Angular momentum conservation for dynamical black holes

Journal Article · Wed Nov 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.74.104013· OSTI ID:20864121

Hayward, Sean A ^[1]

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1. Center for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234 (China)

Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has vanishing transverse divergence, it can be uniquely specified under certain generic conditions. Along a trapping horizon, a conservation law expresses the rate of change of angular momentum of a general black hole in terms of angular momentum densities of matter and gravitational radiation. This identifies the transverse-normal block of an effective gravitational-radiation energy tensor, whose normal-normal block was recently identified in a corresponding energy conservation law. Angular momentum and energy are dual, respectively, to the axial vector and a previously identified vector, the conservation equations taking the same form. Including charge conservation, the three conserved quantities yield definitions of an effective energy, electric potential, angular velocity and surface gravity, satisfying a dynamical version of the so-called first law of black-hole mechanics. A corresponding zeroth law holds for null trapping horizons, resolving an ambiguity in taking the null limit.

• OSTI ID: 20864121
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 74; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
ANGULAR VELOCITY
BLACK HOLES
CHARGE CONSERVATION
COSMOLOGY
DENSITY
ELECTRIC POTENTIAL
ENERGY CONSERVATION
GRAVITATION
GRAVITATIONAL RADIATION
SPACE-TIME
SURFACES
TRAPPING
VECTORS