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

doi:https://doi.org/10.3847/1538-4365/aac9ca

Title: 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 »« less

Authors:

^[1];

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

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

Publication Date:: 2018-07-03

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:: Journal Article: Accepted Manuscript

Journal Name:: The Astrophysical Journal. Supplement Series (Online)

Additional Journal Information:: 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.

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                    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

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                    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.

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@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},

  url          = {https://www.osti.gov/biblio/1542035},
  journal      = {The Astrophysical Journal. Supplement Series (Online)},

  issn         = {1538-4365},

  number       = 1,

  volume       = 237,

  place        = {United States},

  year         = {2018},

  month        = {7}

}

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https://doi.org/10.3847/1538-4365/aac9ca

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Works referenced in this record:

Escape of photons from two fixed extreme Reissner-Nordström black holes
journal, November 2008

Alonso, Daniel; Ruiz, Antonia; Sánchez-Hernández, Manuel
Physical Review D, Vol. 78, Issue 10
https://doi.org/10.1103/physrevd.78.104024

Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code harmrad with M1 closure
journal, May 2014

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

GeodesicViewer – A tool for exploring geodesics in the theory of relativity
journal, February 2010

Müller, Thomas; Grave, Frank
Computer Physics Communications, Vol. 181, Issue 2
https://doi.org/10.1016/j.cpc.2009.10.010

Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity
journal, May 1988

Morris, Michael S.; Thorne, Kip S.
American Journal of Physics, Vol. 56, Issue 5
https://doi.org/10.1119/1.15620

Astrophysical imaging of Kerr black holes with scalar hair
journal, October 2016

Vincent, F. H.; Gourgoulhon, E.; Herdeiro, C.
Physical Review D, Vol. 94, Issue 8
https://doi.org/10.1103/physrevd.94.084045

A Comprehensive Comparison of Relativistic Particle Integrators
journal, March 2018

Ripperda, B.; Bacchini, F.; Teunissen, J.
The Astrophysical Journal Supplement Series, Vol. 235, Issue 1
https://doi.org/10.3847/1538-4365/aab114

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
journal, September 1963

Kerr, Roy P.
Physical Review Letters, Vol. 11, Issue 5
https://doi.org/10.1103/physrevlett.11.237

An Improved Distance and mass Estimate for sgr a* from a Multistar Orbit Analysis
journal, October 2016

Boehle, A.; Ghez, A. M.; Schödel, R.
The Astrophysical Journal, Vol. 830, Issue 1
https://doi.org/10.3847/0004-637x/830/1/17

Understanding Modern Molecular Dynamics: Techniques and Applications
journal, January 2000

Tuckerman, Mark E.; Martyna, Glenn J.
The Journal of Physical Chemistry B, Vol. 104, Issue 2
https://doi.org/10.1021/jp992433y

Stability of a Schwarzschild Singularity
journal, November 1957

Regge, Tullio; Wheeler, John A.
Physical Review, Vol. 108, Issue 4
https://doi.org/10.1103/physrev.108.1063

A periodic table for black hole orbits
journal, May 2008

Levin, Janna; Perez-Giz, Gabe
Physical Review D, Vol. 77, Issue 10
https://doi.org/10.1103/physrevd.77.103005

`ODYSSEY` : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME
journal, March 2016

Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri
The Astrophysical Journal, Vol. 820, Issue 2
https://doi.org/10.3847/0004-637x/820/2/105

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes
journal, December 2011

Psaltis, Dimitrios; Johannsen, Tim
The Astrophysical Journal, Vol. 745, Issue 1
https://doi.org/10.1088/0004-637x/745/1/1

Spectra of black hole accretion models of ultraluminous X-ray sources
journal, April 2017

Narayan, Ramesh; Sa̧dowski, Aleksander; Soria, Roberto
Monthly Notices of the Royal Astronomical Society, Vol. 469, Issue 3
https://doi.org/10.1093/mnras/stx1027

Simulations of relativistic collisionless shocks: shock structure and particle acceleration
conference, January 2005

Spitkovsky, Anatoly
ASTROPHYSICAL SOURCES OF HIGH ENERGY PARTICLES AND RADIATION, AIP Conference Proceedings
https://doi.org/10.1063/1.2141897

RAPTOR: I. Time-dependent radiative transfer in arbitrary spacetimes★
journal, May 2018

Bronzwaer, T.; Davelaar, J.; Younsi, Z.
Astronomy & Astrophysics, Vol. 613
https://doi.org/10.1051/0004-6361/201732149

ipole – semi-analytic scheme for relativistic polarized radiative transport
journal, December 2017

Mościbrodzka, M.; Gammie, C. F.
Monthly Notices of the Royal Astronomical Society, Vol. 475, Issue 1
https://doi.org/10.1093/mnras/stx3162

Viewing the Shadow of the Black Hole at the Galactic Center
journal, January 2000

Falcke, Heino; Melia, Fulvio; Agol, Eric
The Astrophysical Journal, Vol. 528, Issue 1
https://doi.org/10.1086/312423

General relativistic radiative transfer code in rotating black hole space–time: ARTIST
journal, October 2016

Takahashi, Rohta; Umemura, Masayuki
Monthly Notices of the Royal Astronomical Society, Vol. 464, Issue 4
https://doi.org/10.1093/mnras/stw2479

Beyond the event horizon or altogether without it?
journal, March 2017

Lobanov, Andrei
Nature Astronomy, Vol. 1, Issue 3
https://doi.org/10.1038/s41550-017-0069

GYOTO: a new general relativistic ray-tracing code
journal, October 2011

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

Symmetric integrator for nonintegrable Hamiltonian relativistic systems
journal, December 2012

Seyrich, Jonathan; Lukes-Gerakopoulos, Georgios
Physical Review D, Vol. 86, Issue 12
https://doi.org/10.1103/physrevd.86.124013

Modelling the black hole silhouette in Sagittarius A* with ion tori
journal, July 2012

Straub, O.; Vincent, F. H.; Abramowicz, M. A.
Astronomy & Astrophysics, Vol. 543
https://doi.org/10.1051/0004-6361/201219209

Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D
journal, February 2017

Ripperda, B.; Porth, O.; Xia, C.
Monthly Notices of the Royal Astronomical Society
https://doi.org/10.1093/mnras/stx379

Shadows of Bonnor black dihole by chaotic lensing
journal, March 2018

Wang, Mingzhi; Chen, Songbai; Jing, Jiliang
Physical Review D, Vol. 97, Issue 6
https://doi.org/10.1103/physrevd.97.064029

Spherical Photon Orbits Around a Kerr Black Hole
journal, November 2003

Teo, Edward
General Relativity and Gravitation, Vol. 35, Issue 11
https://doi.org/10.1023/a:1026286607562

Higher order explicit symmetric integrators for inseparable forms of coordinates and momenta
journal, April 2016

Liu, Lei; Wu, Xin; Huang, Guoqing
Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 2
https://doi.org/10.1093/mnras/stw807

New method for shadow calculations: Application to parametrized axisymmetric black holes
journal, October 2016

Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano
Physical Review D, Vol. 94, Issue 8
https://doi.org/10.1103/physrevd.94.084025

The black hole accretion code
journal, May 2017

Porth, Oliver; Olivares, Hector; Mizuno, Yosuke
Computational Astrophysics and Cosmology, Vol. 4, Issue 1
https://doi.org/10.1186/s40668-017-0020-2

An Extension of the Athena++ code Framework for Grmhd Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
journal, August 2016

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

Particle acceleration and energy conservation in particle in cell simulations
journal, July 2011

Lapenta, Giovanni; Markidis, Stefano
Physics of Plasmas, Vol. 18, Issue 7
https://doi.org/10.1063/1.3602216

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling
journal, March 2017

Akiyama, Kazunori; Kuramochi, Kazuki; Ikeda, Shiro
The Astrophysical Journal, Vol. 838, Issue 1
https://doi.org/10.3847/1538-4357/aa6305

Why is Boris algorithm so good?
journal, August 2013

Qin, Hong; Zhang, Shuangxi; Xiao, Jianyuan
Physics of Plasmas, Vol. 20, Issue 8
https://doi.org/10.1063/1.4818428

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole
journal, June 2008

Müller, Thomas
Physical Review D, Vol. 77, Issue 12
https://doi.org/10.1103/physrevd.77.124042

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars
journal, June 2012

Bauböck, Michi; Psaltis, Dimitrios; Özel, Feryal
The Astrophysical Journal, Vol. 753, Issue 2
https://doi.org/10.1088/0004-637x/753/2/175

Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87
journal, September 2012

Doeleman, S. S.; Fish, V. L.; Schenck, D. E.
Science, Vol. 338, Issue 6105
https://doi.org/10.1126/science.1224768

Energy conserving schemes for the simulation of musical instrument contact dynamics
journal, March 2015

Chatziioannou, Vasileios; van Walstijn, Maarten
Journal of Sound and Vibration, Vol. 339
https://doi.org/10.1016/j.jsv.2014.11.017

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime
journal, May 2010

Johannsen, Tim; Psaltis, Dimitrios
The Astrophysical Journal, Vol. 716, Issue 1
https://doi.org/10.1088/0004-637x/716/1/187

Studying null and time-like geodesics in the classroom
journal, March 2011

Müller, Thomas; Frauendiener, Jörg
European Journal of Physics, Vol. 32, Issue 3
https://doi.org/10.1088/0143-0807/32/3/011

Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields
journal, May 2017

Higuera, A. V.; Cary, J. R.
Physics of Plasmas, Vol. 24, Issue 5
https://doi.org/10.1063/1.4979989

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE
journal, February 2016

Psaltis, Dimitrios; Wex, Norbert; Kramer, Michael
The Astrophysical Journal, Vol. 818, Issue 2
https://doi.org/10.3847/0004-637x/818/2/121

Observable Emission Features of Black Hole GRMHD Jets on Event Horizon Scales
journal, August 2017

Pu, Hung-Yi; Wu, Kinwah; Younsi, Ziri
The Astrophysical Journal, Vol. 845, Issue 2
https://doi.org/10.3847/1538-4357/aa8136

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability
journal, December 2010

Johannsen, Tim; Psaltis, Dimitrios
The Astrophysical Journal, Vol. 726, Issue 1
https://doi.org/10.1088/0004-637x/726/1/11

Photon Rings Around kerr and Kerr-Like Black Holes
journal, October 2013

Johannsen, Tim
The Astrophysical Journal, Vol. 777, Issue 2
https://doi.org/10.1088/0004-637x/777/2/170

Escape of photons from two fixed extreme Reissner-Nordström black holes
journal, November 2008

Alonso, Daniel; Ruiz, Antonia; Sánchez-Hernández, Manuel
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https://doi.org/10.1103/PhysRevD.78.104024

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journal, June 2012

Bauböck, Michi; Psaltis, Dimitrios; Özel, Feryal
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https://doi.org/10.1088/0004-637X/753/2/175

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journal, October 2016

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The Astrophysical Journal, Vol. 830, Issue 1
https://doi.org/10.3847/0004-637X/830/1/17

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journal, October 2013

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Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime
journal, May 2010

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Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability
journal, December 2010

Johannsen, Tim; Psaltis, Dimitrios
The Astrophysical Journal, Vol. 726, Issue 1
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Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
journal, September 1963

Kerr, Roy P.
Physical Review Letters, Vol. 11, Issue 5
https://doi.org/10.1103/PhysRevLett.11.237

A periodic table for black hole orbits
journal, May 2008

Levin, Janna; Perez-Giz, Gabe
Physical Review D, Vol. 77, Issue 10
https://doi.org/10.1103/PhysRevD.77.103005

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole
journal, June 2008

Müller, Thomas
Physical Review D, Vol. 77, Issue 12
https://doi.org/10.1103/PhysRevD.77.124042

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes
journal, December 2011

Psaltis, Dimitrios; Johannsen, Tim
The Astrophysical Journal, Vol. 745, Issue 1
https://doi.org/10.1088/0004-637X/745/1/1

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE
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Psaltis, Dimitrios; Wex, Norbert; Kramer, Michael
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journal, March 2016

Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri
The Astrophysical Journal, Vol. 820, Issue 2
https://doi.org/10.3847/0004-637X/820/2/105

Stability of a Schwarzschild Singularity
journal, November 1957

Regge, Tullio; Wheeler, John A.
Physical Review, Vol. 108, Issue 4
https://doi.org/10.1103/PhysRev.108.1063

Symmetric integrator for nonintegrable Hamiltonian relativistic systems
journal, December 2012

Seyrich, Jonathan; Lukes-Gerakopoulos, Georgios
Physical Review D, Vol. 86, Issue 12
https://doi.org/10.1103/PhysRevD.86.124013

Spherical Photon Orbits Around a Kerr Black Hole
journal, November 2003

Teo, Edward
General Relativity and Gravitation, Vol. 35, Issue 11
https://doi.org/10.1023/A:1026286607562

Astrophysical imaging of Kerr black holes with scalar hair
journal, October 2016

Vincent, F. H.; Gourgoulhon, E.; Herdeiro, C.
Physical Review D, Vol. 94, Issue 8
https://doi.org/10.1103/PhysRevD.94.084045

Shadows of Bonnor black dihole by chaotic lensing
journal, March 2018

Wang, Mingzhi; Chen, Songbai; Jing, Jiliang
Physical Review D, Vol. 97, Issue 6
https://doi.org/10.1103/PhysRevD.97.064029

New method for shadow calculations: Application to parametrized axisymmetric black holes
journal, October 2016

Younsi, Ziri; Zhidenko, Alexander; Rezzolla, Luciano
Physical Review D, Vol. 94, Issue 8
https://doi.org/10.1103/PhysRevD.94.084025

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

Abstract

Citation Formats

Escape of photons from two fixed extreme Reissner-Nordström black holes journal, November 2008

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Understanding Modern Molecular Dynamics: Techniques and Applications journal, January 2000

Stability of a Schwarzschild Singularity journal, November 1957

A periodic table for black hole orbits journal, May 2008

ODYSSEY : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME journal, March 2016

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes journal, December 2011

Spectra of black hole accretion models of ultraluminous X-ray sources journal, April 2017

Simulations of relativistic collisionless shocks: shock structure and particle acceleration conference, January 2005

RAPTOR: I. Time-dependent radiative transfer in arbitrary spacetimes★ journal, May 2018

ipole – semi-analytic scheme for relativistic polarized radiative transport journal, December 2017

Viewing the Shadow of the Black Hole at the Galactic Center journal, January 2000

General relativistic radiative transfer code in rotating black hole space–time: ARTIST journal, October 2016

Beyond the event horizon or altogether without it? journal, March 2017

GYOTO: a new general relativistic ray-tracing code journal, October 2011

Symmetric integrator for nonintegrable Hamiltonian relativistic systems journal, December 2012

Modelling the black hole silhouette in Sagittarius A* with ion tori journal, July 2012

Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D journal, February 2017

Shadows of Bonnor black dihole by chaotic lensing journal, March 2018

Spherical Photon Orbits Around a Kerr Black Hole journal, November 2003

Higher order explicit symmetric integrators for inseparable forms of coordinates and momenta journal, April 2016

New method for shadow calculations: Application to parametrized axisymmetric black holes journal, October 2016

The black hole accretion code journal, May 2017

An Extension of the Athena++ code Framework for Grmhd Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport journal, August 2016

Particle acceleration and energy conservation in particle in cell simulations journal, July 2011

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling journal, March 2017

Why is Boris algorithm so good? journal, August 2013

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole journal, June 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars journal, June 2012

Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87 journal, September 2012

Energy conserving schemes for the simulation of musical instrument contact dynamics journal, March 2015

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime journal, May 2010

Studying null and time-like geodesics in the classroom journal, March 2011

Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields journal, May 2017

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE journal, February 2016

Observable Emission Features of Black Hole GRMHD Jets on Event Horizon Scales journal, August 2017

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability journal, December 2010

Photon Rings Around kerr and Kerr-Like Black Holes journal, October 2013

Escape of photons from two fixed extreme Reissner-Nordström black holes journal, November 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars journal, June 2012

An Improved Distance and mass Estimate for sgr a* from a Multistar Orbit Analysis journal, October 2016

Photon Rings Around kerr and Kerr-Like Black Holes journal, October 2013

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime journal, May 2010

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability journal, December 2010

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics journal, September 1963

A periodic table for black hole orbits journal, May 2008

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole journal, June 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes journal, December 2011

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE journal, February 2016

ODYSSEY : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME journal, March 2016

Stability of a Schwarzschild Singularity journal, November 1957

Symmetric integrator for nonintegrable Hamiltonian relativistic systems journal, December 2012

Spherical Photon Orbits Around a Kerr Black Hole journal, November 2003

Astrophysical imaging of Kerr black holes with scalar hair journal, October 2016

Shadows of Bonnor black dihole by chaotic lensing journal, March 2018

New method for shadow calculations: Application to parametrized axisymmetric black holes journal, October 2016

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD journal, February 2019

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations journal, September 2019

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project journal, August 2019

A Novel Energy-conserving Scheme for Eight-dimensional Hamiltonian Problems journal, December 2019

Escape of photons from two fixed extreme Reissner-Nordström black holes
journal, November 2008

Three-dimensional general relativistic radiation magnetohydrodynamical simulation of super-Eddington accretion, using a new code harmrad with M1 closure
journal, May 2014

GeodesicViewer – A tool for exploring geodesics in the theory of relativity
journal, February 2010

Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity
journal, May 1988

Astrophysical imaging of Kerr black holes with scalar hair
journal, October 2016

A Comprehensive Comparison of Relativistic Particle Integrators
journal, March 2018

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
journal, September 1963

An Improved Distance and mass Estimate for sgr a* from a Multistar Orbit Analysis
journal, October 2016

Understanding Modern Molecular Dynamics: Techniques and Applications
journal, January 2000

Stability of a Schwarzschild Singularity
journal, November 1957

A periodic table for black hole orbits
journal, May 2008

`ODYSSEY` : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME
journal, March 2016

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes
journal, December 2011

Spectra of black hole accretion models of ultraluminous X-ray sources
journal, April 2017

Simulations of relativistic collisionless shocks: shock structure and particle acceleration
conference, January 2005

RAPTOR: I. Time-dependent radiative transfer in arbitrary spacetimes★
journal, May 2018

ipole – semi-analytic scheme for relativistic polarized radiative transport
journal, December 2017

Viewing the Shadow of the Black Hole at the Galactic Center
journal, January 2000

General relativistic radiative transfer code in rotating black hole space–time: ARTIST
journal, October 2016

Beyond the event horizon or altogether without it?
journal, March 2017

GYOTO: a new general relativistic ray-tracing code
journal, October 2011

Symmetric integrator for nonintegrable Hamiltonian relativistic systems
journal, December 2012

Modelling the black hole silhouette in Sagittarius A* with ion tori
journal, July 2012

Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D
journal, February 2017

Shadows of Bonnor black dihole by chaotic lensing
journal, March 2018

Spherical Photon Orbits Around a Kerr Black Hole
journal, November 2003

Higher order explicit symmetric integrators for inseparable forms of coordinates and momenta
journal, April 2016

New method for shadow calculations: Application to parametrized axisymmetric black holes
journal, October 2016

The black hole accretion code
journal, May 2017

An Extension of the Athena++ code Framework for Grmhd Based on Advanced Riemann Solvers and Staggered-Mesh Constrained Transport
journal, August 2016

Particle acceleration and energy conservation in particle in cell simulations
journal, July 2011

Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope Using Sparse Modeling
journal, March 2017

Why is Boris algorithm so good?
journal, August 2013

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole
journal, June 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars
journal, June 2012

Jet-Launching Structure Resolved Near the Supermassive Black Hole in M87
journal, September 2012

Energy conserving schemes for the simulation of musical instrument contact dynamics
journal, March 2015

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime
journal, May 2010

Studying null and time-like geodesics in the classroom
journal, March 2011

Structure-preserving second-order integration of relativistic charged particle trajectories in electromagnetic fields
journal, May 2017

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE
journal, February 2016

Observable Emission Features of Black Hole GRMHD Jets on Event Horizon Scales
journal, August 2017

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability
journal, December 2010

Photon Rings Around kerr and Kerr-Like Black Holes
journal, October 2013

Escape of photons from two fixed extreme Reissner-Nordström black holes
journal, November 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. ii. Neutron Stars
journal, June 2012

An Improved Distance and mass Estimate for sgr a* from a Multistar Orbit Analysis
journal, October 2016

Photon Rings Around kerr and Kerr-Like Black Holes
journal, October 2013

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. i. Properties of a Quasi-Kerr Spacetime
journal, May 2010

Testing the No-Hair Theorem with Observations in the Electromagnetic Spectrum. iii. Quasi-Periodic Variability
journal, December 2010

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics
journal, September 1963

A periodic table for black hole orbits
journal, May 2008

Einstein rings as a tool for estimating distances and the mass of a Schwarzschild black hole
journal, June 2008

A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. i. Quasi-Kerr Black Holes
journal, December 2011

A QUANTITATIVE TEST OF THE NO-HAIR THEOREM WITH Sgr A* USING STARS, PULSARS, AND THE EVENT HORIZON TELESCOPE
journal, February 2016

`ODYSSEY` : A PUBLIC GPU-BASED CODE FOR GENERAL RELATIVISTIC RADIATIVE TRANSFER IN KERR SPACETIME
journal, March 2016

Stability of a Schwarzschild Singularity
journal, November 1957

Symmetric integrator for nonintegrable Hamiltonian relativistic systems
journal, December 2012

Spherical Photon Orbits Around a Kerr Black Hole
journal, November 2003

Astrophysical imaging of Kerr black holes with scalar hair
journal, October 2016

Shadows of Bonnor black dihole by chaotic lensing
journal, March 2018

New method for shadow calculations: Application to parametrized axisymmetric black holes
journal, October 2016

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD
journal, February 2019

General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations
journal, September 2019

The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project
journal, August 2019

A Novel Energy-conserving Scheme for Eight-dimensional Hamiltonian Problems
journal, December 2019