248 research outputs found
The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
We prove non-existence of static, vacuum, appropriately regular,
asymptotically flat black hole space-times with degenerate (not necessarily
connected) components of the event horizon. This finishes the classification of
static, vacuum, asymptotically flat domains of outer communication in an
appropriate class of space-times, showing that the domains of outer
communication of the Schwarzschild black holes exhaust the space of
appropriately regular black hole exteriors.Comment: This version includes an addendum with a corrected proof of
non-existence of zeros of the Killing vector at degenerate horizons. A
problem with yet another Lemma is pointed out; this problem does not arise if
one assumes analyticity of the metric. An alternative solution, that does not
require analyticity, has been given in arXiv:1004.0513 [gr-qc] under
appropriate global condition
The Angular Tension of Black Holes
Angular tension is an ADM charge that contributes a work term to the first
law of black hole mechanics when the range of an angular coordinate is varied
and leads to a new Smarr formula for stationary black holes. A phase diagram
for singly-spinning D=5 black holes shows that angular tension resolves the
degeneracies between spherical black holes and (dipole) black rings and
captures the physics of the black ring balance condition. Angular tension
depends on the behavior of the metric at rotational axes and we speculate on
its relation to rod/domain structure characterizations of higher dimensional
black holes and black hole uniqueness theorems.Comment: 5 pages, 1 figure; v2 references adde
On the topology of stationary black holes
We prove that the domain of outer communication of a stationary, globally
hyperbolic spacetime satisfying the null energy condition must be simply
connected. Under suitable additional hypotheses, this implies, in particular,
that each connected component of a cross-section of the event horizon of a
stationary black hole must have spherical topology.Comment: 7 pages, Late
Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
We show that static electro-vacuum black hole space-times containing an
asymptotically flat spacelike hypersurface with compact interior and with both
degenerate and non-degenerate components of the event horizon do not exist,
under the supplementary hypothesis that all degenerate components of the event
horizon have charges of the same sign. This extends previous uniqueness
theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were
allowed) and Heusler (where only degenerate horizons were allowed).Comment: Reverted to original v1; v2 was a result of a manipulation error, and
was meant to be an update to gr-qc/9809088. The problems adressed in the
addendum in v2 of gr-qc/9809088 apply also to this paper, and are similarly
taken care of by the addendum to gr-qc/9809088, and by the analysis in
arXiv:1004.0513 [gr-qc
On completeness of orbits of Killing vector fields
A Theorem is proved which reduces the problem of completeness of orbits of
Killing vector fields in maximal globally hyperbolic, say vacuum, space--times
to some properties of the orbits near the Cauchy surface. In particular it is
shown that all Killing orbits are complete in maximal developements of
asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact
manifold. This result gives a significant strengthening of the uniqueness
theorems for black holes.Comment: 16 pages, Latex, preprint NSF-ITP-93-4
On the uniqueness of smooth, stationary black holes in vacuum
We prove a conditional "no hair" theorem for smooth manifolds: if is the
domain of outer communication of a smooth, regular, stationary Einstein vacuum,
and if a technical condition relating the Ernst potential and Killing scalar is
satisfied on the bifurcate sphere, then is locally isometric to the domain
of outer communication of a Kerr space-time.Comment: Various correction
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