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Abstract General relativity, as a diffeomorphism-invariant theory, allows the description of physical phenomena in a wide variety of coordinate systems. In the presence of boundaries, such as event horizons and null infinity, time coordinates must be carefully adapted to the global causal structure of spacetime to ensure a computationally efficient description. Horizon-penetrating time is used to describe the dynamics of infalling matter and radiation across the event horizon, while hyperboloidal time is used to study the propagation of radiation toward the idealized observer at null infinity. In this paper, we explore the historical and mathematical connection between horizon-penetrating and hyperboloidal time coordinates, arguing that both classes of coordinates are simply regular choices of time across null horizons. We review the height-function formalism in stationary spacetimes, providing examples that may be useful in computations, such as source-adapted foliations or Fefferman–Graham–Bondi coordinates near null infinity. We discuss bridges connecting the boundaries of spacetime through a time hypersurface across null horizons, including the event horizon, null infinity, and the cosmological horizon.
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Toward General Relativistic Magnetohydrodynamics Simulations in Stationary Nonvacuum Spacetimes
Abstract Accretion of magnetized gas on compact astrophysical objects such as black holes (BHs) 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 BH in general relativity (GR). The simulations have revealed important clues to the physics of accretion flows 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*. The GRMHD simulations require the spacetime metric to be given in horizon-penetrating coordinates such that all metric coefficients are regular at the event horizon. Only a few metrics, notably the Kerr metric and its electrically charged spinning analog, the Kerr–Newman metric, are currently 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.
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- Award ID(s):
- 1743747
- PAR ID:
- 10468230
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal Letters
- Volume:
- 956
- Issue:
- 1
- ISSN:
- 2041-8205
- Format(s):
- Medium: X Size: Article No. L11
- Size(s):
- Article No. L11
- Sponsoring Org:
- National Science Foundation
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