Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics

Bacchini, F.; Ripperda, B.; Chen, A. Y.; Sironi, L.

doi:10.3847/1538-4365/aac9ca

Title: Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics

Journal Article · Tue Jul 03 00:00:00 EDT 2018 · The Astrophysical Journal. Supplement Series (Online)

DOI:https://doi.org/10.3847/1538-4365/aac9ca· OSTI ID:1542035

^[1];

^[2]; Sironi, L. ^[3]

KU Leuven (Belgium)
Princeton Univ., NJ (United States)
Columbia Univ., New York, NY (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: SC0016542

OSTI ID:: 1542035

Journal Information:: The Astrophysical Journal. Supplement Series (Online), Vol. 237, Issue 1; ISSN 1538-4365

Publisher:: American Astronomical Society/IOPCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 29 works

Citation information provided by
Web of Science

References (64)

Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code harmrad with M1 closure McKinney, Jonathan C.; Tchekhovskoy, Alexander; Sadowski, Aleksander Monthly Notices of the Royal Astronomical Society, Vol. 441, Issue 4 https://doi.org/10.1093/mnras/stu762	journal	May 2014
GeodesicViewer – A tool for exploring geodesics in the theory of relativity Müller, Thomas; Grave, Frank Computer Physics Communications, Vol. 181, Issue 2 https://doi.org/10.1016/j.cpc.2009.10.010	journal	February 2010
Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity Morris, Michael S.; Thorne, Kip S. American Journal of Physics, Vol. 56, Issue 5 https://doi.org/10.1119/1.15620	journal	May 1988
3+1 Formalism in General Relativity Gourgoulhon, Eric Lecture Notes in Physics https://doi.org/10.1007/978-3-642-24525-1	book	February 2012
A Comprehensive Comparison of Relativistic Particle Integrators Ripperda, B.; Bacchini, F.; Teunissen, J. The Astrophysical Journal Supplement Series, Vol. 235, Issue 1 https://doi.org/10.3847/1538-4365/aab114	journal	March 2018
Understanding Modern Molecular Dynamics: Techniques and Applications Tuckerman, Mark E.; Martyna, Glenn J. The Journal of Physical Chemistry B, Vol. 104, Issue 2 https://doi.org/10.1021/jp992433y	journal	January 2000
Spectra of black hole accretion models of ultraluminous X-ray sources Narayan, Ramesh; Sa̧dowski, Aleksander; Soria, Roberto Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 3 https://doi.org/10.1093/mnras/stx1027	journal	April 2017
Simulations of relativistic collisionless shocks: shock structure and particle acceleration Spitkovsky, Anatoly ASTROPHYSICAL SOURCES OF HIGH ENERGY PARTICLES AND RADIATION, AIP Conference Proceedings https://doi.org/10.1063/1.2141897	conference	January 2005
RAPTOR: I. Time-dependent radiative transfer in arbitrary spacetimes★ Bronzwaer, T.; Davelaar, J.; Younsi, Z. Astronomy & Astrophysics, Vol. 613 https://doi.org/10.1051/0004-6361/201732149	journal	May 2018
ipole – semi-analytic scheme for relativistic polarized radiative transport Mościbrodzka, M.; Gammie, C. F. Monthly Notices of the Royal Astronomical Society, Vol. 475, Issue 1 https://doi.org/10.1093/mnras/stx3162	journal	December 2017
Viewing the Shadow of the Black Hole at the Galactic Center Falcke, Heino; Melia, Fulvio; Agol, Eric The Astrophysical Journal, Vol. 528, Issue 1 https://doi.org/10.1086/312423	journal	January 2000
General relativistic radiative transfer code in rotating black hole space–time: ARTIST Takahashi, Rohta; Umemura, Masayuki Monthly Notices of the Royal Astronomical Society, Vol. 464, Issue 4 https://doi.org/10.1093/mnras/stw2479	journal	October 2016
Beyond the event horizon or altogether without it? Lobanov, Andrei Nature Astronomy, Vol. 1, Issue 3 https://doi.org/10.1038/s41550-017-0069	journal	March 2017
GYOTO: a new general relativistic ray-tracing code Vincent, F. H.; Paumard, T.; Gourgoulhon, E. Classical and Quantum Gravity, Vol. 28, Issue 22 https://doi.org/10.1088/0264-9381/28/22/225011	journal	October 2011
The Mathematical Theory of Black Holes Chandrasekhar, S. General Relativity and Gravitation https://doi.org/10.1007/978-94-009-6469-3_2	book	January 1984
Modelling the black hole silhouette in Sagittarius A* with ion tori Straub, O.; Vincent, F. H.; Abramowicz, M. A. Astronomy & Astrophysics, Vol. 543 https://doi.org/10.1051/0004-6361/201219209	journal	July 2012
Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D Ripperda, B.; Porth, O.; Xia, C. Monthly Notices of the Royal Astronomical Society https://doi.org/10.1093/mnras/stx379	journal	February 2017
Higher order explicit symmetric integrators for inseparable forms of coordinates and momenta Liu, Lei; Wu, Xin; Huang, Guoqing Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 2 https://doi.org/10.1093/mnras/stw807	journal	April 2016
The black hole accretion code Porth, Oliver; Olivares, Hector; Mizuno, Yosuke Computational Astrophysics and Cosmology, Vol. 4, Issue 1 https://doi.org/10.1186/s40668-017-0020-2	journal	May 2017
An Extension of the Athena++ code Framework for Grmhd Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport White, Christopher J.; Stone, James M.; Gammie, Charles F. The Astrophysical Journal Supplement Series, Vol. 225, Issue 2 https://doi.org/10.3847/0067-0049/225/2/22	journal	August 2016
Particle acceleration and energy conservation in particle in cell simulations Lapenta, Giovanni; Markidis, Stefano Physics of Plasmas, Vol. 18, Issue 7 https://doi.org/10.1063/1.3602216	journal	July 2011
Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling Akiyama, Kazunori; Kuramochi, Kazuki; Ikeda, Shiro The Astrophysical Journal, Vol. 838, Issue 1 https://doi.org/10.3847/1538-4357/aa6305	journal	March 2017
Why is Boris algorithm so good? Qin, Hong; Zhang, Shuangxi; Xiao, Jianyuan Physics of Plasmas, Vol. 20, Issue 8 https://doi.org/10.1063/1.4818428	journal	August 2013
Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87 Doeleman, S. S.; Fish, V. L.; Schenck, D. E. Science, Vol. 338, Issue 6105 https://doi.org/10.1126/science.1224768	journal	September 2012
Energy conserving schemes for the simulation of musical instrument contact dynamics Chatziioannou, Vasileios; van Walstijn, Maarten Journal of Sound and Vibration, Vol. 339 https://doi.org/10.1016/j.jsv.2014.11.017	journal	March 2015
Studying null and time-like geodesics in the classroom Müller, Thomas; Frauendiener, Jörg European Journal of Physics, Vol. 32, Issue 3 https://doi.org/10.1088/0143-0807/32/3/011	journal	March 2011
Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields Higuera, A. V.; Cary, J. R. Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4979989	journal	May 2017
Observable Emission Features of Black Hole GRMHD Jets on Event Horizon Scales Pu, Hung-Yi; Wu, Kinwah; Younsi, Ziri The Astrophysical Journal, Vol. 845, Issue 2 https://doi.org/10.3847/1538-4357/aa8136	journal	August 2017
Escape of photons from two fixed extreme Reissner-Nordström black holes Alonso, Daniel; Ruiz, Antonia; Sánchez-Hernández, Manuel Physical Review D, Vol. 78, Issue 10 https://doi.org/10.1103/PhysRevD.78.104024	journal	November 2008
A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars Bauböck, Michi; Psaltis, Dimitrios; Özel, Feryal The Astrophysical Journal, Vol. 753, Issue 2 https://doi.org/10.1088/0004-637X/753/2/175	journal	June 2012
An Improved Distance and mass Estimate for sgr a* from a Multistar Orbit Analysis Boehle, A.; Ghez, A. M.; Schödel, R. The Astrophysical Journal, Vol. 830, Issue 1 https://doi.org/10.3847/0004-637X/830/1/17	journal	October 2016
Photon Rings Around kerr and Kerr-Like Black Holes Johannsen, Tim The Astrophysical Journal, Vol. 777, Issue 2 https://doi.org/10.1088/0004-637X/777/2/170	journal	October 2013
Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime Johannsen, Tim; Psaltis, Dimitrios The Astrophysical Journal, Vol. 716, Issue 1 https://doi.org/10.1088/0004-637X/716/1/187	journal	May 2010
Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability Johannsen, Tim; Psaltis, Dimitrios The Astrophysical Journal, Vol. 726, Issue 1 https://doi.org/10.1088/0004-637X/726/1/11	journal	December 2010
Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics Kerr, Roy P. Physical Review Letters, Vol. 11, Issue 5 https://doi.org/10.1103/PhysRevLett.11.237	journal	September 1963
A periodic table for black hole orbits Levin, Janna; Perez-Giz, Gabe Physical Review D, Vol. 77, Issue 10 https://doi.org/10.1103/PhysRevD.77.103005	journal	May 2008
Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole Müller, Thomas Physical Review D, Vol. 77, Issue 12 https://doi.org/10.1103/PhysRevD.77.124042	journal	June 2008
A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes Psaltis, Dimitrios; Johannsen, Tim The Astrophysical Journal, Vol. 745, Issue 1 https://doi.org/10.1088/0004-637X/745/1/1	journal	December 2011
A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE Psaltis, Dimitrios; Wex, Norbert; Kramer, Michael The Astrophysical Journal, Vol. 818, Issue 2 https://doi.org/10.3847/0004-637X/818/2/121	journal	February 2016
`ODYSSEY` : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri The Astrophysical Journal, Vol. 820, Issue 2 https://doi.org/10.3847/0004-637X/820/2/105	journal	March 2016
Stability of a Schwarzschild Singularity Regge, Tullio; Wheeler, John A. Physical Review, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRev.108.1063	journal	November 1957
Symmetric integrator for nonintegrable Hamiltonian relativistic systems Seyrich, Jonathan; Lukes-Gerakopoulos, Georgios Physical Review D, Vol. 86, Issue 12 https://doi.org/10.1103/PhysRevD.86.124013	journal	December 2012
Spherical Photon Orbits Around a Kerr Black Hole Teo, Edward General Relativity and Gravitation, Vol. 35, Issue 11 https://doi.org/10.1023/A:1026286607562	journal	November 2003
Astrophysical imaging of Kerr black holes with scalar hair Vincent, F. H.; Gourgoulhon, E.; Herdeiro, C. Physical Review D, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevD.94.084045	journal	October 2016
Shadows of Bonnor black dihole by chaotic lensing Wang, Mingzhi; Chen, Songbai; Jing, Jiliang Physical Review D, Vol. 97, Issue 6 https://doi.org/10.1103/PhysRevD.97.064029	journal	March 2018
New method for shadow calculations: Application to parametrized axisymmetric black holes Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano Physical Review D, Vol. 94, Issue 8 https://doi.org/10.1103/PhysRevD.94.084025	journal	October 2016
Understanding Modern Molecular Dynamics: Techniques and Applications Tuckerman, Mark E.; Martyna, Glenn J. The Journal of Physical Chemistry B, Vol. 105, Issue 31 https://doi.org/10.1021/jp011879n	journal	July 2001
Studying null and time-like geodesics in the classroom Müller, Thomas; Frauendiener, Jörg arXiv https://doi.org/10.48550/arxiv.1105.0109	text	January 2011
GYOTO: a new general relativistic ray-tracing code Vincent, Frederic H.; Paumard, Thibaut; Gourgoulhon, Eric arXiv https://doi.org/10.48550/arxiv.1109.4769	text	January 2011
A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems Seyrich, Jonathan; Lukes-Gerakopoulos, Georgios arXiv https://doi.org/10.48550/arxiv.1207.3175	text	January 2012
Jet Launching Structure Resolved Near the Supermassive Black Hole in M87 Doeleman, Sheperd S.; Fish, Vincent L.; Schenck, David E. arXiv https://doi.org/10.48550/arxiv.1210.6132	text	January 2012
Energy conserving schemes for the simulation of musical instrument contact dynamics Chatziioannou, Vasileios; van Walstijn, Maarten arXiv https://doi.org/10.48550/arxiv.1501.01493	text	January 2015
Photon Rings around Kerr and Kerr-like Black Holes Johannsen, Tim arXiv https://doi.org/10.48550/arxiv.1501.02814	text	January 2015
A Quantitative Test of the No-Hair Theorem with Sgr A* using stars, pulsars, and the Event Horizon Telescope Psaltis, Dimitrios; Wex, Norbert; Kramer, Michael arXiv https://doi.org/10.48550/arxiv.1510.00394	text	January 2015
An Extension of the Athena++ Code Framework for GRMHD Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport White, Christopher J.; Stone, James M.; Gammie, Charles F. arXiv https://doi.org/10.48550/arxiv.1511.00943	text	January 2015
Odyssey: A Public GPU-Based Code for General-Relativistic Radiative Transfer in Kerr Spacetime Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri arXiv https://doi.org/10.48550/arxiv.1601.02063	text	January 2016
A new method for shadow calculations: application to parameterised axisymmetric black holes Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano arXiv https://doi.org/10.48550/arxiv.1607.05767	text	January 2016
Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D Ripperda, Bart; Porth, Oliver; Xia, Chun arXiv https://doi.org/10.48550/arxiv.1611.09966	text	January 2016
Observable Emission Features of Black Hole GRMHD Jets on Event Horizon Scales Pu, Hung-Yi; Wu, Kinwah; Younsi, Ziri arXiv https://doi.org/10.48550/arxiv.1707.07023	text	January 2017
Shadows of Bonnor black dihole by chaotic lensing Wang, Mingzhi; Chen, Songbai; Jing, Jiliang arXiv https://doi.org/10.48550/arxiv.1710.07172	text	January 2017
RAPTOR I: Time-dependent radiative transfer in arbitrary spacetimes Bronzwaer, Thomas; Davelaar, Jordy; Younsi, Ziri arXiv https://doi.org/10.48550/arxiv.1801.10452	text	January 2018
Viewing the Shadow of the Black Hole at the Galactic Center Falcke, Heino; Melia, Fulvio; Agol, Eric arXiv https://doi.org/10.48550/arxiv.astro-ph/9912263	text	January 1999
Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling Akiyama, Kazunori; Kuramochi, Kazuki; Ikeda, Shiro arXiv https://doi.org/10.48550/arxiv.1702.07361	text	January 2017
A comprehensive comparison of relativistic particle integrators Ripperda, Bart; Bacchini, Fabio; Teunissen, Jannis arXiv https://doi.org/10.48550/arxiv.1710.09164	text	January 2017

Cited By (9)

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD Bacchini, F.; Ripperda, B.; Porth, O. The Astrophysical Journal Supplement Series, Vol. 240, Issue 2 https://doi.org/10.3847/1538-4365/aafcb3	journal	February 2019
General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations Ripperda, B.; Bacchini, F.; Porth, O. The Astrophysical Journal Supplement Series, Vol. 244, Issue 1 https://doi.org/10.3847/1538-4365/ab3922	journal	September 2019
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project Porth, Oliver; Chatterjee, Koushik; Narayan, Ramesh The Astrophysical Journal Supplement Series, Vol. 243, Issue 2 https://doi.org/10.3847/1538-4365/ab29fd	journal	August 2019
A Novel Energy-conserving Scheme for Eight-dimensional Hamiltonian Problems Hu, Shiyang; Wu, Xin; Huang, Guoqing The Astrophysical Journal, Vol. 887, Issue 2 https://doi.org/10.3847/1538-4357/ab5061	journal	December 2019
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project Porth, Oliver; Chatterjee, Koushik; Narayan, Ramesh Maryland Shared Open Access Repository https://doi.org/10.13016/m2htjg-wbul	collection	January 2019
Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD Bacchini, Fabio; Ripperda, Bart; Porth, Oliver arXiv https://doi.org/10.48550/arxiv.1810.00842	text	January 2018
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project Porth, Oliver; Chatterjee, Koushik; Narayan, Ramesh arXiv https://doi.org/10.48550/arxiv.1904.04923	text	January 2019
Numerical methods for General Relativistic particles Bacchini, Fabio; Ripperda, Bart; Sironi, Lorenzo arXiv https://doi.org/10.48550/arxiv.1810.01153	text	January 2018
Structure preserving algorithms for simulation of linearly damped acoustic systems Chatziioannou, Vasileios arXiv https://doi.org/10.48550/arxiv.2008.09479	text	January 2020

Similar Records

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD

Journal Article · Fri Feb 15 00:00:00 EST 2019 · The Astrophysical Journal. Supplement Series (Online) · OSTI ID:1542035

Bacchini, F.; Ripperda, B.; Porth, O.; +1 more

Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields · OSTI ID:1542035

Canizares, Priscilla; Sopuerta, Carlos F; Jaramillo, Jose Luis

Spacetime completeness of non-singular black holes in conformal gravity

Journal Article · Mon May 01 00:00:00 EDT 2017 · Journal of Cosmology and Astroparticle Physics · OSTI ID:1542035

Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
gravitation
methods: numerical
relativistic processes
stars: black holes
stars: imaging

Title: Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. I. Time-like and Null Geodesics

Citation Formats

References (64)

Cited By (9)

Similar Records

Related Subjects