59 research outputs found
Entropy current and equilibrium partition function in fluid dynamics
Existence of an entropy current with non-negative divergence puts a lot of
constraints on the transport coefficients of a fluid, so does the existence of
equilibrium. In all the cases we have studied so far we have seen an overlap
between these two sets of constraints. In this note we shall try to explore the
reason for such an overlap. We shall also see how a part of the entropy current
could be determined from the equilibrium partition function.Comment: 39 pages, Version-2: Added a new section and some more arguments in
the old sections, added new references and corrected typos. 45 pages Version
3: 50 pages, introduction has been modified, added a new section, added
reference
Second order transport from anomalies
We study parity odd transport at second order in derivative expansion for a
non-conformal charged fluid. We see that there are 27 parity odd transport
coefficients, of which 12 are non-vanishing in equilibrium. We use the
equilibrium partition function method to express 7 of these in terms of the
anomaly, shear viscosity, charge diffusivity and thermodynamic functions. The
remaining 5 are constrained by 3 relations which also involve the anomaly. We
derive Kubo formulae for 2 of the transport coefficients and show these agree
with that derived from the equilibrium partition function.Comment: Error in total number of independent parity odd transport
coefficients has been corrected from 29 to 27. Results for the relation of
the transport coefficients to the anomaly unchanged. Added a section on
chiral dispersion relations, includes additional references. Added two
appendices and corrected some typos. 34 page
Fluid-gravity and membrane-gravity dualities - Comparison at subleading orders
In this note we have compared two different perturbation techniques that
could be used to generate solutions of Einstein's equations in presence of
negative cosmological constant. One of these two methods is derivative
expansion and the other is an expansion in inverse powers of dimension. Both
the techniques generate space-time with a singularity shielded by a dynamical
event horizon. We have shown that in the appropriate regime of parameter space
and with appropriate choice of coordinates, the metrics and corresponding
horizon dynamics, generated by these two different techniques, are exactly
equal to the order the solutions are known both sides. This work is essentially
extension of \cite{prevwork} where the authors have shown the equivalence of
the two techniques up to the first non-trivial order
A One-Loop Test of Quantum Supergravity
The partition function on the three-sphere of ABJM theory and its
generalizations has, at large N, a universal, subleading logarithmic term.
Inspired by the success of one-loop quantum gravity for computing the
logarithmic corrections to black hole entropy, we try to reproduce this
universal term by a one-loop calculation in Euclidean eleven-dimensional
supergravity on AdS_4 \times X_7. We find perfect agreement between the results
of ABJM theory and the eleven dimensional supergravity.Comment: 12 pages, accepted for publication in Classical and Quantum Gravit
Large rotating AdS black holes from fluid mechanics
We use the AdS/CFT correspondence to argue that large rotating black holes in
global AdS(D) spaces are dual to stationary solutions of the relativistic
Navier-Stokes equations on S**(D-2). Reading off the equation of state of this
fluid from the thermodynamics of non-rotating black holes, we proceed to
construct the nonlinear spinning solutions of fluid mechanics that are dual to
rotating black holes. In all known examples, the thermodynamics and the local
stress tensor of our solutions are in precise agreement with the thermodynamics
and boundary stress tensor of the spinning black holes. Our fluid dynamical
description applies to large non-extremal black holes as well as a class of
large non-supersymmetric extremal black holes, but is never valid for
supersymmetric black holes. Our results yield predictions for the
thermodynamics of all large black holes in all theories of gravity on AdS
spaces, for example, string theory on AdS(5) x S**5 and M theory on AdS(4) x
S**7 and AdS(7) x S**4.Comment: 62 pages, 1 figure. v2: references, typo
A membrane paradigm at large D
We study invariant solutions of the classical vacuum Einstein
equations in dimensions. In the limit with held
fixed we construct a class of solutions labelled by the shape of a membrane
(the event horizon), together with a `velocity' field that lives on this
membrane. We demonstrate that our metrics can be corrected to nonsingular
solutions at first sub-leading order in if and only if the
membrane shape and `velocity' field obey equations of motion which we
determine. These equations define a well posed initial value problem for the
membrane shape and this `velocity' and so completely determinethe dynamics of
the black hole. They may be viewed as governing the non-linear dynamics of the
light quasi normal modes of Emparan, Suzuki and Tanabe.Comment: The main results emphasised better, The presentation of the
quasinormal modes improved for clarity and typos correcte
The large D black hole dynamics in AdS/dS backgrounds
We have constructed a class of perturbative dynamical black hole solutions in
presence of cosmological constant. We have done our calculation in large number
of dimensions. The inverse power of dimension has been used as the perturbation
parameter and our calculation is valid upto the first subleading order. The
solutions are in one to one correspondence with a dynamical membrane and a
velocity field embedded in the asymptotic geometry. Our method is manifestly
covariant with respect to the asymptotic geometry. One single calculation and
the same universal result works for both dS and AdS geometry or in case of AdS
for both global AdS and Poincare patch. We have checked our final answer with
various known exact solutions and the known spectrum of Quasi Normal modes in
AdS/dS.Comment: 74 pages. v2: Minor changes, typos correcte
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