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

Journal Article · · The Astrophysical Journal. Supplement Series (Online)
 [1];  [2];  [3];  [4]
  1. KU Leuven (Belgium); DOE/OSTI
  2. KU Leuven (Belgium)
  3. Princeton Univ., NJ (United States)
  4. Columbia Univ., New York, NY (United States)
+ Show Author Affiliations
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.
Research Organization:
Columbia Univ., New York, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Grant/Contract Number:
SC0016542
OSTI ID:
1542035
Journal Information:
The Astrophysical Journal. Supplement Series (Online), Journal Name: The Astrophysical Journal. Supplement Series (Online) Journal Issue: 1 Vol. 237; ISSN 1538-4365
Publisher:
American Astronomical Society/IOPCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (9)

Generalized, Energy-conserving Numerical Simulations of Particles in General Relativity. II. Test Particles in Electromagnetic Fields and GRMHD journal February 2019
Numerical methods for General Relativistic particles text January 2018
Structure preserving algorithms for simulation of linearly damped acoustic systems text January 2020
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project collection January 2019
A Novel Energy-conserving Scheme for Eight-dimensional Hamiltonian Problems journal December 2019
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project journal August 2019
General-relativistic Resistive Magnetohydrodynamics with Robust Primitive-variable Recovery for Accretion Disk Simulations journal September 2019
Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD text January 2018
The Event Horizon General Relativistic Magnetohydrodynamic Code Comparison Project text January 2019

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Related Subjects

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