The exterior gravitational field of a slowly-rotating neutron star can becharacterized by its multipole moments, the first few being the neutron starmass, moment of inertia, and quadrupole moment to quadratic order in spin. Inprinciple, all of these quantities depend on the neutron star's internalstructure, and thus, on unknown nuclear physics at supra-nuclear energydensities. We here find relations between the moment of inertia, the Lovenumbers and the quadrupole moment (I-Love-Q relations) that do not dependsensitively on the neutron star's internal structure. Three importantconsequences derive from these I-Love-Q relations. On an observationalastrophysics front, the measurement of a single member of the I-Love-Q triowould automatically provide information about the other two, even when thelatter may not be observationally accessible. On a gravitational wave front,the I-Love-Q relations break the degeneracy between the quadrupole moment andthe neutron-star spins in binary inspiral waveforms, allowing second-generationground-based detectors to determine the (dimensionless) averaged spin to$\mathcal{O}(10)%$, given a sufficiently large signal-to-noise ratio detection.On a fundamental physics front, the I-Love-Q relations allow for tests ofGeneral Relativity in the neutron-star strong-field that are both theory- andinternal structure-independent. As an example, by combining gravitational-waveand electromagnetic observations, one may constrain dynamical Chern-Simonsgravity in the future by more than 6 orders of magnitude more stringently thanSolar System and table-top constraints.
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