487 research outputs found
Relative contribution of abundant and rare species to speciesâenergy relationships
A major goal of ecology is to understand spatial variation in species richness. The latter is markedly influenced by energy availability and appears to be influenced more by common species than rare ones; speciesâenergy relationships should thus be stronger for common species. Speciesâenergy relationships may arise because high-energy areas support more individuals, and these larger populations may buffer species from extinction. As extinction risk is a negative decelerating function of population size, this more-individuals hypothesis (MIH) predicts that rare species should respond more strongly to energy. We investigate these opposing predictions using British breeding bird data and find that, contrary to the MIH, common species contribute more to speciesâenergy relationships than rare ones
Dilaton black holes in grand canonical ensemble near the extreme state
Dilaton black holes with a pure electric charge are considered in a framework
of a grand canonical ensemble near the extreme state. It is shown that there
exists such a subset of boundary data that the Hawking temperature smoothly
goes to zero to an infinite value of a horizon radius but the horizon area and
entropy are finite and differ from zero. In string theory the existence of a
horizon in the extreme limit is due to the finiteness of a system only.Comment: 8 pages, RevTex 3.0. Presentation improved, discussion on metrics in
string theory simplified. To be published in Phys.Rev.
No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black Holes
The vanishing of the electromagnetic field, for purely electric
configurations of spontaneously broken Abelian models, is established in the
domain of outer communications of a static asymptotically flat black hole. The
proof is gauge invariant, and is accomplished without any dependence on the
model. In the particular case of the Abelian Higgs model, it is shown that the
only solutions admitted for the scalar field become the vacuum expectation
values of the self-interaction.Comment: 8 pages, 2 figures, RevTeX; some changes to match published versio
The "physical process" version of the first law and the generalized second law for charged and rotating black holes
We investigate both the ``physical process'' version of the first law and the
second law of black hole thermodynamics for charged and rotating black holes.
We begin by deriving general formulas for the first order variation in ADM mass
and angular momentum for linear perturbations off a stationary, electrovac
background in terms of the perturbed non-electromagnetic stress-energy, , and the perturbed charge current density, . Using these
formulas, we prove the "physical process version" of the first law for charged,
stationary black holes. We then investigate the generalized second law of
thermodynamics (GSL) for charged, stationary black holes for processes in which
a box containing charged matter is lowered toward the black hole and then
released (at which point the box and its contents fall into the black hole
and/or thermalize with the ``thermal atmosphere'' surrounding the black hole).
Assuming that the thermal atmosphere admits a local, thermodynamic description
with respect to observers following orbits of the horizon Killing field, and
assuming that the combined black hole/thermal atmosphere system is in a state
of maximum entropy at fixed mass, angular momentum, and charge, we show that
the total generalized entropy cannot decrease during the lowering process or in
the ``release process''. Consequently, the GSL always holds in such processes.
No entropy bounds on matter are assumed to hold in any of our arguments.Comment: 35 pages; 1 eps figur
All the Four Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory
We present the explicit form for all the four dimensional, static,
spherically symmetric solutions in -d Abelian Kaluza-Klein theory by
performing a subset of transformations corresponding to four
boosts on the Schwarzschild solution, supplemented by
transformations. The solutions are parameterized by the mass , Taub-Nut
charge , electric and magnetic
charges. Non-extreme black holes (with zero Taub-NUT charge) have either the
Reissner-Nordstr\" om or Schwarzschild global space-time. Supersymmetric
extreme black holes have a null or naked singularity, while non-supersymmetric
extreme ones have a global space-time of extreme Reissner-Nordstr\" om black
holes.Comment: 8 pages, uses RevTex, improved version to appear in Phys. Rev. Let
A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes
The entropy of stationary black holes has recently been calculated by a
number of different approaches. Here we compare the Noether charge approach
(defined for any diffeomorphism invariant Lagrangian theory) with various
Euclidean methods, specifically, (i) the microcanonical ensemble approach of
Brown and York, (ii) the closely related approach of Ba\~nados, Teitelboim, and
Zanelli which ultimately expresses black hole entropy in terms of the Hilbert
action surface term, (iii) another formula of Ba\~nados, Teitelboim and Zanelli
(also used by Susskind and Uglum) which views black hole entropy as conjugate
to a conical deficit angle, and (iv) the pair creation approach of Garfinkle,
Giddings, and Strominger. All of these approaches have a more restrictive
domain of applicability than the Noether charge approach. Specifically,
approaches (i) and (ii) appear to be restricted to a class of theories
satisfying certain properties listed in section 2; approach (iii) appears to
require the Lagrangian density to be linear in the curvature; and approach (iv)
requires the existence of suitable instanton solutions. However, we show that
within their domains of applicability, all of these approaches yield results in
agreement with the Noether charge approach. In the course of our analysis, we
generalize the definition of Brown and York's quasilocal energy to a much more
general class of diffeomorphism invariant, Lagrangian theories of gravity. In
an appendix, we show that in an arbitrary diffeomorphism invariant theory of
gravity, the ``volume term" in the ``off-shell" Hamiltonian associated with a
time evolution vector field always can be expressed as the spatial
integral of , where are the constraints
associated with the diffeomorphism invariance.Comment: 29 pages (double-spaced) late
Entropy and Action of Dilaton Black Holes
We present a detailed calculation of the entropy and action of
dilaton black holes, and show that both quantities coincide with one quarter of
the area of the event horizon. Our methods of calculation make it possible to
find an explanation of the rule for all static, spherically symmetric
black holes studied so far. We show that the only contribution to the entropy
comes from the extrinsic curvature term at the horizon, which gives
independently of the charge(s) of the black hole, presence of scalar fields,
etc. Previously, this result did not have a general explanation, but was
established on a case-by-case basis. The on-shell Lagrangian for maximally
supersymmetric extreme dilaton black holes is also calculated and shown to
vanish, in agreement with the result obtained by taking the limit of the
expression obtained for black holes with regular horizon.The physical meaning
of the entropy is discussed in relation to the issue of splitting of extreme
black holes.Comment: 15 p., SU-ITP-92-2
Topology, Entropy and Witten Index of Dilaton Black Holes
We have found that for extreme dilaton black holes an inner boundary must be
introduced in addition to the outer boundary to give an integer value to the
Euler number. The resulting manifolds have (if one identifies imaginary time)
topology and Euler number in contrast to
the non-extreme case with . The entropy of extreme dilaton black
holes is already known to be zero. We include a review of some recent ideas due
to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black
holes as having an inner boundary, we conclude that the entropy of {\sl all}
extreme black holes, including black holes, vanishes. We discuss the
relevance of this to the vanishing of quantum corrections and the idea that the
functional integral for extreme holes gives a Witten Index. We have studied
also the topology of ``moduli space'' of multi black holes. The quantum
mechanics on black hole moduli spaces is expected to be supersymmetric despite
the fact that they are not HyperK\"ahler since the corresponding geometry has
torsion unlike the BPS monopole case. Finally, we describe the possibility of
extreme black hole fission for states with an energy gap. The energy released,
as a proportion of the initial rest mass, during the decay of an
electro-magnetic black hole is 300 times greater than that released by the
fission of an nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New
sections include discussion of the Witten index, topology of the moduli
space, black hole sigma model, and black hole fission with huge energy
releas
STATIC FOUR-DIMENSIONAL ABELIAN BLACK HOLES IN KALUZA-KLEIN THEORY
Static, four-dimensional (4-d) black holes (BH's) in ()-d Kaluza-Klein
(KK) theory with Abelian isometry and diagonal internal metric have at most one
electric () and one magnetic () charges, which can either come from the
same -gauge field (corresponding to BH's in effective 5-d KK theory) or
from different ones (corresponding to BH's with isometry
of an effective 6-d KK theory). In the latter case, explicit non-extreme
solutions have the global space-time of Schwarzschild BH's, finite temperature,
and non-zero entropy. In the extreme (supersymmetric) limit the singularity
becomes null, the temperature saturates the upper bound
, and entropy is zero. A class of KK BH's with
constrained charge configurations, exhibiting a continuous electric-magnetic
duality, are generated by global transformations on the above classes
of the solutions.Comment: 11 pages, 2 Postscript figures. uses RevTeX and psfig.sty (for figs)
paper and figs also at ftp://dept.physics.upenn.edu/pub/Cvetic/UPR-645-
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