Figure 5

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"Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays"

Nicolás Yunes and Xavier Siemens

	Abstract
1	Introduction
	1.1	The importance of testing
	1.2	Testing general relativity versus testing alternative theories
	1.3	Gravitational-wave tests versus other tests of general relativity
	1.4	Ground-based vs space-based detectors and interferometers vs pulsar timing
	1.5	Notation and conventions
2	Alternative Theories of Gravity
	2.1	Desirable theoretical properties
	2.2	Well-posedness and effective theories
	2.3	Explored theories
	2.4	Currently unexplored theories in the gravitational-wave sector
3	Detectors
	3.1	Gravitational-wave interferometers
	3.2	Pulsar timing arrays
4	Testing Techniques
	4.1	Coalescence analysis
	4.2	Burst analyses
	4.3	Stochastic background searches
5	Compact Binary Tests
	5.1	Direct and generic tests
	5.2	Direct tests
	5.3	Generic tests
	5.4	Tests of the no-hair theorems
6	Musings About the Future
	Acknowledgements
	References
	Footnotes
	Figures
	Tables

Figure 5: Top: Fitting curves (solid curve) and numerical results (points) of the universal I-Love (left) and Q-Love (right) relations for various equations of state, normalized as $I¯= I ∕M 3NS$ , $¯λ (tid) = λ(tid)∕M 5NS$ and $Q¯ = − Q(rot)∕[M 3NS(S∕M N2S )2]$ , $MNS$ is the neutron-star mass, $λ(tid)$ is the tidal Love number, $Q(rot)$ is the rotation-induced quadrupole moment, and $S$ is the magnitude of the neutron-star spin angular momentum. The neutron-star central density is the parameter varied along each curve, or equivalently the neutron-star compactness. The top axis shows the neutron star mass for the APR equation of state, with the vertical dashed line showing $MNS = 1M ⊙$ . Bottom: Relative fractional errors between the fitting curve and the numerical results. Observe that these relations are essentially independent of the equation of state, with loss of universality at the 1% level. Image reproduced by permission from [452], copyright by APS.