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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Studying the dynamical, nonlinear regime of modified theories of gravity
remains a theoretical challenge that limits our ability to test general
relativity. Here we consider two generally applicable, but approximate methods
for treating modifications to full general relativity that have been used to
study binary black hole mergers and other phenomena in this regime, and compare
solutions obtained by them to those from solving the full equations of motion.
The first method evolves corrections to general relativity order by order in a
perturbative expansion, while the second method introduces extra dynamical
fields in such a way that strong hyperbolicity is recovered. We use
shift-symmetric Einstein-scalar-Gauss-Bonnet gravity as a benchmark theory to
illustrate the differences between these methods for several spacetimes of
physical interest. We study the formation of scalar hair about initially
non-spinning black holes, the collision of black holes with scalar charge, and
the inspiral and merger of binary black holes. By directly comparing
predictions, we assess the extent to which those from the approximate
treatments can be meaningfully confronted with gravitational wave observations.
We find that the order-by-order approach cannot faithfully track the solutions
when the corrections to general relativity are non-negligible. The second
approach, however, can provide consistent solutions, provided the ad-hoc
timescale over which the dynamical fields are driven to their target values is
made short compared to the physical timescales.
