The first law for stationary axisymmetric multi-black hole systems
Résumé
In the framework of Einstein-Maxwell theory, we consider collinear arrays of rotating electrically charged black holes connected by Misner-Dirac strings carrying gravimagnetic and magnetic fluxes. The first law of mechanics for these systems is derived. It involves as dynamical variables the areas, angular momenta and electric charges of the various Killing horizons -- black holes and Misner strings. When the gravimagnetic fluxes all vanish, the first law reduces to a form where the dynamical variables associated with the strings are the string tensions and magnetic fluxes. This form is not generically invariant under electric-magnetic duality.
Mots clés
angular momentum
S-duality
string: Dirac
flux: magnetic
gravitation: magnetic field
Kerr-Newman
gravitation: surface
potential: electric
asymptotic behavior
regularization
thermodynamics
dyon
cosmic string
charge: magnetic
string: massive
symmetry breaking
current: conservation law
black hole: charge
symmetry: axial
horizon: Killing
charge: electric
mechanics
string tension
Misner
collinear
Einstein-Maxwell equation
rotation