theory. In a subsequent paper these equations have been used to calculate the luminosities and…
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to…
The investigation of the transverse effect of gravitational waves (GWs) could constitute a further tool to discriminate among several relativistic theories of gravity on the ground. After a review of the TT gauge, the transverse effect of…
In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein…
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…
This chapter provides an overview of gravitational wave (GW) astronomy, providing background material that underpins the other, more specialized chapters in this handbook. It starts with a brief historical review of the development of GW…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
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…
In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…
It is expected that the quantum nature of spacetime leaves its imprint in all semiclassical gravitational systems, at least in certain regimes, including gravitational waves. In this paper we investigate such imprints on gravitational waves…
In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the…
In this short paper we investigate quantum gravitational effects on Einstein's equations using effective field theory techniques. We consider the leading order quantum gravitational correction to the wave equation. Besides the usual…
We discuss an approach to gravitational waves based on Geometric Algebra and Gauge Theory Gravity. After a brief introduction to Geometric Algebra (GA), we consider Gauge Theory Gravity, which uses symmetries expressed within the GA of flat…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the…