Covariant formulations of BSSN and the standard gauge

Abstract

The BSSN and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data using two different coordinate systems and to relate the results using the familiar tensor transformation rules. Two variants of the covariant equations are considered. These differ from one another in the way that the determinant of the conformal metric is evolved.

6 pages, no figures. Notation has been improved and typos have been corrected

References in corpus (3)

• How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
• BSSN in Spherical Symmetry
• Comments on Bona-Masso type slicing conditions in long-term black hole evolutions

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