1,580 research outputs found
Entropy, Extremality, Euclidean Variations, and the Equations of Motion
We study the Euclidean gravitational path integral computing the Renyi
entropy and analyze its behavior under small variations. We argue that, in
Einstein gravity, the extremality condition can be understood from the
variational principle at the level of the action, without having to solve
explicitly the equations of motion. This set-up is then generalized to
arbitrary theories of gravity, where we show that the respective entanglement
entropy functional needs to be extremized. We also extend this result to all
orders in Newton's constant , providing a derivation of quantum
extremality. Understanding quantum extremality for mixtures of states provides
a generalization of the dual of the boundary modular Hamiltonian which is given
by the bulk modular Hamiltonian plus the area operator, evaluated on the
so-called modular extremal surface. This gives a bulk prescription for
computing the relative entropies to all orders in . We also comment on how
these ideas can be used to derive an integrated version of the equations of
motion, linearized around arbitrary states.Comment: 37 pages; v2: typos fixed and new references added; v3: new
references and minor clarifications adde
Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS black holes
We present a holographic derivation of the entropy of supersymmetric
asymptotically AdS black holes. We define a BPS limit of black hole
thermodynamics by first focussing on a supersymmetric family of complexified
solutions and then reaching extremality. We show that in this limit the black
hole entropy is the Legendre transform of the on-shell gravitational action
with respect to three chemical potentials subject to a constraint. This
constraint follows from supersymmetry and regularity in the Euclidean bulk
geometry. Further, we calculate, using localization, the exact partition
function of the dual SCFT on a twisted with
complexified chemical potentials obeying this constraint. This defines a
generalization of the supersymmetric Casimir energy, whose Legendre transform
at large exactly reproduces the Bekenstein-Hawking entropy of the black
hole.Comment: v4: minor changes, version published in JHE
Evolution of near extremal black holes
Near extreme black holes can lose their charge and decay by the emission of
massive BPS charged particles. We calculate the greybody factors for low energy
charged and neutral scalar emission from four and five dimensional near
extremal Reissner-Nordstrom black holes. We use the corresponding emission
rates to obtain ratios of the rates of loss of excess energy by charged and
neutral emission, which are moduli independent, depending only on the integral
charges and the horizon potentials. We consider scattering experiments, finding
that evolution towards a state in which the integral charges are equal is
favoured, but neutral emission will dominate the decay back to extremality
except when one charge is much greater than the others. The implications of our
results for the agreement between black hole and D-brane emission rates and for
the information loss puzzle are then discussed.Comment: 25 pages, RevTe
Computing the vertices of tropical polyhedra using directed hypergraphs
We establish a characterization of the vertices of a tropical polyhedron
defined as the intersection of finitely many half-spaces. We show that a point
is a vertex if, and only if, a directed hypergraph, constructed from the
subdifferentials of the active constraints at this point, admits a unique
strongly connected component that is maximal with respect to the reachability
relation (all the other strongly connected components have access to it). This
property can be checked in almost linear-time. This allows us to develop a
tropical analogue of the classical double description method, which computes a
minimal internal representation (in terms of vertices) of a polyhedron defined
externally (by half-spaces or hyperplanes). We provide theoretical worst case
complexity bounds and report extensive experimental tests performed using the
library TPLib, showing that this method outperforms the other existing
approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section
5 (using directed hypergraphs), detailed appendix; v3: major revision of the
article (adding tropical hyperplanes, alternative method by arrangements,
etc); v4: minor revisio
Classical and Thermodynamic Stability of Black Branes
It is argued that many non-extremal black branes exhibit a classical
Gregory-Laflamme instability if, and only if, they are locally
thermodynamically unstable. For some black branes, the Gregory-Laflamme
instability must therefore disappear near extremality. For the black -branes
of the type II supergravity theories, the Gregory-Laflamme instability
disappears near extremality for but persists all the way down to
extremality for (the black D3-brane is not covered by the analysis of
this paper). This implies that the instability also vanishes for the
near-extremal black M2 and M5-brane solutions.Comment: 21 pages, LaTeX. v2: Various points clarified, typos corrected and
reference adde
The tropical double description method
We develop a tropical analogue of the classical double description method
allowing one to compute an internal representation (in terms of vertices) of a
polyhedron defined externally (by inequalities). The heart of the tropical
algorithm is a characterization of the extreme points of a polyhedron in terms
of a system of constraints which define it. We show that checking the
extremality of a point reduces to checking whether there is only one minimal
strongly connected component in an hypergraph. The latter problem can be solved
in almost linear time, which allows us to eliminate quickly redundant
generators. We report extensive tests (including benchmarks from an application
to static analysis) showing that the method outperforms experimentally the
previous ones by orders of magnitude. The present tools also lead to worst case
bounds which improve the ones provided by previous methods.Comment: 12 pages, prepared for the Proceedings of the Symposium on
Theoretical Aspects of Computer Science, 2010, Nancy, Franc
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