The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes

Details The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes

2009-07-07

arxiv.org/abs/0907.1151v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 6 figures, some typos fixed and references added

Scientific paper

10.1103/PhysRevD.80.104022

We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their hyperbolic properties are analyzed, showing that the resulting system is symmetric hyperbolic. We also focus on the problem of finding initial data for multiple charged black holes assuming time-symmetric initial data and using a puncture-like method to solve the Hamiltonian and the Gauss constraints. We study the behavior of the resulting initial data families, and show that previous results in this direction can be obtained as particular cases of our approach.

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