202 research outputs found
Classification of Static Charged Black Holes in Higher Dimensions
The uniqueness theorem for static charged higher dimensional black hole
containing an asymptotically flat spacelike hypersurface with compact interior
and with both degenerate and non-degenerate components of event horizon is
proposed. By studies of the near-horizon geometry of degenerate horizons one
was able to eliminate the previous restriction concerning the inequality
fulfilled by the charges of the adequate components of the aforementioned
horizons.Comment: 9 pages, RevTex, to be published in Phys.Rev. D1
On the Topology of Black Hole Event Horizons in Higher Dimensions
In four dimensions the topology of the event horizon of an asymptotically
flat stationary black hole is uniquely determined to be the two-sphere .
We consider the topology of event horizons in higher dimensions. First, we
reconsider Hawking's theorem and show that the integrated Ricci scalar
curvature with respect to the induced metric on the event horizon is positive
also in higher dimensions. Using this and Thurston's geometric types
classification of three-manifolds, we find that the only possible geometric
types of event horizons in five dimensions are and . In
six dimensions we use the requirement that the horizon is cobordant to a
four-sphere (topological censorship), Friedman's classification of topological
four-manifolds and Donaldson's results on smooth four-manifolds, and show that
simply connected event horizons are homeomorphic to or .
We find allowed non-simply connected event horizons and
, and event horizons with finite non-abelian first homotopy
group, whose universal cover is . Finally, following Smale's results we
discuss the classification in dimensions higher than six.Comment: 12 pages, minor edits 27/09/0
Topology Change of Coalescing Black Holes on Eguchi-Hanson Space
We construct multi-black hole solutions in the five-dimensional
Einstein-Maxwell theory with a positive cosmological constant on the
Eguchi-Hanson space, which is an asymptotically locally Euclidean space. The
solutions describe the physical process such that two black holes with the
topology of S^3 coalesce into a single black hole with the topology of the lens
space L(2;1)=S^3/Z_2. We discuss how the area of the single black hole after
the coalescence depends on the topology of the horizon.Comment: 10 pages, Some comments are added. to be published as a letter in
Classical and Quantum Gravit
A Reformulation of the Hoop Conjecture
A reformulation of the Hoop Conjecture based on the concept of trapped circle
is presented. The problems of severe compactness in every spatial direction,
and of how to superpose the hoops with the surface of the black hole, are
resolved. A new conjecture concerning "peeling" properties of
dynamical/trapping horizons is propounded. A novel geometric Hoop inequality is
put forward. The possibility of carrying over the results to arbitrary
dimension is discussed.Comment: 6 pages, no figures. New references included, typos corrected,
explanatory comments added. Much shorter version, in order to match EPL
length restrictions. To be published in EP
On the Gannon-Lee Singularity Theorem in Higher Dimensions
The Gannon-Lee singularity theorems give well-known restrictions on the
spatial topology of singularity-free (i.e., nonspacelike geodesically
complete), globally hyperbolic spacetimes. In this paper, we revisit these
classic results in the light of recent developments, especially the failure in
higher dimensions of a celebrated theorem by Hawking on the topology of black
hole horizons. The global hyperbolicity requirement is weakened, and we expand
the scope of the main results to allow for the richer variety of spatial
topologies which are likely to occur in higher-dimensional spacetimes.Comment: 13 pages, no figures, to appear in Class. Quantum Gra
Charged Rotating Kaluza-Klein Black Holes Generated by G2(2) Transformation
Applying the G_{2(2)} generating technique for minimal D=5 supergravity to
the Rasheed black hole solution, we present a new rotating charged Kaluza-Klein
black hole solution to the five-dimensional Einstein-Maxwell-Chern-Simons
equations. At infinity, our solution behaves as a four-dimensional flat
spacetime with a compact extra dimension and hence describes a Kaluza-Klein
black hole. In particlar, the extreme solution is non-supersymmetric, which is
contrast to a static case. Our solution has the limits to the asymptotically
flat charged rotating black hole solution and a new charged rotating black
string solution.Comment: 24 page
Small doubling in groups
Let A be a subset of a group G = (G,.). We will survey the theory of sets A
with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}.
The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos
Centenary conferenc
Expansion in perfect groups
Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an
integer q, denote by Ga_q the subgroup of Ga consisting of the elements that
project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q
with respect to the generating set S form a family of expanders when q ranges
over square-free integers with large prime divisors if and only if the
connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas
are explained in more details in the introduction, typos corrected, results
and proofs unchange
Nonexistence of marginally trapped surfaces and geons in 2+1 gravity
We use existence results for Jang's equation and marginally outer trapped
surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity.
In particular, our results show that any 2+1 initial data set, which obeys the
dominant energy condition with cosmological constant \Lambda \geq 0 and which
satisfies a mild asymptotic condition, must have trivial topology. Moreover,
any data set obeying these conditions cannot contain a MOTS. The asymptotic
condition involves a cutoff at a finite boundary at which a null mean convexity
condition is assumed to hold; this null mean convexity condition is satisfied
by all the standard asymptotic boundary conditions. The results presented here
strengthen various aspects of previous related results in the literature. These
results not only have implications for classical 2+1 gravity but also apply to
quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have
been combined to give a single proof, thereby circumventing an issue with the
second proof associated with potential blow-ups of solutions to Jang's
equation. To appear in Commun. Math. Phy
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