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GR: Fachverband Gravitation und Relativitätstheorie

GR 6: Poster

GR 6.3: Poster

Dienstag, 31. März 2020, 17:00–18:30, Zelt

First and second order hyperbolic formulations of the Einstein equations: a review. — •Daniela Cors and Bernd Brügmann — Theoretisch-Physikalisches Institut, Fröbelstieg 1, 07743 Jena

The BSSN and Z4 formulations of the Einstein equations have been very successful for numerical simulations of black holes and neutron stars. However, these are of first order in time but second order in space. A fully first order formulation in time and space offers additional advantages. For instance, higher order methods such as spectral methods do benefit from first order formulations. Here we present a review of these different hyperbolic reformulations of the Einstein equations in vaccum. We compare their adequacy for different numerical simulations and assess the possibility of first order reductions. An example of such reductions is the recently introduced FOCCZ4 system, which is a first order reformulation of the conformal and covariant formulation of the Z4 system, the so called CCZ4. We propose to pursue a similar strategy in order to reduce the conformal Z4c formulation to first order in time and space.