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Leonard E Parker

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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.

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

Advanced LIGO's ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections Madeline Wade, Jolien D. E. Creighton, Evan Ochsner, Alex B. Nielsen (Paper)
No-Hair Violation

The smallest violation of the black hole no-hair theorem, as measured by a parameter describing the tidal deformability Λ, that can be measured by the Advanced LIGO detector using only the dominant waveform harmonic (blue ellipse). The vertical axis is the symmetric mass ratio η. Credit: M. Wade

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. mi > 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.

Cosmic-Censorship and No-Hair Violation

The ellipses shown in this figure are 1-σ error ellipses in the symmetric mass ratio and symmetric spin plane (top plots) or the symmetric mass ratio and tidal parameter plane (bottom plots). The symmetric mass ratio is defined as η=m1m2/(m1+2)², and the symmetric spin is defined as χs=(χ12)/2, where χi is the Kerr parameter for the ith body in the binary. The tidal parameter Λ is a measure of the equation of state and should be zero for Kerr black holes. The grayed out areas in each plot indicates unphysical values of the symmetric mass ratio. The region bounded by the vertical lines in the top plots indicates the region of parameter space that is consistent with the cosmic censorship conjecture. The vertical line in the bottom plots indicates the line for which the no-hair theorem is not violated. The blue ellipses have true parameters marked by the blue x and represent the error ellipse for the minimum detectable violation of cosmic censorship (top plots) and the no-hair theorem (bottom plots). The smallest violations that could be detected by aLIGO are given as inlays in each plot. The red ellipses have true parameters marked by the red x and are calculated for the same fiducial values across each row of plots. The plots in the left column use only the leading order correction in the amplitude of the gravitational waveform. The plots in the right column use waveforms that include higher order corrections in the amplitude. This figure shows how aLIGO will be able to detect smaller violations of cosmic censorship and the no-hair theorem for near equal mass BBH systems when higher order corrections are included in the amplitude of the waveform. Credit: M. Wade.


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