GRDzhadzha: A code for evolving relativistic matter on analytic metric backgrounds

Abstract

Strong gravity environments such as those around black holes provide us with unique opportunities to study questions in fundamental physics (see e.g Barack et al., 2019;Barausse et al., 2015;Bertone et al., 2020;Macedo et al., 2013), such as the existence and properties of dark matter and dark energy. Characterising the behaviour of new fields and other types of matter in highly relativistic environments usually necessitates numerical simulations unless one imposes significant symmetries. Therefore we need to turn to numerical methods to study the dynamics and evolution of the complex systems of black holes and other compact objects in different environments, using numerical relativity (NR). These methods allow us to split the four-dimensional Einstein equations into three-dimensional spatial hypersurfaces and a time-like direction. Then if a solution is known at the initial spatial hypersurface, it can be numerically evolved in time, where an analytic solution no longer exists. Whilst the tools of NR provide the most complete (i.e., approximation free) method for evolving matter in such environments, in many cases of interest, the density of the matter components is negligible in comparison to the curvature scales of the background spacetime metric (Clough, 2021). In such cases it is a reasonable approximation to neglect the backreaction of the matter environment onto the metric and treat it as fixed (assuming the background itself is stationary or otherwise has an analytic form).