Nonlinear studies of modifications to general relativity: Comparing different approaches

TL;DR

This paper compares two approximate methods for studying nonlinear modifications to general relativity, assessing their accuracy and applicability in modeling black hole phenomena relevant to gravitational wave observations.

Contribution

It evaluates the effectiveness of perturbative and dynamical field approaches in nonlinear gravity theories using Einstein-scalar-Gauss-Bonnet gravity as a benchmark.

Findings

Order-by-order approach fails for significant deviations from GR.

Dynamical field approach yields consistent solutions with proper timescale management.

Comparison informs the reliability of approximate methods for gravitational wave data analysis.

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.