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"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

	Abstract
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
	Acknowledgements
	References
	Footnotes
	Figures
	Tables

List of Tables

Table 1:
Hierarchy of formulations of the equivalence principle.

Table 2:
Leading-order effects of alternative theories of gravity, as represented in the ppE framework [Eq. (52

)]. For GR $α = β = 0$ . This table is copied from [134], except for the two entries labeled with an asterisk. The quadratic curvature ppE exponent given in [134] was $b = − 1∕3$ , coming from the conservative dynamics. However, it was shown in [483] that the dissipative correction is larger, giving the value $b = − 7∕3$ quoted above. The dynamical Chern–Simons ppE exponent given in [134] was $b = 4∕3$ , which was derived using the slow-rotation metric accurate to linear order in the spin [496]. At quadratic order in the spin [488], the corrections to both conservative and dissipative dynamics occur at lower post-Newtonian order, giving $b = 1∕3$ [487].

Table 3:
Accuracy with which a LISA observation could determine the multipole moments of a spacetime decreases as more multipoles are included in the model, taken from Ryan [388]. The third column indicates the highest multipole included in the particular model. Results are shown for two typical cases, a $10M ⊙ + 105 M ⊙$ inspiral and a $10M ⊙ + 106 M ⊙$ inspiral; in both cases the SNR of the inspiral is 10.