We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian containing the information about the elastic dynamics of the brane embedding as well as the hydrodynamics of the effective fluid living on the brane. The Lagrangian is corrected order-by-order in a derivative expansion, where we take into account the dipole moment of the brane which encompasses finite-thickness corrections, including transverse spin. We describe how to extract the thermodynamics from the Lagrangian and we obtain constraints on the higher-derivative terms with one and two derivatives. These constraints follow by comparing the brane thermodynamics with the conserved currents associated with background Killing vector fields. In particular, we fix uniquely the one- and two-derivative terms describing the coupling of the transverse spin to the background space-time. Finally, we apply our formalism to two blackfold examples, the black tori and charged black rings and compare the latter to a numerically generated solution.
Fluid mechanics can be formulated on dynamical surfaces of arbitrary co-dimension embedded in a background space-time. This has been the main object of study of the blackfold approach in which the emphasis has primarily been on stationary fluid configurations. Motivated by this approach we show under certain conditions that a given stationary fluid configuration living on a dynamical surface of vanishing thickness and satisfying locally the first law of thermodynamics will behave like an elastic brane when the surface is subject to small deformations. These results, which are independent of th…
We demonstrate complete integrability of the Nambu-Goto equations for a stationary string in the general Kerr-NUT-(A)dS spacetime describing the higher-dimensional rotating black hole. The stationary string in D dimensions is generated by a 1-parameter family of Killing trajectories and the problem of finding a string configuration reduces to a problem of finding a geodesic line in an effective (D-1)-dimensional space. Resulting integrability of this geodesic problem is connected with the existence of hidden symmetries which are inherited from the black hole background. In a spacetime with p m…
We present recent results on the asymptotics of a brane-world that consists of a flat 3-brane embedded in a five-dimensional bulk. The bulk matter is modelled by a fluid that satisfies a nonlinear equation of state. We show that for appropriate ranges of the equation of state parameters, it is possible to construct a regular solution, compatible with energy conditions, that successfully localizes gravity on the brane. These results improve significantly previous findings on the study of a bulk fluid with a linear equation of state.
We construct a regular five-dimensional brane-world with localised gravity on a flat 3-brane. The matter content in the bulk is parametrised by an analog of a non-linear fluid with equation of state $p=γρ^λ$ between the `pressure' $p$ and the `density' $ρ$ dependent on the 5th dimension. For $γ$ negative and $λ>1$, the null energy condition is satisfied, and the geometry is free of singularities within finite distance from the brane, while the induced four-dimensional Planck mass is finite.
Two flat Randall - Sundrum three-branes are analyzed, at fixed mutual distance, in the case where each brane contains an ideal isotropic fluid. Both fluids are to begin with assumed to obey the equation of state p=(γ-1)ρ, where γis a constant. Thereafter, we impose the condition that there is zero energy flux from the branes into the bulk, and assume that the tension on either brane is zero. It then follows that constant values of the fluid energies at the branes are obtained only if the value of γis equal to zero (i.e., a `vacuum' fluid). The fluids on the branes are related: if one brane is …
We study a stationary "black" brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a traveling wave for the Einstein equations in $D$-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2-M5 intersectin…
We consider the lower bound for the shear viscosity-to-entropy density ratio, obtained from the fluid/gravity correspondence, in order to constrain the post-Newtonian parameter of brane-world metrics. In particular, we analyse the Casadio-Fabbri-Mazzacurati (CFM) effective solutions for the gravity side of the correspondence and argue that including higher order terms in the hydrodynamic expansion can lead to a full agreement with the experimental bounds, for the Eddington-Robertson-Schiff post-Newtonian parameter in the CFM metrics. This lends further support to the physical relevance of the …
An effective fluid description, for a brane world model in five dimensions, is discussed for both signs of the brane tension. We found several cosmological scenarios where the effective equation differs widely from the bare equation of state. For universes with negative brane tension, with a bare fluid satisfying the strong energy condition, the effective fluid can cross the barrier $ω_{eff} =-1$.
Bianchi black branes (black brane solutions with homogeneous but anisotropic horizons classified by the Bianchi type) provide a simple holographic setting with lattice structures taken into account. In the case of holographic superconductor, we have a persistent current with lattices. Accordingly, we expect that in the dual gravity side, a black brane should carry some momentum along a direction of lattice structure, where translational invariance is broken. Motivated by this expectation, we consider whether---and if possible, in what circumstances---a Bianchi black brane can have momentum alo…
Using the method of asymptotic splittings, the possible singularity structures and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk are classified, in the case where the bulk field content is parametrized by an analog of perfect fluid with an arbitrary equation of state $P=γρ$ between the `pressure' $P$ and the `density' $ρ$. In this analogy with homogeneous cosmologies, the time is replaced by the extra coordinate transverse to the 3-brane, whose world-volume can have an arbitrary constant curvature. The results depend crucially on the constant parameter $γ$: (i) …
We develop a technique to study relativistic perturbations in the generalised brane cosmological scenario, which is a generalisation of the multi-fluid cosmological perturbations to brane cosmology. The novelty of the technique lies in the inclusion of a radiative bulk which is responsible for bulk-brane energy exchange, and in turn, modifies the standard perturbative analysis to a great extent. The analysis involves a geometric fluid -- called the Weyl fluid -- whose nature and role have been studied extensively both for the empty bulk and the radiative bulk scenario. Subsequently, we find th…
The Shiromizu et al. \cite{SMS} covariant decomposition formalism is used to find out the brane properties rooted from the 5-dimensional Witten bubble spacetime. The non-local tensor $E_{ab}$ generated by the 5-dimensional Weyl tensor gives rise at an anisotropic energy-momentum tensor on the brane with negative energy density and $p = ρ/3$ as equation of state. The tidal acceleration is towards the brane and that is in accordance with the negative energy density on the brane. The anisotropic fluid has vanishing "bulk" viscosity but the shear viscosity coefficient is $r$- and $t$- dependent. T…
We first obtain the analogue of Vaidya's solution on the brane for studying the collapse of null fluid onto a flat Minkowski cavity on the brane. Since the back-reaction of the bulk onto the brane is supposed to strengthen gravity on the brane, it would favour formation of black hole as against naked singularity. That is the parameter window in the initial data set giving rise to naked singularity in the 4D Vaidya case would now get partially covered.
We derive all the dynamical second order transport coefficients for Dp-brane with $p$ from 1 to 6 within the framework of fluid/gravity correspondence in this paper. The D5 and D6-brane do not have dual relativistic fluids; D3-brane corresponds to 4-dimensional conformal relativistic fluid; D1, D2 and D4-brane separately correspond to nonconformal relativistic fluids of dimensions 2, 3 and 5. The Haack-Yarom relation only exists for Dp-branes with $p$ larger than 2 and is also satisfied by them. We also find that the Romatschke and Kleinert-Probst relations need to be generalized in order to b…
Backgrounds depending on time and on "angular" variable, namely polarized and unpolarized $S^1 \times S^2$ Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary $D$-branes, $iD$-branes allows one to find $S$-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzchild and the Kerr metrics. The possibility of studying the $i$-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generali…
A family of spherically symmetric solutions with horizon in the model with m-component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n-1 Ricci-flat "internal" spaces. The equation of state for any s-th component is defined by a vector U^s belonging to R^{n + 1}. The solutions are governed by moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M_2-M_5 configuration (in D…
The glueball dark matter, in the pure SU(N) Yang-Mills theory, engenders dark SU(N) stars that comprise self-gravitating compact configurations of scalar glueball fields. Corrections to the highest frequency of gravitational wave radiation emitted by dark SU(N) star mergers on a fluid brane with variable tension, implemented by the minimal geometric deformation, are derived and their consequences analysed. Hence, dark SU(N) stars mergers on a fluid brane-world are shown to be better detectable by the LIGO and the eLISA experiments.
All the 7 dynamical second order transport coefficients of the nonconformal fluids that correspond to Dp-branes with one or more world-volume directions compactified are derived via fluid/gravity correspondence. The conditions considered in this paper include D4-brane with 1, 2 or 3 compact directions, D3-brane with 1 or 2 compact directions, as well as D2-brane with 1 direction compactified. The derived second order transport coefficients satisfy the Haack-Yarom, Romatschke and Kleinert-Probst relations.
A class of generalized Randall-Sundrum type II (RS) brane-world models with Weyl fluid are confronted with the Gold supernovae data set and BBN constraints. We consider three models with different evolutionary history of the Weyl fluid, characterized by the parameter $α$. For $α=0$ the Weyl curvature of the bulk appears as dark radiation on the brane, while for $α=2$ and 3 the brane radiates, leaving a Weyl fluid on the brane with energy density decreasing slower than that of (dark) matter. In each case the contribution $Ω_d$ of the Weyl fluid represents but a few percent of the energy content…
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 review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a `perfect fluid' with an equation of state with the `pressure' and the `density' of the fluid depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane with an EoS parameter equal to -1, or of AdS branes for EoS parameter values in suitable intervals. More cases can be found by gluing two regular branches of solutions at the position of the brane. However, …
We assume a flat brane located at y=0, surrounded by an AdS space, and consider the 5D Einstein equations when the energy flux component of the energy-momentum tensor is related to the Hubble parameter through a constant Q. We calculate the metric tensor, as well as the Hubble parameter on the brane, when Q is small. As a special case, if the brane is tensionless, the influence from Q on the Hubble parameter is absent. We also consider the emission of gravitons from the brane, by means of the Boltzmann equation. Comparing the energy conservation equation derived herefrom with the energy conser…
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 vorticity statistics characterises both the direct and the inverse turbulent cascades of two-dimensional fluid flows. The fluid/gravity correspondence relates fluid flows to black brane dynamics. We construct the holographic vorticity for relativistic and non-relativistic fluids in terms of the gravitational black brane data, and relate it to the horizon vorticity expressed as a Weyl scalar. We discuss the statistical scaling structure of the horizon geometry.
We consider the dynamics of a viscous cosmological fluid in the generalized Randall-Sundrum model for an isotropic brane. To describe the dissipative effects we use the Israel-Hiscock-Stewart full causal thermodynamic theory. In the limiting case of a stiff cosmological fluid with pressure equal to the energy density, the general solution of the field equations can be obtained in an exact parametric form for a cosmological fluid with constant bulk viscosity and with a bulk viscosity coefficient proportional to the square root of the energy density, respectively. The obtained solutions describe…
We study the problem of evolution of bulk 5-fluids having an embedded braneworld with a flat, de Sitter, or anti-de Sitter geometry. We introduce new variables to express the Einstein equations as a dynamical system that depends on the equation of state parameter $γ$ and exponent $λ$. For linear fluids (i.e., $λ=1$), our formulation leads to a partial decoupling of the equations and thus to an exact solution. We find that such a fluid develops a transcritical bifurcation around the value $γ=-1/2$, and study how this behaviour affects to stability of the solutions. For nonlinear fluids, the sit…
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parametrizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite distance singularity contrary to previous claims. We then study the possibility of avoiding finite distance singularities by cutting the bulk and gluing…
We investigate constraints for including bulk and brane matter in the Randall- Sundrum model. In static configurations with two zero thickness branes, we find that no realistic brane matter is possible. We also consider the possibility that the radion has stabilized by dissipating its energy into the bulk in the form of some unspecified matter, and find the Randall-Sundrum cosmological solutions in the presence of bulk ideal fluid. We discover that the metric is necessarily in a static configuration. We also discover that there is only one allowed equation of state for the bulk fluid, $p=ρ$, c…
By considering 5--dimensional cosmological models with a bulk filled with a perfect fluid and a cosmological constant, we have found regular instantonic solution which is free from any singularity at the origin of the extra--coordinate and describe 5--dimensional asymptotically anti de Sitter wormhole, when the bulk has a topology $ R \times S^4 $ and is filled with dust and a negative cosmological constant. Compactified brane-world instantons which are built up from such instantonic solution describe either a single brane or a string of branes. Their analytical continuation to the pseudo--Rie…
In this talk, I review how four dimensional stationary supergravity solutions that are more general than spherically symmetric black holes emerge naturally in the low energy description of BPS states in type II Calabi-Yau compactifications. An explicit construction of multicenter solutions using single center attractor flows as building blocks is presented, and some interesting properties of these solutions are examined. We end with a brief remark on non-BPS configurations.
We consider 5D brane world models with broken global 4D Poincar\a'{e} invariance (4D part of the spacetime metric is not conformal to the Minkowski spacetime). The bulk is filled with the negative cosmological constant and may contain a perfect fluid. In the case of empty bulk (the perfect fluid is absent), it is shown that one brane solution always has either a physical or a coordinate singularity in the bulk. We cut off these singularities in the case of compact two brane model and obtain regular exact solutions for both 4D Poincar\a'{e} broken and restored invariance. When the perfect fluid…
The brane world description of our universe entails a large extra dimension and a fundamental scale of gravity that may be lower than the Planck scale by several orders of magnitude. An interesting consequence of this scenario occurs in the nature of spherically-symmetric vacuum solutions to the brane gravitational field equations, which often have properties quite distinct from the standard black hole solutions of general relativity. In this paper, the spherically-symmetric collapse on the brane world of four types of null fluid, governed by the barotropic, polytropic, strange quark "bag" mod…
We study long wavelength perturbations of neutral black p-branes in asymptotically flat space and show that, as anticipated in the blackfold approach, solutions of the relativistic hydrodynamic equations for an effective p+1-dimensional fluid yield solutions to the vacuum Einstein equations in a derivative expansion. Going beyond the perfect fluid approximation, we compute the effective shear and bulk viscosities of the black brane. The values we obtain saturate generic bounds. Sound waves in the effective fluid are unstable, and have been previously related to the Gregory-Laflamme instability…
We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi type I geometry, with a generalized Chaplygin gas as matter source. The generalized Chaplygin gas, which interpolates between a high density relativistic era and a non-relativistic matter phase, is a popular dark energy candidate. For a Bianchi type I space-time brane filled with a cosmological fluid obeying the generalized Chaplygin equation of state the general solution of the gravitational field equations can be expressed in an exact parametric form,…
A (1 + d)-dimensional thick "brane world" model with varying Lambda-term is considered. The model is generalized to the case of a chain of Ricci-flat internal spaces when the matter source is an anisotropic perfect fluid. The "horizontal" part of potential is obtained in the Newtonian approximation. In the multitemporal case (with a Lambda-term) a set of equations for potentials is presented.
Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalize…
The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analogue of perfect fluid with an arbitrary equation of state P=γρbetween the `pressure' P and …
In the current letter, we study isotropic static spherically symmetric gravastars without charge under the framework of braneworld gravity (dimensionally reduced RS-II braneworld with positive brane tension) using the metric potential of Kuchowicz type (which is physically acceptable, non-singular and stable) in the Mazur-Motolla conjuncture. We derived the Kuchowicz free parameters from the junction conditions assuming Schwarzschild vacuum without cosmological constant. As well, we assume that the interior is filled with Dark Energy (DE-like) fluid, shell with ultrarelativistic stiff fluid. A…
We develop the boundary derivative expansion (BDE) formalism of fluid/gravity correspondence to nonconformal version through the compactified, near-extremal black D4-brane. We offer an explicit calculation of 9 second order transport coefficients, i.e., the $τ_π,~τ_π^*,~τ_Π,~λ_{1,2,3}$ and $ξ_{1,2,3}$ for the strongly coupled, uncharged and nonconformal relativistic fluid which is the holographic dual of compactified, near extremal black D4-brane. We also show that the nonconformal fluid considered in this work is free of causal problem and admits the Haack-Yarom relation $4λ_1+λ_2=2ητ_π$.
Stationary, D-dimensional test branes, interacting with N-dimensional Myers-Perry bulk black holes, are investigated in arbitrary brane and bulk dimensions. The branes are asymptotically flat and axisymmetric around the rotation axis of the black hole with a single angular momentum. They are also spherically symmetric in all other dimensions allowing a total of O(1)xO(D-2) group of symmetry. It is shown that even though this setup is the most natural extension of the spherical symmetric problem to the simplest rotating case in higher dimensions, the obtained solutions are not compatible with t…
We consider Sen's effective action for unstable D-branes, and study its classical dynamics exactly. In the true vacuum, the Hamiltonian dynamics remains well-defined despite a vanishing action, and is that of massive relativistic string fluid of freely moving electric flux lines. The energy(tension) density equals the flux density in the local co-moving frame. Furthermore, a finite dual Lagrangian exists and is related to the Nielsen-Olesen field theory of ``dual'' strings, supplemented by a crucial constraint. We conclude with discussion on the endpoint of tachyon condensation.
We study interaction of rotating higher dimensional black holes with a brane in space-times with large extra dimensions. We demonstrate that in a general case a rotating black hole attached to a brane can loose bulk components of its angular momenta. A stationary black hole can have only those components of the angular momenta which are connected with Killing vectors generating transformations preserving a position of the brane. In a final stationary state the null Killing vector generating the black hole horizon is tangent to the brane. We discuss first the interaction of a cosmic string and …
We show how braneworld cosmology with bulk matter can explain structure formation. In this scenario, the nonlocal corrections to the Friedmann equations supply a Weyl fluid that can dominate over matter at late times due to the energy exchange between the brane and the bulk. We demonstrate that the presence of the Weyl fluid radically changes the perturbation equations, which can take care of the fluctuations required to account for the large amount of inhomogeneities observed in the local universe. Further, we show how this Weyl fluid can mimic dark matter. We also investigate the bulk geomet…
By using the boundary derivative expansion formalism of fluid/gravity correspondence, we study the chiral vortical effect from the compactified D4-branes with smeared D0-brane charge. This background corresponds to a strongly coupled, nonconformal relativistic fluid with a conserved vector current. The presence of the chiral vortical effect is induced by the addition of a Chern-Simons term in the bulk action. Except that the non-dissipative anomalous viscous coefficient and the sound speed rely only on the chemical potential, most of the other thermal and hydrodynamical quantities of the first…
Using branes in massive Type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. The filling fraction is given by the ratio of the number of D2-branes and the number of D8-branes, and therefore by the ratio rank/level of the Chern-Simons gauge theory. Quasiparticles and quasiholes are realized…
The presence of a bulk viscosity for the cosmic fluid on a single Randall-Sundrum brane is considered. The spatial curvature is assumed to be zero. The five-dimensional Friedmann equation is derived, together with the energy conservation equation for the viscous fluid. These governing equations are solved for some special cases: (i) in the low-energy limit when the matter energy density is small compared with brane tension; (ii) for a matter-dominated universe, and (iii) for a radiation-dominated universe. Rough numerical estimates, for the extreme case when the universe is at its Planck time,…
Various fluid mechanical systems, governed by nonlinear differential equations, enjoy a hidden, higher-dimensional dynamical Poincaré symmetry, which arises owing to their descent from a Nambu-Goto action. Also, for the same reason, there are equivalence transformations between different models. These interconnections are discussed in this lecture, and are summarized in Fig. 3.
We develop the framework of boundary derivative expansion (BDE) formalism of fluid/gravity correspondence in compactified D4-brane system, which is a nonconformal background used in top-down holographic QCD models. Such models contain the D4-D6 model and the Sakai-Sugimoto (SS) model, with the background of the compactified black D4 branes under the near horizon limit. By using the dimensional reduction technique, we derive a 5D Einstein gravity minimally coupled with 3 scalar fields from the 10D D4-brane background. Following the BDE formalism of fluid/gravity correspondence in the conformal …
Flowing black holes are asymptotically locally AdS spacetimes that are stationary but have non-Killing horizons. Holographically, they are dual to a steady-state heat flow in the boundary field theory. We investigate the stability of these black holes in the limit in which they are well-described by the relativistic conformal Navier-Stokes equations. More precisely, we study the quasi-normal modes of the linearized ideal fluid equations. Though we find no unstable modes, there are an infinite number at finite transverse momentum which are arbitrarily long-lived. This suggests the possibility t…
We numerically construct large Randall-Sundrum II brane black holes in 4 and 5 dimensions from associated AdS/CFT spacetimes. Our solutions are leading order perturbations of a representative of the boundary conformal structure of the AdS spacetime sourced by the dual CFT stress tensor. The 4-dimensional solutions are static perturbations of the Euclidean Schwarzschild metric, while the 5-dimensional solutions are perturbations of the Myers-Perry metric with equal angular momenta. We compare the former with previous numerical results for Randall-Sundrum bulk black holes and find good agreement…
Recently a brane world perspective on the cosmological constant and the hierarchy problems was presented. Here, we elaborate on some aspects of that particular scenario and discuss the stability of the stationary brane solution and the dynamics of a probe brane. Even though the brane is unstable under a small perturbation from its stationary position, such instability is harmless when the 4-D cosmological constant is very small, as is the case of our universe. One may also introduce radion stabilizing potentials in a more realistic scenario.
It has been conjectured that at a stationary point of the tachyon potential for the D-brane of bosonic string theory, the negative energy density exactly cancels the D-brane tension. We evaluate this tachyon potential by off-shell calculations in open string field theory. Surprisingly, the condensation of the tachyon mode alone into the stationary point of its cubic potential is found to cancel about 70% of the D-brane tension. Keeping relevant scalars up to four mass levels above the tachyon, the energy density at the shifted stationary point cancels 99% of the D-brane tension.
In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The …
We examine several different types of five dimensional stationary spacetimes with bulk scalar fields and parallel 3-branes. We study different methods for avoiding the appearance of spacetime singularities in the bulk for models with and without cosmological expansion. For non-expanding models, we demonstrate that in general the Randall-Sundrum warp factor is recovered in the asymptotic bulk region, although elsewhere the warping may be steeper than exponential. We show that nonsingular expanding models can be constructed as long as the gradient of the bulk scalar field vanishes at zeros of th…
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 …
This monograph is derived from a series of six lectures I gave at the Centre de Recherches Mathematiques in Montreal, in March and June 2000, while titulary of the Aisenstadt Chair.
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eötvös. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a…
