Nonlinear Dynamics of Quadratic Gravity in Spherical Symmetry

TL;DR

This paper demonstrates the first stable numerical evolution of quadratic gravity in spherical symmetry, confirming the feasibility of simulating higher-derivative gravitational theories.

Contribution

It introduces a novel stable numerical method for quadratic gravity using harmonic gauge, the Cartoon method, and order reduction, enabling evolution of complex gravitational systems.

Findings

Numerical stability confirmed for flat-space initial data.

Stable evolution demonstrated for black-hole initial data.

Proof-of-principle for higher-derivative gravity simulations.

Abstract

We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (Quadratic Gravity) in the spherically-symmetric sector. The formulation relies on (i) harmonic gauge to cast the evolution system into quasi-linear form (ii) the Cartoon method to reduce to spherical symmetry in keeping with harmonic gauge, and (iii) order-reduction to 1st-order (in time) by means of introducing auxiliary variables. Well-posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. Our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.