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In testing gravity a model-independent way, one of crucial tests is measuring the propagation speed of a gravitational wave (GW). In general relativity, a GW propagates with the speed of light, while in the alternative theories of gravity…
Gravitational-wave observations provide a unique opportunity to test general relativity (GR) in the strong-field and highly dynamical regime of the theory. Parametrized tests of GR are one well-known approach for quantifying violations of…
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.…
Searches for gravitational-wave counterparts have been going in earnest since GW170817 and the discovery of AT2017gfo. Since then, the lack of detection of other optical counterparts connected to binary neutron star or black hole - neutron…
The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation.…
The direct discovery of gravitational waves (GWs) from the coalescence of compact binary components by the LIGO/Virgo/KAGRA Collaboration provides an unprecedented opportunity for exploring the underlying theory of gravity that drives the…
The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein's general theory of relativity at…
In light of the newly opened and rapidly growing gravitational waves window in multi-messenger astronomy, in order to fully take advantage of the new opportunities we are provided with, new ideas are required for a better and deeper employ…
Binary Systems are the most studied sources of gravitational waves. The mechanisms of emission and the behavior of the orbital parameters are well known and can be written in analytic form in several cases. Besides, the strongest indication…
Current searches for signals of departures from the fundamental symmetries of General Relativity using gravitational waves are largely dominated by propagation effects like dispersion and birefringence from highly dynamic sources such as…
Coalescing compact binaries have been pointed out as the most promising source of gravitational waves for kilometer-size interferometers such as LIGO. Gravitational wave signals are extracted from the noise in the detectors by matched…
Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves.…
This decade will see the first direct detections of gravitational waves by observatories such as Advanced LIGO and Virgo. Among the prime sources are coalescences of binary neutron stars and black holes, which are ideal probes of dynamical…
The direct detection of gravitational waves (GW) from merging binary black holes and neutron stars mark the beginning of a new era in gravitational physics, and it brings forth new opportunities to test theories of gravity. To this end, it…
Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves…
Inspiralling compact binaries are expected to circularize before their gravitational-wave signals reach the sensitive frequency band of ground-based detectors. Current searches for gravitational waves from compact binaries using the LIGO…
The various materials of test masses, and the difference of arm lengths of global ground-based gravitational-wave interferometer detectors offer a unique approach to test Newton's second law, weak equivalence principle, and Einstein…
We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ~0.01mHz - 1Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the…
Gravitational waves emitted from compact binary coalescence can be subject to wave diffraction if they are gravitationally lensed by an intervening mass clump whose Schwarzschild timescale matches the wave period. Waves in the ground-based…
Several assumptions at the foundation of the standard cosmological model have as a direct consequence a specific relation between cosmological distances, known as the distance duality relation, whose violation would be a smoking gun of…