Advanced LIGO’s ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections

We study the ability of the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem. The cosmic censorship conjecture, which is believed to be true in the theory of general relativity, limits the spin-to-mass-squared ratio of a Kerr black hole, $\ensuremath{\chi}\ensuremath{\equiv}j/{m}^{2}\ensuremath{\le}1$. The no-hair theorem, which is also believed to be true in the theory of general relativity, suggests a particular value for the tidal Love number of a nonrotating black hole (${k}_{2}=0$). Using the Fisher matrix formalism, we examine the measurability of the spin and tidal deformability of compact binary systems involving at least one putative black hole. Using parameter measurement errors and correlations obtained from the Fisher matrix, we determine the smallest detectable violation of bounds implied by the cosmic censorship conjecture and the no-hair theorem. We examine the effect of excluding unphysical areas of parameter space when determining the smallest detectable apparent violations, and we examine the effect of different post-Newtonian corrections to the amplitude of the compact binary coalescence gravitational waveform, as given in Arun et al. [Phys. Rev. D 79, 104023 (2009)]. In addition, we perform a brief study of how the recently calculated 3.0 pN and 3.5 pN spin-orbit corrections to the phase [Marsat et al., Classical Quantum Gravity 30, 055007 (2013)] affect spin and mass parameter measurability. We find that physical priors on the symmetric mass ratio and higher harmonics in the gravitational waveform could significantly affect the ability of aLIGO to investigate cosmic censorship and the no-hair theorem for certain systems.