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Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and --- correspondingly --- unphysical quantities. This is particularly true for ground-based…
It is pointed out that if gravitational interactions among ordinary bodies propagate in extra space-time dimensions the velocity of gravitational waves in vacuum could be different from the speed of light $c$.
We first review some aspects of gravitational wave and the thermodynamic expression of Einstein field equations, these achieved conclusions allow people to think of Einstein's gravitational wave as a kind of sound wave in ordinary gas which…
There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the…
Gravitational waves (GWs) are regarded as standard sirens for Cosmology. GWs from compact binary coalescence (CBC) can directly determine the luminosity distance but usually can not obtain information about the redshift. However, if the…
The dynamics of a gravitational wave propagating through a cosmic gauge field are dramatically different than in vacuum. We show that a gravitational wave acquires an effective mass, is birefringent, and its normal modes are a linear…
This chapter introduces gravitational wave cosmology, focusing on the use of gravitational waves as standard sirens to probe the expansion history of the Universe. It presents and explains the methodologies behind bright and dark siren…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
Gravitational waves (GWs) are direct probes of cosmological gravity, sensitive to space-time inhomogeneities along their propagation. The presence of massive objects breaks homogeneity and isotropy, allowing for new interactions between…
Gravitational waves affect the observed direction of light from distant sources. At telescopes, this change in direction appears as periodic variations in the apparent positions of these sources on the sky; that is, as proper motion. A wave…
We develop a unified formalism for describing the interaction of gravitational waves with matter that clearly separates the effects of general relativity from those due to interactions in the matter. Using it, we derive a general expression…
The detection of gravitational waves is possible thanks to a multidisciplinary approach, involving different disciplines such as astrophysics, physics, engineering and quantum optics. Consequently, it is important today for teachers to…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
General relativity and its cosmological solution predicts the existence of tensor modes of perturbations evolving on top of our Friedman-Lema\^itre-Robertson-Walker expanding Universe. Being gauge invariant and not necessarily coupled to…
We study the gravitational waves in modified Gauss-Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is…
This article, produced as part of an undergraduate research class, aims to provide an overview of gravitational waves, though it does not offer a comprehensive review. We begin with a brief discussion regarding the history of gravitational…
With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of…
Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen…
We study the propagation of a gravitational wave in an Ads spacetime. We find that, in presence of the cosmological constant, the graviton mass cannot be measured with higher precision than the square root of the cosmological constant.