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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Approximate solutions to the Einstein field equations are a valuable tool to
investigate gravitational phenomena. An important aspect of any approximation
is to investigate and quantify its regime of validity. We present a study that
evaluates the effects that approximate puncture initial data, based on
"skeleton" solutions to the Einstein constraints as proposed by Faye et al.
[PRD 69, 124029 (2004)], have on numerical evolutions. Using data analysis
tools, we assess the effectiveness of these constraint-violating initial data
and show that the matches of waveforms from skeleton data with the
corresponding waveforms from constraint-satisfying initial data are > 0.97 when
the total mass of the binary is > 40M(solar). In addition, we demonstrate that
the differences between the skeleton and the constraint-satisfying initial data
evolutions, and thus waveforms, are due to negative Hamiltonian constraint
violations present in the skeleton initial data located in the vicinity of the
punctures. During the evolution, the skeleton data develops both Hamiltonian
and momentum constraint violations that decay with time, with the binary system
relaxing to a constraint-satisfying solution with black holes of smaller mass
and thus different dynamics.
