7 research outputs found
Nonlinear Hydrodynamics from Flow of Retarded Green's Function
We study the radial flow of retarded Green's function of energy-momentum
tensor and -current of dual gauge theory in presence of generic higher
derivative terms in bulk Lagrangian. These are first order non-linear Riccati
equations. We solve these flow equations analytically and obtain second order
transport coefficients of boundary plasma. This way of computing transport
coefficients has an advantage over usual Kubo approach. The non-linear equation
turns out to be a linear first order equation when we study the Green's
function perturbatively in momentum. We consider several examples including
term and generic four derivative terms in bulk. We also study the flow
equations for -charged black holes and obtain exact expressions for second
order transport coefficients for dual plasma in presence of arbitrary chemical
potentials. Finally we obtain higher derivative corrections to second order
transport coefficients of boundary theory dual to five dimensional gauge
supergravity.Comment: Version 2, reference added, typos correcte
Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics
We perform a general study of the thermodynamic properties of static
electrically charged black hole solutions of nonlinear electrodynamics
minimally coupled to gravitation in three space dimensions. The Lagrangian
densities governing the dynamics of these models in flat space are defined as
arbitrary functions of the gauge field invariants, constrained by some
requirements for physical admissibility. The exhaustive classification of these
theories in flat space, in terms of the behaviour of the Lagrangian densities
in vacuum and on the boundary of their domain of definition, defines twelve
families of admissible models. When these models are coupled to gravity, the
flat space classification leads to a complete characterization of the
associated sets of gravitating electrostatic spherically symmetric solutions by
their central and asymptotic behaviours. We focus on nine of these families,
which support asymptotically Schwarzschild-like black hole configurations, for
which the thermodynamic analysis is possible and pertinent. In this way, the
thermodynamic laws are extended to the sets of black hole solutions of these
families, for which the generic behaviours of the relevant state variables are
classified and thoroughly analyzed in terms of the aforementioned boundary
properties of the Lagrangians. Moreover, we find universal scaling laws (which
hold and are the same for all the black hole solutions of models belonging to
any of the nine families) running the thermodynamic variables with the electric
charge and the horizon radius. These scale transformations form a one-parameter
multiplicative group, leading to universal "renormalization group"-like
first-order differential equations. The beams of characteristics of these
equations generate the full set of black hole states associated to any of these
gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex
style; minor corrections added; final version appearing in General Relativity
and Gravitatio
Non-extremal black holes of N=2, d=4 supergravity
We propose a generic recipe for deforming extremal black holes into
non-extremal black holes and we use it to find and study the non-extremal
black-hole solutions of several N=2,d=4 supergravity models (SL(2,R)/U(1), CPn
and STU with four charges). In all the cases considered, the non-extremal
family of solutions smoothly interpolates between all the different extremal
limits, supersymmetric and not supersymmetric. This fact can be used to find
explicitly extremal non-supersymmetric solutions in the cases in which the
attractor mechanism does not completely fix the values of the scalars on the
event horizon and they still depend on the boundary conditions at spatial
infinity.
We compare (supersymmetry) Bogomol'nyi bounds with extremality bounds, we
find the first-order flow equations for the non-extremal solutions and the
corresponding superpotential, which gives in the different extremal limits
different superpotentials for extremal black holes. We also compute the
"entropies" (areas) of the inner (Cauchy) and outer (event) horizons, finding
in all cases that their product gives the square of the moduli-independent
entropy of the extremal solution with the same electric and magnetic charges.Comment: Many small, inessential changes. Some misprints corrected and a few
references adde