TY - JOUR

T1 - Equilibrium initial data for moving puncture simulations

T2 - The stationary 1 + log slicing

AU - Baumgarte, T. W.

AU - Etienne, Z. B.

AU - Liu, Y. T.

AU - Matera, K.

AU - Murchadha, N. Ó

AU - Shapiro, S. L.

AU - Taniguchi, K.

PY - 2009

Y1 - 2009

N2 - We discuss a 'stationary 1 + log' slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data give a stationary foliation when evolved with 'moving puncture' gauge conditions that are often used in black hole evolutions. The resulting slicing is time independent and agrees with the slicing generated by being dragged along a timelike Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution should be minimized. While these properties appear very promising, suggesting that this slicing condition should be an attractive alternative to, for example, maximal slicing, we demonstrate in this paper that solutions can be constructed only for a small class of problems. For binary black hole initial data, in particular, it is often assumed that there exists an approximate helical Killing vector that generates the binary's orbit. We show that 1 + log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.

AB - We discuss a 'stationary 1 + log' slicing condition for the construction of solutions to Einstein's constraint equations. For stationary spacetimes, these initial data give a stationary foliation when evolved with 'moving puncture' gauge conditions that are often used in black hole evolutions. The resulting slicing is time independent and agrees with the slicing generated by being dragged along a timelike Killing vector of the spacetime. When these initial data are evolved with moving puncture gauge conditions, numerical errors arising from coordinate evolution should be minimized. While these properties appear very promising, suggesting that this slicing condition should be an attractive alternative to, for example, maximal slicing, we demonstrate in this paper that solutions can be constructed only for a small class of problems. For binary black hole initial data, in particular, it is often assumed that there exists an approximate helical Killing vector that generates the binary's orbit. We show that 1 + log slices that are stationary with respect to such a helical Killing vector cannot be asymptotically flat, unless the spacetime possesses an additional axial Killing vector.

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U2 - 10.1088/0264-9381/26/8/085007

DO - 10.1088/0264-9381/26/8/085007

M3 - Article

AN - SCOPUS:68949141799

SN - 0264-9381

VL - 26

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 8

M1 - 085007

ER -