Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics
Abstract
The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms capable of handling generic metrics are needed for studies of both standard (Schwarzschild and Kerr metrics) and nonstandard (e.g., Schwarzschild metric plus nonclassical perturbations or multiple black hole metrics) spacetimes. The most commonly employed explicit numerical schemes (e.g., Runge–Kutta) are incapable of producing highly accurate results at critical points, e.g., in the regions close to the event horizon where gravity causes extreme curvature of the spacetime, at an acceptable computational cost. In this work we describe a generalized algorithm for the numerical integration of time-like (massive particles) and null (photons) geodesics in any given 3 + 1 split spacetime. We introduce a new, exactly energy-conserving implicit integration scheme based on the preservation of the underlying Hamiltonian, and we compare its properties with a standard fourth-order Runge–Kutta explicit scheme and an implicit midpoint scheme. We test the numerical performance of the three schemes against analytic solutions of particle and photon orbits in Schwarzschild and Kerr spacetimes. We additionally prove the versatility of our framework in handling more exotic metrics,more »
- Authors:
-
- KU Leuven (Belgium)
- Princeton Univ., NJ (United States)
- Columbia Univ., New York, NY (United States)
- Publication Date:
- Research Org.:
- Columbia Univ., New York, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1542035
- Grant/Contract Number:
- SC0016542
- Resource Type:
- Accepted Manuscript
- Journal Name:
- The Astrophysical Journal. Supplement Series (Online)
- Additional Journal Information:
- Journal Name: The Astrophysical Journal. Supplement Series (Online); Journal Volume: 237; Journal Issue: 1; Journal ID: ISSN 1538-4365
- Publisher:
- American Astronomical Society/IOP
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; gravitation; methods: numerical; relativistic processes; stars: black holes; stars: imaging
Citation Formats
Bacchini, F., Ripperda, B., Chen, A. Y., and Sironi, L. Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics. United States: N. p., 2018.
Web. doi:10.3847/1538-4365/aac9ca.
Bacchini, F., Ripperda, B., Chen, A. Y., & Sironi, L. Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics. United States. https://doi.org/10.3847/1538-4365/aac9ca
Bacchini, F., Ripperda, B., Chen, A. Y., and Sironi, L. Tue .
"Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics". United States. https://doi.org/10.3847/1538-4365/aac9ca. https://www.osti.gov/servlets/purl/1542035.
@article{osti_1542035,
title = {Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics},
author = {Bacchini, F. and Ripperda, B. and Chen, A. Y. and Sironi, L.},
abstractNote = {The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms capable of handling generic metrics are needed for studies of both standard (Schwarzschild and Kerr metrics) and nonstandard (e.g., Schwarzschild metric plus nonclassical perturbations or multiple black hole metrics) spacetimes. The most commonly employed explicit numerical schemes (e.g., Runge–Kutta) are incapable of producing highly accurate results at critical points, e.g., in the regions close to the event horizon where gravity causes extreme curvature of the spacetime, at an acceptable computational cost. In this work we describe a generalized algorithm for the numerical integration of time-like (massive particles) and null (photons) geodesics in any given 3 + 1 split spacetime. We introduce a new, exactly energy-conserving implicit integration scheme based on the preservation of the underlying Hamiltonian, and we compare its properties with a standard fourth-order Runge–Kutta explicit scheme and an implicit midpoint scheme. We test the numerical performance of the three schemes against analytic solutions of particle and photon orbits in Schwarzschild and Kerr spacetimes. We additionally prove the versatility of our framework in handling more exotic metrics, such as Morris–Thorne wormholes and quantum-perturbed Schwarzschild black holes. The generalized method is also discussed in the perspective of future extensions to more complex particle dynamics, e.g., the addition of the Lorentz force acting on charged particles, which allows for test particle diagnostics in GRMHD simulations.},
doi = {10.3847/1538-4365/aac9ca},
journal = {The Astrophysical Journal. Supplement Series (Online)},
number = 1,
volume = 237,
place = {United States},
year = {Tue Jul 03 00:00:00 EDT 2018},
month = {Tue Jul 03 00:00:00 EDT 2018}
}
Web of Science
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Works referencing / citing this record:
Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD
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