Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
Jonathan R. Gair, Michele Vallisneri, Shane L. Larson, John G., Baker

TL;DR
Space-based low-frequency gravitational-wave detectors will enable comprehensive tests of general relativity, probing fundamental aspects like gravitational wave polarization, propagation speed, and the nature of black holes, significantly advancing astrophysics and cosmology.
Contribution
This paper reviews the potential of space-based gravitational-wave detectors to test various fundamental aspects of general relativity and astrophysics in the low-frequency band.
Findings
Potential to test gravitational wave polarization states
Ability to measure gravitational wave propagation speed
Insights into the true nature of black holes
Abstract
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 presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band…
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