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This is an overview article of the mathematics of gravitational waves. We explain the mathematics and physics of these waves in general relativity theory, discuss the gravitational wave experiment aLIGO and their detection of gravitational…
The analysis of a general multibody physical system governed by Einstein's equations in quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties -- many coupled degrees of freedom, dynamic instability --…
Observations of gravitational waves (GWs) by the advanced LIGO--Virgo detectors provide us with ground breaking opportunities to test predictions of Einstein's theory of general relativity (GR) in the strong field regime. In this article,…
Modified gravitational wave propagation is a smoking gun of modifications of gravity at cosmological scales, and can be the most promising observable for testing such theories. The observation of gravitational waves (GW) in recent years has…
Gravitational wave detectors are formidable tools to explore strong-field gravity, especially black holes and neutron stars. These compact objects are extraordinarily efficient at producing electromagnetic and gravitational radiation. As…
By precisely monitoring the "ticks" of Nature's most precise clocks (millisecond pulsars), scientists are trying to detect the "ripples in spacetime" (gravitational waves) produced by the inspirals of supermassive black holes in the centers…
A particle of mass $\mu$ moves on a circular orbit around a nonrotating black hole of mass $M$. Under the assumption $\mu \ll M$ the gravitational waves emitted by such a binary system can be calculated exactly numerically using black-hole…
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…
We hereby propose an alternative and additional angle on the nature of gravitational waves (GWs), postulating the theoretical and experimental possibility that GWs carry a deformation of the time component of spacetime, other than the…
Gravitational waves are ripples in the space time fabric when high energy events such as black hole mergers or neutron star collisions take place. The first Gravitational Wave (GW) detection (GW150914) was made by the Laser Interferometer…
We provide a simple transfer function that determines the effect of an early matter dominated era on the gravitational wave background and show that a large class of compactifications of superstring theory might be tested by observations of…
Gravitational wave detection requires an in-depth understanding of the physical properties of gravitational wave signals, and the noise from which they are extracted. Understanding the statistical properties of noise is a complex endeavor,…
The potential realization of a gravitational wave (GW) astronomy in next years is a great challenge for the scientific community. By giving a significant amount of new information, GWs will be a cornerstone for a better understanding of the…
Parity violation in the gravitational interaction has an important impact on fundamental observables and the evolution of the universe. We here investigate for the first time our ability to probe the parity violating nature of the…
We discuss gravitational waves from merging binaries using a Newtonian approach with some inputs from the Post-Newtonian formalism. We show that it is possible to understand the key features of the signal using fundamental physics and also…
Gravitational waves (GW) are expected to interact with dark energy and dark matter, affecting their propagation on cosmological scales. In order to model this interaction, we derive a gauge invariant effective equation and action valid for…
Gravitational wave astronomy is established with direct observation of gravitational wave from merging binary black holes and binary neutron stars during the first and second observing run of LIGO and Virgo detectors. The gravitational-wave…
Gravitational waves from inspiraling sub-solar mass compact objects would provide almost definitive evidence for the existence of primordial black holes. In this chapter, we explain why these exotic objects are interesting candidates for…
Black holes are the most compact objects in the Universe. According to general relativity, black holes have a horizon that hides a singularity where Einstein's theory breaks down. Recently, gravitational waves opened the possibility to…
It is argued that, in order for the gravitational field to be propagated as a wave, it is necessary for it to satisfy a further set of field equations, in addition to those of Einstein and Hilbert, and these equations mean there is a…