A generalization of entropy to near-equilibrium phenomena is provided by the notion of a hydrodynamic entropy current. Recent advances in holography have lead to the formulation of fluid-gravity duality, a remarkable connection between the hydrodynamics of certain strongly coupled media and dynamics of higher dimensional black holes. This Letter introduces a correspondence between phenomenologically defined entropy currents in relativistic hydrodynamics and quasilocal horizons of near-equilibrium black objects in a dual gravitational description. A general formula is given, expressing the divergence of the entropy current in terms of geometric objects which appear naturally in the gravity dual geometry. The proposed definition is explicitly covariant with respect to boundary diffeomorphisms and reproduces known results when evaluated for the event horizon.
We study the effective hydrodynamics of neutral black branes enclosed in a finite cylindrical cavity with Dirichlet boundary conditions. We focus on how the Gregory-Laflamme instability changes as we vary the cavity radius R. Fixing the metric at the cavity wall increases the rigidity of the black brane by hindering gradients of the redshift on the wall. In the effective fluid, this is reflected in the growth of the squared speed of sound. As a consequence, when the cavity is smaller than a critical radius the black brane becomes dynamically stable. The correlation with the change in thermodyn…
The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-extremal D3-brane, as we move our cutoff surface from the asymptotically flat near-boundary region to the near-horizon region, this hydrodynamical system interpolates between a non-conformal relativistic…
The framework of slowly evolving horizons is generalized to the case of black branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The results are used to analyze the behavior of both event and apparent horizons in the gravity dual to boost-invariant flow. These considerations are motivated by the fact that at second order in the gradient expansion the hydrodynamic entropy current in the dual Yang-Mills theory appears to contain an ambiguity. This ambiguity, in the case of boost-invariant flow, is linked with a similar freedom on the gravity side. This leads to a phenomenolo…
We present the long-wavelength effective description of non-extremal spinning black D3-branes in flat space. Our setup is motivated by recent explorations of low energy dynamics on black brane world-volumes within the blackfold approach and its connections to the fluid/gravity correspondence. The spinning D3-branes with a rigid radial Dirichlet cut-off give rise to an effective field theory. This theory describes a charged plasma which is driven by external forces, given by one vector and two scalar operators. Furthermore, the flavour charge of this plasma is anomalous, allowing us to examine …
We construct $SL(2,R)$ invariant in anisotropic medium, with a dual anisotropic charged black hole geometry in massive gravity. We show how to obtain $SL(2,R)$ elements in terms of new degrees of freedom for Electromagnetic configuration, and construct the general expressions for conductivity with $SL(2,R)$ invariant. The holographic conductivities can be calculated using horizon data in an external magnetic field, and we show the numerical results using the linear response theory.
The entropy of the Reissner-Nördstrom black hole is studied within the context of a brane-world scenario. Such a black hole is a solution of the Einstein field equations on the brane, possessing a tidal charge which is a reflection of the extra dimension. We use the modified dispersion relation to obtain the entropy of such brane-world black holes. The resulting entropy differs from that of the standard Bekenstein-Hawking's and contains information on the extra dimension.
We investigate thermodynamic and dynamical stability of a family of six-dimensional braneworld solutions with de Sitter branes. First, we investigate thermodynamic stability in terms of de Sitter entropy. We see that the family of solutions is divided into two distinct branches: the high-entropy branch and the low-entropy branch. By analogy with ordinary thermodynamics, the high-entropy branch is expected to be stable and the low-entropy branch to be unstable. Next, we investigate dynamical stability by analyzing linear perturbations around the solutions. Perturbations are decomposed into scal…
A family of deformed AdS$_5$-Schwarzschild black branes is here derived, employing the membrane paradigm of AdS/CFT. The solution of the Einstein-Hilbert action, with the Gibbons-Hawking term and a counter-term that eliminates eventual divergences, yields a partition function associated with the dual theory which allows the computation of the entropy, pressure and free energy, as state functions, in the canonical ensemble. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio, then restricting the range of the parameter that defines a family of defor…
In the context of string theory, it is possible to explain the microscopic origin of the entropy of certain black holes in terms of D-brane systems. To date, most of the cases studied in detail refer to extremal (supersymmetric) or near-extremal black holes. In this work we propose a microscopic model for certain black branes (extended versions of black holes) which would apply to cases arbitrarily far from extremality, including the Schwarzschild case. The model is based on a system of D-branes and anti-D-branes, and is able to reproduce several properties of the corresponding supergravity so…
A proposal towards a microscopic understanding of the Bekenstein-Hawking entropy for D=4 spacetimes with event horizon is made. Since we will not rely on supersymmetry these spacetimes need not be supersymmetric. Euclidean D-branes which wrap the event horizon's boundary will play an important role. After arguing for a discretization of the Euclidean D-brane worldvolume based on the worldvolume uncertainty relation, we count chainlike excitations on the worldvolume of specific dual Euclidean brane pairs. Without the need for supersymmetry it is shown that one can thus reproduce the D=4 Bekenst…
We study the entanglement entropy for open bosonic strings on multiple $Dp$-branes by using the covariant open string field theory. Choosing one of the spatial coordinates which are tangential to the hyperplane on which $Dp$-branes are located, we divide the hyperplane into two halves. By using the string wavefunction in the Fock space representation, we evaluate the entanglement entropy. The entanglement entropy is found to be proportional to the area of $(p-1)$-dimensional boundary of the bipartite hyperplanes and divergent in the ultraviolet (UV) region as well as in the infrared (IR) regio…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
We study the relation between approximate horizon symmetries of AdS black branes and approximately conserved currents in their dual hydrodynamic description. We argue that the existence of an approximately conserved enstrophy current unique to $2+1$ dimensional fluid flow implies that AdS${}_4$ black branes possess a special class of approximate supertranslations (which we identify).
A Lifshitz black brane at generic dynamical critical exponent $z > 1$, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz p…
We examine the hydrodynamic limit of non-conformal branes using the recently developed precise holographic dictionary. We first streamline the discussion of holography for backgrounds that asymptote locally to non-conformal brane solutions by showing that all such solutions can be obtained from higher dimensional asymptotically locally AdS solutions by suitable dimensional reduction and continuation in the dimension. As a consequence, many holographic results for such backgrounds follow from the corresponding results of the Asymptotically AdS case. In particular, the hydrodynamics of non-confo…
We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at $z=1/2$. The cosmological constant depends on $z$ as $Λ=-(1+2z)/L^{2}$. We compute the shear viscosity in the 2+1-dimensional dual boundary field theory via holographic correspondence. We investigate the violation of the bound for viscosity to entropy density ratio of $η/s\geq1/(4π)$ at $z=1/2$.
We show that a model based on a D3-brane--anti-D3-brane system at finite temperature, proposed previously as a microscopic description of the non-rotating black threebrane of type IIB supergravity arbitrarily far from extremality, can also successfully reproduce the entropy of the rotating threebrane with arbitrary charge (including the neutral case, which corresponds to the Kerr black hole in seven dimensions). Our results appear to confirm in particular the need for a peculiar condition on the energy of the two gases involved in the model, whose physical interpretation remains to be elucidat…
A family of deformed AdS4-Reissner-Nordström black branes, governed by a free parameter, is derived using the ADM formalism, in the context of the membrane paradigm. Their new event horizons, the Hawking temperature and other aspects are scrutinized. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio for the deformed AdS4-Reissner-Nordström metric. The Killing equation is shown to yield new values for the free parameter and the shear viscosity-to-entropy ratio is used to derive a reliable range for tidal charge.
We consider tachyon effective theory with Born-Infeld electromagnetic fields and investigate the configurational entropy of the various tachyon kink solutions. We find that the configurational entropy stats at a minimum value and saturates to a maximum value as the negative pressure of pure tachyonic field increases. In particular, when an electric field is turned on and its magnitude is larger than or equal to the critical value, we find the configurational entropy has a global minimum, which is related to the predominant tachyonic states.
We investigate the geometry of lightsheets comprised of null geodesics near a brane. Null geodesics which begin parallel to a brane a distance d away are typically gravitationally bound to the brane, so that the maximum distance from the geodesic to the brane never exceeds d. The geometry of resulting lightsheets is similar to that of the brane if one coarse grains over distances of order d. We discuss the implications for the covariant entropy bound applied to brane worlds.
Assuming $ω=\sum_n C^{(n)}q^{2n}$ in the low-frequency limit, we apply the refined recipe to compute the dispersion relation of shear quasinormal modes of the Gauss-Bonnet black brane. Treating the Gauss-Bonnet parameter $\lagb$ nonperturbatively and the momentum $q$ perturbatively, we work out $C^{(1)}$, $C^{(2)}$, confirm previous results in the literature and pave the way to a general formula for $C^{(n)}$.
In this paper, we focus on the possible correlation between conjectures KSS bound and weak gravity conjecture (WGC). The hydrodynamic values KSS bound and weak gravity conjecture constraint the low-energy effective field theory. These conjectures identify UV complete theories. We give four, six and eight order derivative corrections to corresponding action and employ the hyperscaling violating charged AdS$_{d+2}$ black brane solution. These corrections lead us to find correlation between conjectures KSS bound and weak gravity conjecture. We see that, with increasing perturbation correction, th…
In this paper we consider a metric with hyperscaling violation on black brane background. In this background we calculate the ratio of shear viscosity to entropy density with hydrodynamics information. The calculation of this quantity lead us to constraint $θ$ as $3\leqθ<4$, and $θ\leq0$. In that case we show that the quantity of $\fracη{s}$ not dependent to hyperscaling violation parameter $θ.$ Our results about ratio of shear viscosity to entropy density in direct of $QCD$ point of view agree with other works in literature as $1/4π$.
We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral …
We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4π. This ratio continues to be $1/4π$ also in the regime when the D1-brane Yang-Mills theory is dual to the gravitation…
Dynamical Chern-Simons (DCS) theory is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity violating term. We study perturbations of anti-de Sitter black holes and branes in such a theory, and show that the relevant equations reduce to a set of coupled ODEs which can be solved efficiently through a series expansion. We prove numerically that black holes and branes in DCS gravity are stable against gravitational and scalar perturbations in the entire parameter space. Furthermore, by applying the AdS/CFT duality, we relate black hole …
We construct effective hydrodynamics for composite particles in (2+1) dimensions carrying a magnetic flux by employing a holographic approach. The hydrodynamics is obtained by perturbation of the dyonic black brane solutions in the derivative expansion. We introduce a consistent way to avoid mixing of different orders in the expansion. Thanks to this method, it is possible to take the strong external magnetic field limit in the dual field theory. To compare our result with those for a composite particle system, we study several cases that correspond to special solutions of Einstein's equation …
We investigate the stability of the extremal black p-brane which contains a n-form and a dilaton. We show that the instability due to the s-mode, which was present in the uncharged and non-extremal p-brane, disappears in the extreme case. This is shown to be consistent with an entropy argument which shows that the zero entropy of the extremal black hole is approached more rapidly than the zero entropy of the black p-brane, which would mean an instability would violate the second law of thermodynamics.
The quantum corrections to the counting of statistical entropy for the 5+1-dimensional extremal black string in type-IIB supergravity with two observers are studied using anomalous Wess-Zumino actions for the corresponding intersecting D-brane description. The electric-magnetic duality symmetry of the anomalous theory implies a new symmetry between D-string and D-fivebrane sources and renders opposite sign for the RR charge of one of the intersecting D-branes relative to that of the black string. The electric-magnetic symmetric Hilbert space decomposes into subspaces associated with interior a…
We obtain new transport coefficients of causal hydrodynamics for the M2 and the M5-brane using a Kubo-like formula proposed by Baier, Romatschke, Son, Starinets, and Stephanov (arXiv:0712.2451 [hep-th]). The relaxation times agree with the ones obtained from the "sound mode" in our paper (arXiv:0712.2916 [hep-th]).
By using the quantum tunneling approach over semiclassical approximations, we study the quantum corrections to the Hawking temperature, entropy and Bekenstein-Hawking entropy-area relation for a black hole lying on a brane.
The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the actio…
A black brane solution to a Gauss-Bonnet massive gravity is introduced. In the context of AdS/CFT correspondence, the viscosity to entropy ratio is found by the Green-Kubo formula. The result indicates violation of the well-known KSS bound as expected in a higher derivative theory. Setting mass zero gives back the known viscosity to entropy ratio dependent on the Gauss-Bonnet coupling, while without Gauss-Bonnet term, a nonzero mass parameter doesn't contribute to the ratio which saturates the bound of $1/4π$.
We construct a new class of 4-dimensional z=2 Lifshitz black branes that have a nonzero linear momentum. These are solutions of an Einstein-Proca-dilaton model that can be obtained by Scherk-Schwarz circle reduction of AdS_5 gravity coupled to a free real scalar field. The boundary of a bulk Lifshitz space-time is a Newton-Cartan geometry. We show that the fluid dual to the moving Lifshitz black brane leads to a novel form of Lifshitz hydrodynamics on a Newton-Cartan space-time. Since the linear momentum of the black brane cannot be obtained by a boost transformation the velocity of the fluid …
Entropy bounds applied to a system of N species of light quantum fields in thermal equilibrium at temperature T are saturated in four dimensions at a maximal temperature T_max=M_Planck/N^1/2. We show that the correct setup for understanding the reason for the saturation is a cosmological setup, and that a possible explanation is the copious production of black holes at this maximal temperature. The proposed explanation implies, if correct, that N light fields cannot be in thermal equilibrium at temperatures T above T_max. However, we have been unable to identify a concrete mechanism that is ef…
We complete the computation of viscous transport coefficients in the near horizon geometries that arise from a stack of black Dp-branes for p=2,...,6 in the decoupling limit. The main new result is the obtention of the bulk viscosity which, for all p, is found to be related to the speed of sound by the simple relation ζ/η= -2(v_s^2-1/p). For completeness the shear viscosity is rederived from gravitational perturbations in the shear and scalar channels. We comment on technical issues like the counterterms needed, or the possible dependence on the conformal frame.
A general black-branes system under the T-duality transformation will become another smeared system with different dimensional black branes. We first use some simple examples to see that both systems have a same value of entropy and then present a rigorous method to prove this general property. Using the property we could easily know the entropy of some complex black-brane systems.
We show that the exact entropy and the temperature (including coeffecient) of non-extremal black p-brane are calculated by maximizing the entropy under several assumptions. We argue the relation of those assumptions and certain Dp-D(p-2) system in compactified space.
At energies higher than the brane tension, the dynamics of a scalar field rolling down a potential are modified relative to the predictions of General Relativity. The modifications imply, among other things, that steeper potentials can be used to drive an epoch of slow--roll inflation. We investigate the evolution of entropy and adiabatic modes during inflation driven by two scalar fields confined on the brane. We show that the amount of entropy perturbations produced during inflation is suppressed compared to the predictions made by General Relativity. As a consequence, the initial conditions…
We examine in details the entropy function formalism for non-extremal D3, M2, and M5-branes that their throat approximation is given by Schwarzschild black hole in AdS_{p+2} \times S^{D-(p+2)}. We show that even though there is no attractor mechanism in the non-extremal black holes/branes, the entropy function formalism does work and the entropy is given by the entropy function at its saddle point.
We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all o…
A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the D- and M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation, and information loss; D-branes as probes of black holes; and the Matrix theory approach to charged and neutral black holes. Some introductory material is included.
It is shown that quantum-induced (inflationary) brane Universe occurs in the bulk 5d AdS black hole in accordance with AdS/CFT correspondence. Brane stress tensor is induced by quantum effects of dual CFT and brane crosses the horizon of AdS black hole. Quantum-corrected Hubble constant, Hawking temperature and entropy are found on the brane (and at the horizon). The similarity between CFT entropy at the horizon and FRW equations is extended on the quantum level. This suggests the way to understand cosmological entropy bounds in quantum gravity.
We consider asymptotically-AdS $n$-dimensional black brane solutions in a theory of gravity coupled to a set of $N$ $p$-form field strengths, in which the field strengths carry magnetic charges. For appropriately chosen charges, the metrics are isotropic in the $(n-2)$ transverse directions. However, in general the field strength configurations break the full Euclidean symmetry of the $(n-2)$-dimensional transverse space. We then study the linearised equation for transverse traceless metric perturbations in these backgrounds, and by employing the Kubo formula we obtain expressions for $η/S$, t…
We study the long-wavelength effective description of two general classes of charged dilatonic (asymptotically flat) black p-branes including D/NS/M-branes in ten and eleven dimensional supergravity. In particular, we consider gravitational brane solutions in a hydrodynamic derivative expansion (to first order) for arbitrary dilaton coupling and for general brane and co-dimension and determine their effective electro-fluid-dynamic descriptions by exacting the characterizing transport coefficients. We also investigate the stability properties of the corresponding hydrodynamic systems by analyzi…
In this work an algorithm is proposed to calculate entropy for field theories living on NS five branes, which gives a result invariant under T-duality. This is a deformation of the well known Ryu-Takayanagi formula, which takes into account dependence of localized backgrounds for the branes on winding modes of strings.
We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the left-moving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. W…
An M-brane and anti-M-brane scheme is proposed to study nonextremal 4D and 5D black holes. The improved nonextremal intersecting M-brane solutions proposed here, involve two sets of harmonic functions. The constraints among the pressures are found, and new features in the M-brane and anti-M-brane picture are demonstrated, which resolve the discrepancy in the number of free parameters in the D-brane picture. In terms of the ``numbers'' of M-branes and anti-M-branes, the prefactors of the entropies are found to be model independent, and the Bekenstein-Hawking entropy assumes the duality invarian…
The entropy of the four dimensional Schwarzschild black hole is derived by mapping it onto a configuration of intersecting branes with four charges. This configuration is obtained by performing several boosts and dualities on a neutral black brane of M-theory to which the Schwarzschild black hole is related by trivial compactification. The infinite boost limit is well-defined and corresponds to extremality where the intersecting brane configuration is a marginal one on which a standard microscopic counting of the entropy can be safely performed. The result reproduces exactly the Bekenstein-Haw…
The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both…
We study two-dimensional eternal black holes with non-zero mass, where each asymptotic boundary is in contact with a CFT on a circle, following the doubly holographic braneworld models constructed in [arXiv:2006.04851, arXiv:2010.00018, arXiv:2010.16398]. We compute the Page curve of the black hole (or the bath CFTs), which amounts to finding different geodesics in the bulk BTZ geometry with a Randall-Sundrum brane falling into the black hole. We also explore the possibility of including an intrinsic JT gravity action on the brane. As expected, the generalized entropy rises linearly at early t…
We discuss the known microscopic interpretations of the Bekenstein-Hawking entropy for configurations of intersecting M-branes. In some cases the entropy scales as that of a massless field theory on the intersection. A different situation, found for configurations which reduce to 1-charge D=5 black holes or 2-charge D=4 black holes, is explained by a gas of non-critical strings at their Hagedorn temperature. We further suggest that the entropy of configurations reducing to 1-charge D=4 black holes is due to 3-branes moving within 5-branes.
We study the time evolution of entanglement entropy in expanding universes with various matters. To describe expanding universes holographically, we take into account a braneworld moving in an asymptotic AdS space involving a uniform $p$-brane gas. In the braneworld model, an observer living in the braneworld detects the bulk motion of the braneworld as an expanding universe. We show that the entanglement entropy of expanding universes increases by the volume law in the early time and by the area law in the late time. We further consider the cosmological horizon, which is the border of the vis…
The thick brane scenario built on the f(T,B) teleparallel gravity theory was considered for the study of phase transitions, internal structures, and new classes of solutions in a model. In this theory, T denotes the torsion scalar, and B is a boundary term. An interesting result was observed when brane splitting occurs, i. e., internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multi-kink) so that for appropriate values of the parameters $k_{1,2}$ m…
The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT which lives on the brane by using Friedmann-Robertson-Walker (FRW) equations and Cardy-Verlinde formula is discussed. We show that when the time-like brane crosses the black hole horizon of dS Schwarzschild black hole, the entropy of the CFT exactly agrees with the black hole entropy of 5-dimensional dS background.
