Local and Approximate classification of spacetimes in the transverse frames
- Resource Type
- Authors
- Carlos O. Lousto; Nicole Rosato; Hiroyuki Nakano
- Source
- Subject
- Physics
High Energy Astrophysical Phenomena (astro-ph.HE)
High Energy Physics - Theory
Spacetime
010308 nuclear & particles physics
Computation
FOS: Physical sciences
General Relativity and Quantum Cosmology (gr-qc)
Type (model theory)
01 natural sciences
General Relativity and Quantum Cosmology
Binary black hole
High Energy Physics - Theory (hep-th)
0103 physical sciences
Algebraic number
Invariant (mathematics)
010306 general physics
Tetrad
Astrophysics - High Energy Astrophysical Phenomena
Mathematical physics
Spin-½
- Language
- English
We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and approximate algebraic Petrov types in the strong field regime. We define an index $\mathcal{D}=\sqrt{12/I}\left(\Psi_2 - \Psi_3^2/\Psi_4\right)$ able to discriminate between Petrov types II and D and define regions of spacetime of those approximate types when used in conjunction with the speciality invariant $S=27J^2/I^3$. We provide an explicit example applying this method to Brill-Lindquist initial data corresponding to two nonspinning black holes from rest at a given initial separation. We find a doughnut-like region that is approximately of Petrov type II surrounded by an approximately Petrov type D region. We complete the study by proposing a totally symmetric tetrad fixing of the transverse frame that can be simply implemented in numerically generated spacetimes through the computation of spin coefficients ratios. We provide an application by explicitly deriving the Kerr-perturbative equations in this tetrad.
Comment: 18 pages, 11 figures