Leonard E Parker Center for Gravitation, Cosmology and Astrophysics

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The Leonard E Parker Center for Gravitation, Cosmology and Astrophysics is supported by NASA, the National Science Foundation, UW-Milwaukee College of Letters and Science, and UW-Milwaukee Graduate School. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.

The era of advanced gravitational-wave detectors is expected to provide the first direct observations of gravitational-waves. Compact binary coalescence (CBC) events are comprised of the inspiral, merger, and and ringdown of two massive, compact objects, such as neutron stars and black holes. The inspiral portion of CBC events are the most promising sources for gravitational-wave detections in ground-based interferometers, such as the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO). The form of the gravitational-wave strain depends on the chosen metric theory of gravity. The most accepted theory of gravity is Einstein's theory of general relativity. An important use of gravitational-wave detectors will be to test the theory of general relativity and cosmological conjectures associated with general relativity.

Even within the confines of general relativity, there are conjectures that, while widely believed, have not been absolutely established, and violations could be uncovered by gravitational-wave observations. One such conjecture that is believed to be true in general relativity is the cosmic censorship conjecture, which states roughly that all singularities in spacetime must have an event horizon that conceals the singularity from a distant observer. In the Kerr geometry of a spinning black hole, the event horizon can only exist for mass and spin ratios that satisfy the Kerr bound j ≤ m² in geometric units where G=c=1, where j is the spin of the black hole and m is the mass of the black hole. If the spin of a compact object exceeds the value of its mass squared, then the compact object violates the cosmic censorship conjecture within the context of the Kerr geometry. This limit is often expressed in terms of the Kerr parameter χ = j/m² ≤ 1.

The no-hair theorem is a consequence of the theory of general relativity.
The no-hair theorem states that a regular black hole that has settled down to
its final stationary vacuum state is determined only by its mass, spin and
electric charge. Astrophysical black holes are thought to be electrically
neutral, and therefore would be just categorized by their mass and spin. It is
widely expected that black holes in binary systems will be closely described by
such simple states for most of the inspiral phase. Although the black hole will
be slightly tidally distorted by its binary partner, it has been shown that the
relativistic tidal Love number of a non-rotating black hole will still be zero.
Thus if the post-Newtonian tidal Love number Λ is found to deviate from
zero for a non-rotating object, it can be seen as evidence that the
requirements of the no-hair theorem are not fulfilled, since the black hole is
no longer uniquely defined by its mass, spin and electric charge. If the object
is too massive to be a neutron star (i.e. m_{i} > 3M_{⊙}),
then it is likely to be some exotic object far from the Schwarzschild
solution.

The gravitational-wave strain produced by the inspiral portion of a CBC event depends on the system's parameters, such as component masses, component spins, and component tidal Love numbers. Once a gravitational-wave detection is made by aLIGO, parameter estimation techniques will be used to extract the system's most likely parameters from the raw data. This will be done using full Bayesian analyses that involve techniques such as Markov-chain Monte Carlo and nested sampling. Based on the results of parameter estimation, if at least one of the system's measured component masses indicates that body should nominally be a black hole, then the system can be used to test for apparent violations of the cosmic censorship conjecture and the no-hair theorem.

The ability of aLIGO to test the cosmic censorship conjecture and the no-hair theorem depends on the accuracy to which parameters are measured. For near equal mass binary black hole (BBH) systems, aLIGO will be able to detect the smallest violations of cosmic censorship and the no-hair theorem when the gravitational waveform includes corrections to the amplitude beyond the leading order. Including spin corrections in the amplitude of the waveform also leads to immense improvement in the ability of aLIGO to detect violations of the cosmic censorship conjecture. The higher order amplitude corrections work to break parameter degeneracies and improve overall parameter measurability, which in turn leads to more accurate testing of general relativity.