Nonlinear dynamics of quadratic gravity in spherical symmetry

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) the harmonic gauge to cast the evolution system into quasilinear form (ii) the Cartoon method to reduce to spherical symimetry in keeping with the harmonic gauge, and (iii) order reduction to first order (in time) by means of introducing auxiliary variables. The 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.

Automated summary

This study presents the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory in the spherically-symmetric sector, confirming the well posedness of the respective initial-value problem through evolving randomly perturbed flat-space and black-hole initial data. It serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.