A Tetrad-First Approach to Robust Numerical Algorithms in General Relativity Article Swipe
Jonathan Gorard
,
Ammar Hakim
,
James Juno
,
Jason TenBarge
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.02549
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.02549
General relativistic Riemann solvers are typically complex, fragile and unwieldy, at least in comparison to their special relativistic counterparts. In this paper, we present a new high-resolution shock-capturing algorithm on curved spacetimes that employs a local coordinate transformation at each inter-cell boundary, transforming all primitive and conservative variables into a locally flat spacetime coordinate basis (i.e., the tetrad basis), generalizing previous approaches developed for relativistic hydrodynamics. This algorithm enables one to employ a purely special relativistic Riemann solver, combined with an appropriate post-hoc flux correction step, irrespective of the geometry of the underlying Lorentzian manifold. We perform a systematic validation of the algorithm using the Gkeyll simulation framework for both general relativistic electromagnetism and general relativistic hydrodynamics, highlighting the algorithm's superior convergence and stability properties in each case when compared against standard analytical solutions for black hole magnetosphere and ultra-relativistic black hole accretion problems. However, as an illustration of the generality and practicality of the algorithm, we also apply it to more astrophysically realistic magnetosphere and fluid accretion problems in the limit of high black hole spin, for which standard general relativistic Riemann solvers are often too unstable to produce useful solutions.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2410.02549
- https://arxiv.org/pdf/2410.02549
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4403884059
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4403884059Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2410.02549Digital Object Identifier
- Title
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A Tetrad-First Approach to Robust Numerical Algorithms in General RelativityWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-10-03Full publication date if available
- Authors
-
Jonathan Gorard, Ammar Hakim, James Juno, Jason TenBargeList of authors in order
- Landing page
-
https://arxiv.org/abs/2410.02549Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2410.02549Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2410.02549Direct OA link when available
- Concepts
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Tetrad, Algorithm, Theory of relativity, Computer science, Mathematics, Theoretical physics, Physics, Mathematical physicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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