34 research outputs found
Numerical Relativity Beyond General Relativity
Einstein’s theory of general relativity has passed all precision tests to date. At some length scale, however, general relativity (GR) must break down and be reconciled with quantum mechanics in a quantum theory of gravity (a beyond-GR theory). Binary black hole mergers probe the non-linear, highly dynamical regime of gravity, and gravitational waves from these systems may contain signatures of such a theory. In this thesis, we seek to make gravitational wave predictions for binary black hole mergers in a beyond-GR theory. These predictions can then be used to perform model-dependent tests of GR with gravitational wave detections.
We make predictions using numerical relativity, the practice of precisely numerically solving the equations governing spacetime. This allows us to probe the behavior of a binary black hole system through full inspiral, merger, and ringdown. We choose to work in dynamical Chern-Simons gravity (dCS), a higher-curvature beyond-GR effective field theory that couples spacetime curvature to a scalar field, and has motivations in string theory and loop quantum gravity. In order to obtain a well-posed initial value formalism, we perturb this theory around GR. We compute the leading-order behavior of the dCS scalar field in a binary black hole merger, as well as the leading-order dCS correction to the spacetime metric and hence gravitational radiation. We produce the first numerical relativity beyond-GR waveforms in a higher-curvature theory of gravity.
This thesis contains additional results, all of which harness the power of numerical relativity to test GR. We compute black hole shadows in dCS gravity, numerically prove the leading-order stability of rotating black holes in dCS gravity, and lay out a formalism for determining the start time of binary black hole ringdown using information from the strong-field region of a binary black hole simulation.</p
Numerical relativity simulation of GW150914 beyond general relativity
We produce the first astrophysically-relevant numerical binary black hole
gravitational waveform in a higher-curvature theory of gravity beyond general
relativity. We simulate a system with parameters consistent with GW150914, the
first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory
with motivations in string theory and loop quantum gravity. We present results
for the leading-order corrections to the merger and ringdown waveforms, as well
as the ringdown quasi-normal mode spectrum. We estimate that such corrections
may be discriminated in detections with signal to noise ratio , with the precise value depending on the dimension of the GR waveform
family used in data analysis.Comment: 7 pages + appendices, 8 figures, Updated to match Phys. D. Rev
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Numerical black hole initial data and shadows in dynamical Chern–Simons gravity
We present a scheme for generating first-order metric perturbation initial data for an arbitrary background and source. We then apply this scheme to derive metric perturbations in order-reduced dynamical Chern–Simons gravity (dCS). In particular, we solve for metric perturbations on a black hole background that are sourced by a first-order dCS scalar field. This gives us the leading-order metric perturbation to the spacetime in dCS gravity. We then use these solutions to compute black hole shadows in the linearly perturbed spacetime by evolving null geodesics. We present a novel scheme to decompose the shape of the shadow into multipoles parametrized by the spin of the background black hole and the perturbation parameter . We find that we can differentiate the presence of a pure Kerr spacetime from a spacetime with a dCS perturbation using the shadow, allowing in part for a null-hypothesis test of general relativity. We then consider these results in the context of the event horizon telescope
On choosing the start time of binary black hole ringdown
The final stage of a binary black hole merger is ringdown, in which the
system is described by a Kerr black hole with quasinormal mode perturbations.
It is far from straightforward to identify the time at which the ringdown
begins. Yet determining this time is important for precision tests of the
general theory of relativity that compare an observed signal with quasinormal
mode descriptions of the ringdown, such as tests of the no-hair theorem. We
present an algorithmic method to analyze the choice of ringdown start time in
the observed waveform. This method is based on determining how close the strong
field is to a Kerr black hole (Kerrness). Using numerical relativity
simulations, we characterize the Kerrness of the strong-field region close to
the black hole using a set of local, gauge-invariant geometric and algebraic
conditions that measure local isometry to Kerr. We produce a map that
associates each time in the gravitational waveform with a value of each of
these Kerrness measures; this map is produced by following outgoing null
characteristics from the strong and near-field regions to the wave zone. We
perform this analysis on a numerical relativity simulation with parameters
consistent with GW150914- the first gravitational wave detection. We find that
the choice of ringdown start time of after merger used in the
GW150914 study to test general relativity corresponds to a high dimensionless
perturbation amplitude of in the strong-field
region. This suggests that in higher signal-to-noise detections, one would need
to start analyzing the signal at a later time for studies that depend on the
validity of black hole perturbation theory.Comment: 23+4 pages, 22 figure