The affine-null formulation of the gravitational equations: spherical case

Crespo, J. A.; de Oliveira, H. P.; Winicour , J.

doi:10.1103/PhysRevD.100.104017

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The affine-null formulation of the gravitational equations: spherical case

MPS-Authors

Winicour , J.
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Crespo, J. A., de Oliveira, H. P., & Winicour, J. (2019). The affine-null formulation of the gravitational equations: spherical case. Physical Review D, 100(10): 104017. doi:10.1103/PhysRevD.100.104017.

Cite as: https://hdl.handle.net/21.11116/0000-0005-51DD-7

Abstract

A new evolution algorithm for the characteristic initial value problem based
upon an affine parameter rather than the areal radial coordinate used in the
Bondi-Sachs formulation is applied in the spherically symmetric case to the
gravitational collapse of a massless scalar field. The advantages over the
Bondi-Sachs version are discussed, with particular emphasis on the application
to critical collapse. Unexpected quadratures lead to a simple evolution
algorithm based upon ordinary differential equations which can be integrated
along the null rays. For collapse to a black hole in a Penrose compactified
spacetime, these equations are regularized throughout the exterior and interior
of the horizon up to the final singularity. They are implemented as a global
numerical evolution code based upon the Galerkin method. New results regarding
the global properties of critical collapse are presented.