Numerical black hole initial data and shadows in dynamical Chern-Simons gravity

TL;DR

This paper develops a method to generate initial data for metric perturbations in dynamical Chern-Simons gravity, computes black hole shadows affected by these perturbations, and proposes a way to test deviations from general relativity using observational data.

Contribution

It introduces a scheme for initial data generation in dCS gravity, computes black hole shadows in perturbed spacetimes, and suggests observational tests to distinguish dCS from Kerr black holes.

Findings

Black hole shadows can be decomposed into multipoles influenced by spin and perturbation.

Shadows in dCS gravity differ from Kerr, enabling null-hypothesis tests of GR.

The method can inform analysis of Event Horizon Telescope data.

Abstract

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 $\varepsilon^2$. 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.