Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c

TL;DR

This paper develops stable numerical methods for evolving black holes in spherical symmetry using hyperboloidal slices, employing generalized BSSN and Z4 formulations coupled with scalar fields, advancing simulations of radiating compact objects.

Contribution

It introduces unconstrained hyperboloidal evolution schemes for black holes in spherical symmetry with new gauge conditions, improving numerical stability and efficiency.

Findings

Achieved stable evolutions of black hole initial data.

Demonstrated the effectiveness of gauge conditions in stability.

Progressed towards efficient simulation of radiating compact objects.

Abstract

We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry already poses nontrivial problems and constitutes an important first step to regularize the resulting singular PDEs. We evolve the Einstein equations in their generalized BSSN and Z4 formulations coupled to a massless self-gravitating scalar field. Stable numerical evolutions are achieved for black hole initial data, and critically rely on the construction of appropriate gauge conditions.