Toward General-Relativistic Magnetohydrodynamics Simulations in Stationary Non-Vacuum Spacetimes

TL;DR

This paper develops horizon-penetrating forms of various stationary, axisymmetric metrics to enable general relativistic magnetohydrodynamics simulations of accretion onto spinning, non-vacuum black holes and other objects, extending current capabilities beyond Kerr solutions.

Contribution

It introduces a broad class of horizon-penetrating metrics for stationary, axisymmetric spacetimes, facilitating GRMHD simulations in non-vacuum and non-GR contexts.

Findings

Provides horizon-penetrating forms for many stationary, axisymmetric metrics.

Enables GRMHD simulations of accretion on non-vacuum and non-GR spacetimes.

Extends simulation capabilities beyond Kerr and Kerr-Newman metrics.

Abstract

Accretion of magnetized gas on compact astrophysical objects such as black holes has been successfully modeled using general relativistic magnetohydrodynamic (GRMHD) simulations. These simulations have largely been performed in the Kerr metric, which describes the spacetime of a vacuum and stationary spinning black hole (BH) in general relativity (GR). The simulations have revealed important clues on the physics of accretion and jets near the BH event horizon, and have been used to interpret recent Event Horizon Telescope images of the supermassive BHs, M87$^*$ and Sgr A$^*$. GRMHD simulations require the spacetime metric in horizon-penetrating coordinates such that all metric coefficients are regular at the event horizon. The Kerr metric and its electrically charged spinning analog, the Kerr-Newman metric, are currently the only metrics available in such coordinates. We report here horizon-penetrating forms of a large class of stationary, axisymmetric, spinning metrics. These can be used to carry out GRMHD simulations of accretion on spinning, nonvacuum BHs and non-BHs within GR, as well as accretion on spinning objects described by non-GR metric theories of gravity.