Living Reviews in Relativity

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

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1 Introduction
2 The Theory of Gravitation
2.1 Will’s “standard model” of gravitational theories
2.2 Alternative theories
2.3 The black-hole paradigm
3 Space-Based Missions to Detect Gravitational Waves
3.1 The classic LISA architecture
3.2 LISA-like observatories
3.3 Mid-frequency space-based observatories
4 Summary of Low-Frequency Gravitational-Wave Sources
4.1 Massive black-hole coalescences
4.2 Extreme-mass-ratio inspirals
4.3 Galactic binaries
5 Gravitational-Wave Tests of Gravitational Physics
5.1 The “classic tests” of general relativity with gravitational waves
5.2 Tests of general relativity with phenomenological inspiral template families
5.3 Beyond the binary inspiral
6 Tests of the Nature and Structure of Black Holes
6.1 Current observational status
6.2 Tests of black-hole structure using EMRIs
6.3 Tests of black-hole structure using ringdown radiation: black-hole spectroscopy
6.4 Prospects from gravitational-wave and other observations
7 Discussion