623 research outputs found
BTZ Black Hole with Chern-Simons and Higher Derivative Terms
The entropy of a BTZ black hole in the presence of gravitational Chern-Simons
terms has previously been analyzed using Euclidean action formalism. In this
paper we treat the BTZ solution as a two dimensional black hole by regarding
the angular coordinate as a compact direction, and use Wald's Noether charge
method to calculate the entropy of this black hole in the presence of higher
derivative and gravitational Chern-Simons terms. The parameters labelling the
black hole solution can be determined by extremizing an entropy function whose
value at the extremum gives the entropy of the black hole.Comment: LaTeX file, 11 page
R^2 Corrections for 5D Black Holes and Rings
We study higher-order corrections to two BPS solutions of 5D supergravity,
namely the supersymmetric black ring and the spinning black hole. Due in part
to our current relatively limited understanding of F-type terms in 5D
supergravity, the nature of these corrections is less clear than that of their
4D cousins. Effects of certain terms found in Calabi-Yau compactification
of M-theory are specifically considered. For the case of the black ring, for
which the microscopic origin of the entropy is generally known, the
corresponding higher order macroscopic correction to the entropy is found to
match a microscopic correction, while for the spinning black hole the
corrections are partially matched to those of a 4D black hole.Comment: 9 page
Lodged in the throat: Internal infinities and AdS/CFT
In the context of AdS3/CFT2, we address spacetimes with a certain sort of
internal infinity as typified by the extreme BTZ black hole. The internal
infinity is a null circle lying at the end of the black hole's infinite throat.
We argue that such spacetimes may be described by a product CFT of the form
CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary
while CFT-L is associated with the null circle. Our particular calculations
analyze the CFT dual of the extreme BTZ black hole in a linear toy model of
AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dual CFT state
is a corresponding quotient of the CFT vacuum state. This state turns out to
live in the aforementioned product CFT. We discuss this result in the context
of general issues of AdS/CFT duality and entanglement entropy.Comment: 11 pages, 2 figures; v2 - some typos corrected, minor revision
Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem
Short distance structure of spacetime may show up in the form of high
freqency dispersion. Although such dispersion is not locally Lorentz invariant,
we show in a scalar field model how it can nevertheless be incorporated into a
generally covariant metric theory of gravity provided the locally preferred
frame is dynamical. We evaluate the resulting energy-momentum tensor and
compute its expectation value for a quantum field in a thermal state. The
equation of state differs at high temperatures from the usual one, but not by
enough to impact the problems of a hot big bang cosmology. We show that a
superluminal dispersion relation can solve the horizon problem via superluminal
equilibration, however it cannot do so while remaining outside the Planck
regime unless the dispersion relation is artificially chosen to have a rather
steep dependence on wavevector.Comment: 4 pages, 1 figure; New section added with discussion of solution to
the cosmological horizon problem using superluminal dispersion, title changed
to reflect new content, various additional minor change
Entanglement Interpretation of Black Hole Entropy in String Theory
We show that the entropy resulting from the counting of microstates of non
extremal black holes using field theory duals of string theories can be
interpreted as arising from entanglement. The conditions for making such an
interpretation consistent are discussed. First, we interpret the entropy (and
thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons
as arising from entanglement. We use a path integral method to define the
Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its
entangled nature and its relation to the geometry. If string theory on such
spacetimes has a field theory dual, then, in the low-energy, weak coupling
limit, the field theory state that is dual to the Hartle-Hawking state is a
thermofield double state. This allows the comparison of the entanglement
entropy with the entropy of the field theory dual, and thus, with the
Bekenstein-Hawking entropy of the black hole. As an example, we discuss in
detail the case of the five dimensional anti-de Sitter, black hole spacetime
How Does a Fundamental String Stretch its Horizon?
It has recently been shown that if we take into account a class of higher
derivative corrections to the effective action of heterotic string theory, the
entropy of the black hole solution representing elementary string states
correctly reproduces the statistical entropy computed from the degeneracy of
elementary string states. So far the form of the solution has been analyzed at
distance scales large and small compared to the string scale. We analyze the
solution that interpolates between these two limits and point out a subtlety in
constructing such a solution due to the presence of higher derivative terms in
the effective action. We also study the T-duality transformation rules to
relate the moduli fields of the effective field theory to the physical
compactification radius in the presence of higher derivative corrections and
use these results to find the physical radius of compactification near the
horizon of the black hole. The radius approaches a finite value even though the
corresponding modulus field vanishes. Finally we discuss the non-leading
contribution to the black hole entropy due to space-time quantum corrections to
the effective action and the ambiguity involved in comparing this result to the
statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference
Topological censorship for Kaluza-Klein space-times
The standard topological censorship theorems require asymptotic hypotheses
which are too restrictive for several situations of interest. In this paper we
prove a version of topological censorship under significantly weaker
conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic
behavior. In particular we prove simple connectedness of the quotient of the
domain of outer communications by the group of symmetries for models which are
asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense.
This allows one, e.g., to define the twist potentials needed for the reduction
of the field equations in uniqueness theorems. Finally, the methods used to
prove the above are used to show that weakly trapped compact surfaces cannot be
seen from Scri.Comment: minor correction
Entropy Function for Heterotic Black Holes
We use the entropy function formalism to study the effect of the Gauss-Bonnet
term on the entropy of spherically symmetric extremal black holes in heterotic
string theory in four dimensions. Surprisingly the resulting entropy and the
near horizon metric, gauge field strengths and the axion-dilaton field are
identical to those obtained by Cardoso et. al. for a supersymmetric version of
the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet
term. We also study the effect of holomorphic anomaly on the entropy using our
formalism. Again the resulting attractor equations for the axion-dilaton field
and the black hole entropy agree with the corresponding equations for the
supersymmetric version of the theory. These results suggest that there might be
a simpler description of supergravity with curvature squared terms in which we
supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.Comment: LaTeX file, 23 pages; v2: references added; v3: minor addition; v4:
minor change
Black Hole Entropy Function and the Attractor Mechanism in Higher Derivative Gravity
We study extremal black hole solutions in D dimensions with near horizon
geometry AdS_2\times S^{D-2} in higher derivative gravity coupled to other
scalar, vector and anti-symmetric tensor fields. We define an entropy function
by integrating the Lagrangian density over S^{D-2} for a general AdS_2\times
S^{D-2} background, taking the Legendre transform of the resulting function
with respect to the parameters labelling the electric fields, and multiplying
the result by a factor of 2\pi. We show that the values of the scalar fields at
the horizon as well as the sizes of AdS_2 and S^{D-2} are determined by
extremizing this entropy function with respect to the corresponding parameters,
and the entropy of the black hole is given by the value of the entropy function
at this extremum. Our analysis relies on the analysis of the equations of
motion and does not directly make use of supersymmetry or specific structure of
the higher derivative terms.Comment: LaTeX file, 12page
Non-Supersymmetric Attractors and Entropy Function
We study the entropy of non-supersymmetric extremal black holes which exhibit
attractor mechanism by making use of the entropy function. This method, being
simple, can be used to calculate corrections to the entropy due to higher order
corrections to the action. In particular we apply this method for five
dimensional non-supersymmetric extremal black hole which carries two magnetic
charges and find the R^2 corrections to the entropy. Using the behavior of the
action evaluated for the extremal black hole near the horizon, we also present
a simple expression for C-function corrected by higher order corrections.Comment: 15 pages, Latex file, v2: references and some additional comments
added, minor corrections, some comments about 5D supersymmetric BH added.
v3:minor corrections, few comments added, refs. adde
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