Robust evolution system for Numerical Relativity

Abstract

The paper combines theoretical and applied ideas which have been previously considered separately into a single set of evolution equations for Numerical Relativity. New numerical ingredients are presented which avoid gauge pathologies and allow one to perform robust 3D calculations. The potential of the resulting numerical code is demonstrated by using the Schwarzschild black hole as a test-bed. Its evolution can be followed up to times greater than one hundred black hole masses.

11 pages, 4 figures; figure corrected

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Cited by in corpus (30)

• Numerical Relativity: A review
• Turduckening black holes: an analytical and computational study
• Towards a Stable Numerical Evolution of Strongly Gravitating Systems in General Relativity: The Conformal Treatments
• Simple excision of a black hole in 3+1 numerical relativity
• Toward standard testbeds for numerical relativity
• Towards an understanding of the stability properties of the 3+1 evolution equations in general relativity
• Strongly hyperbolic second order Einstein's evolution equations
• Hyperbolicity of the BSSN system of Einstein evolution equations
• Improved numerical stability of stationary black hole evolution calculations
• Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
• Numerical Relativity of Compact Binaries in the 21st Century
• Excision without excision: the relativistic turducken
• Gravitational Collapse of Gravitational Waves in 3D Numerical Relativity
• Hyperbolicity of scalar-tensor theories of gravity
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Black hole evolution with the BSSN system by pseudo-spectral methods
• Cauchy boundaries in linearized gravitational theory
• Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
• Ekman layers and the damping of inertial r-modes in a spherical shell: application to neutron stars
• A hyperbolic slicing condition adapted to Killing fields and densitized lapses
• Towards a gauge-polyvalent Numerical Relativity code
• Constraint propagation in the family of ADM systems
• Spherical symmetry as a test case for unconstrained hyperboloidal evolution II: gauge conditions
• Efficient implementation of finite volume methods in Numerical Relativity
• A $r$-mode in a magnetic rotating spherical layer: application to neutron stars
• Gauge stability of 3+1 formulations of General Relativity
• Hamiltonian Relaxation
• The constraints as evolution equations for numerical relativity
• Modifications for numerical stability of black hole evolution
• The BSSN formulation is a partially constrained evolution system