Spherical symmetry as a test case for unconstrained hyperboloidal evolution

Abstract

We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution schemes promise optimal efficiency, but are difficult to regularize at null infinity, where the compactified Einstein equations are formally singular. In this work we treat the spherically symmetry case, which already poses nontrivial problems and constitutes an important first step. We have carried out stable numerical evolutions with the generalized BSSN and Z4 equations coupled to a scalar field. The crucial ingredients have been to find an appropriate evolution equation for the lapse function and to adapt constraint damping terms to handle null infinity.

30 pages, 7 figures

References in corpus (9)

• Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing
• Covariant formulations of BSSN and the standard gauge
• Implementation of standard testbeds for numerical relativity
• Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations
• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• Discontinuous Galerkin method for the spherically reduced BSSN system with second-order operators
• Fully covariant and conformal formulation of the Z4 system in a reference-metric approach: comparison with the BSSN formulation in spherical symmetry
• Stationary hyperboloidal slicings with evolved gauge conditions
• Algebraic stability analysis of constraint propagation

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