Simulating extreme-mass-ratio systems in full general relativity

Abstract

We introduce a new method for numerically evolving the full Einstein field equations in situations where the spacetime is dominated by a known background solution. The technique leverages the knowledge of the background solution to subtract off its contribution to the truncation error, thereby more efficiently achieving a desired level of accuracy. We demonstrate the method by applying it to the radial infall of a solar-type star into supermassive black holes with mass ratios $\ge 10^6$. The self-gravity of the star is thus consistently modeled within the context of general relativity, and the star's interaction with the black hole computed with moderate computational cost, despite the over five orders of magnitude difference in gravitational potential (as defined by the ratio of mass to radius). We compute the tidal deformation of the star during infall, and the gravitational wave emission, finding the latter is close to the prediction of the point-particle limit.

6 pages, 5 figures; added one figure, revised to match PRD RC version

References in corpus (10)

• Hydrodynamical Simulations to Determine the Feeding Rate of Black Holes by the Tidal Disruption of Stars: The Importance of the Impact Parameter and Stellar Structure
• An ultraviolet-optical flare from the tidal disruption of a helium-rich stellar core
• UV/Optical Detections of Candidate Tidal Disruption Events by GALEX and CFHTLS
• The Tidal Disruption of Giant Stars and Their Contribution to the Flaring Supermassive Black Hole Population
• Orbital Evolution of Extreme-Mass-Ratio Black-Hole Binaries with Numerical Relativity
• A candidate tidal disruption event in the Galaxy cluster Abell 3571
• Black-Hole Spin Dependence in the Light Curves of Tidal Disruption Events
• Conformal Thin-Sandwich Solver for Generic Initial Data
• Head-on collisions of binary white dwarf--neutron stars: Simulations in full general relativity
• Tidal disruption flares from stars on eccentric orbits

Cited by in corpus (13)

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• Massive Boson Superradiant Instability of Black Holes: Nonlinear Growth, Saturation, and Gravitational Radiation
• Quasinormal ringing of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy
• Spacetime Dynamics of a Higgs Vacuum Instability During Inflation
• Tidal disruption of a star in the Schwarzschild spacetime: relativistic effects in the return rate of debris
• Nonlinear treatment of a black hole mimicker ringdown
• A cosmologically motivated reference formulation of numerical relativity
• Simulations of Tidal Disruption Events
• A Post-Newtonian approach to black hole-fluid systems
• Numerical-relativity simulation for tidal disruption of white dwarfs by a supermassive black hole
• Non-linear instability of slowly rotating Kerr-AdS black holes