Hristu Culetu
A classical membrane model is developed for a dynamic wormhole. Its throat expands hyperbolically with an acceleration proportional to the surface energy density $σ$. The model leads to a negative bulk viscosity coefficient $ζ= - 1/6 π$ on the throat, expressing the instability against perturbations (expansions or contractions).
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We shortly outline the principal results concerning the reparametrization-invariant world-volume Lagrangian formulation of lightlike brane dynamics and its impact as a source for gravity and (nonlinear) electromagnetism in black hole and wormhole physics.
We discuss the generalized Plateau problem in the 3+1 dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane (thin domain wall) is located near a black hole. Considering stationary axially symmetric membranes, three different membrane-topologies are possible depending on the boundary conditions at infinity: 2+1 Minkowski topology, 2+1 wormhole topology and 2+1 black hole topology. Interestingly, we find that the different membrane-topologies are connected via phase transitions of the fo…
We show that a generic relativistic membrane with in-plane pressure and surface density having the same sign is unstable with respect to a series of warping mode instabilities with high wave numbers. We also examine the criteria of instability for commonly studied exotic compact objects with membranes, such as gravastars, AdS bubbles and thin-shell wormholes. For example, a gravastar which satisfies the weak energy condition turns out to be dynamically unstable. A thin-layer black hole mimicker is stable only if it has positive pressure and negative surface density (such as a wormhole), or vic…
Black hole membrane paradigm suggests to consider the black hole horizon as a fluid membrane. The membrane has a particular energy-momentum tensor which characterizes the interactions with the falling matter. In this paper, we show that we can construct an action from the scalar field on the horizon which can give the same energy-momentum tensor for the membrane. That is, the membrane can be described effectively by the scalar field on it.
To an outside observer, a black hole's event horizon appears to behave exactly like a dynamical fluid membrane. We extend this membrane paradigm to black holes in general $f(R)$ theories of gravity. We derive the stress tensor and various transport coefficients of the fluid and find that the membrane behaves as a non-Newtonian fluid except for the special case of Einstein gravity. Using Euclidean methods, we study the thermodynamics of the membrane. We speculate on what theories of gravity admit horizons with fluid properties.
In this paper we aim to provide new examples of the application and the generality of the membrane paradigm. The membrane paradigm is a formalism for studying the event horizon of black holes. After analyzing it with some technical details and realizing it in the Reissner-Nordstrom black hole, we apply the paradigm to cosmological horizons, firstly to the pure de Sitter horizon, and then to the trapping horizon of the Friedmann-Lemaitre-Robertson-Walker universe. In the latter case, the cosmological stretched horizon is oblique, thus the running of renormalization parameter is nonzero in the t…
The membrane paradigm posits that black hole microstates are dynamical degrees of freedom associated with a physical membrane vanishingly close to the black hole's event horizon. The soft hair paradigm postulates that black holes can be equipped with zero-energy charges associated with residual diffeomorphisms that label near horizon degrees of freedom. In this essay we argue that the latter paradigm implies the former. More specifically, we exploit suitable near horizon boundary conditions that lead to an algebra of `soft hair charges' containing infinite copies of the Heisenberg algebra, ass…
Black rings are the black objects found in $D$ spacetime dimensional gravity when $D \geq 5$. These have event horizon topology $S^{D-3}\times S^1$. In this work the solutions of the large $D$ membrane paradigm dual to stationary black rings in Einstein-Maxwell theory with or without cosmological constant are studied. It is shown that the first order membrane equations can only admit static asymptotically flat black rings, and the equilibrium angular velocity for the asymptotically AdS black rings at large $D$ was obtained. The thermodynamic and dynamic stability of the asymptotically flat bla…
Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outsi…
We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.
We find the membrane equations which describe the leading order in $1/D$ dynamics of black holes in the $D\rightarrow\infty$ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor f…
One version of the membrane paradigm states that as far as outside observers are concerned, black holes can be replaced by a dissipative membrane with simple physical properties located at the stretched horizon. We demonstrate that such a membrane paradigm is incomplete in several aspects. We argue that it generically fails to capture the massive quasinormal modes, unless we replace the stretched horizon by the exact event horizon, and illustrate this with a scalar field in a BTZ black hole background. We also consider as a concrete example linearized metric perturbations of a five-dimensional…
We find the equations of motion of membranes dual to the black holes in Einstein-Gauss-Bonnet (EGB) gravity to leading order in 1/D in the large D regime. We also find the metric solutions to the EGB equations to first subleading order in 1/D in terms of membrane variables. We propose a world volume stress tensor for the membrane whose conservation equations are equivalent to the leading order membrane equations. We also work out the light quasi-normal mode spectrum of static black holes in EGB gravity from the linearised fluctuations of static, round membranes. Also, the effective equations f…
I discuss a correspondence between a fictitious fluid in the black hole membrane paradigm and highly excited closed string states according to the black hole correspondence principle. I calculate the membrane transport coefficients of an electric NS-NS 2-charged black hole and transport coefficients of the highly excited closed string states which possess a Kaluza-Klein number and a winding number. Comparing both the transport coefficients at the correspondence point, I show that, except for the bulk viscosity, the membrane transport coefficients are of the same order as the transport coeffici…
We study $SO(d+1)$ invariant solutions of the classical vacuum Einstein equations in $p+d+3$ dimensions. In the limit $d \to \infty$ with $p$ 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 $\frac{1}{d}$ 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 s…
We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes. From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum. The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken. The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically. Similarly, area preserving superrotations are spontaneously broken on the horizon membrane and we identify the corresponding gapless modes. In as…
In the large D limit, and under certain circumstances, it has recently been demonstrated that black hole dynamics in asymptotically flat spacetime reduces to the dynamics of a non gravitational membrane propagating in flat D dimensional spacetime. We demonstrate that this correspondence extends to all orders in a 1/D expansion and outline a systematic method for deriving the corrected membrane equation in a power series expansion in 1/D. As an illustration of our method we determine the first subleading corrections to the membrane equations of motion. A qualitatively new effect at this order i…
In [J. Blazquez-Salcedo, C. Knoll, E. Radu, Phys. Rev. Lett. 126 (2021) no.10, 101102] asymptotically flat traversable wormhole solutions were obtained in the Einstein-Dirac-Maxwell theory without using phantom matter. The normalizable numerical solutions found therein require a peculiar behavior at the throat: the mirror symmetry relatively the throat leads to the nonsmoothness of gravitational and matter fields. In particular, one must postulate changing of the sign of the fermionic charge density at the throat, requiring coexistence of particle and antiparticles without annihilation and pos…
Correspondences between black holes and fluids have been discussed in two different frameworks, the Fluid/Gravity correspondence and membrane paradigm. Recently, it has been discussed that these two theories can be understood as the same theory if the cutoff surface is placed slightly outside the horizon. The bulk viscosity is different for these two theories, but it does not contribute to physics since the fluid becomes incompressible in the near horizon limit. In the AdS/CFT correspondence, it is known that the fluid becomes compressible and the bulk viscosity is zero, apart from the near ho…
Membrane paradigm is a powerful tool to study properties of black hole horizons. We first explore the properties of the nonlinear electromagnetic membrane of black holes. For a general nonlinear electrodynamics field, we show that the conductivities of the horizon usually have off-diagonal components and depend on the normal electric and magnetic fields on the horizon. Via the holographic duality, we find a model-independent expression for the holographic DC conductivities of the conserved current dual to a probe nonlinear electrodynamics field in a neutral and static black brane background. I…
Following the Membrane Paradigm, we show that the stretched horizon of a black hole retains information about particles thrown into the hole for a time of order the scrambling time m ln(m/M_P), after the particles cross the horizon. One can, for example, read off the proper time at which a particle anti-particle pair thrown into the hole, annihilates behind the horizon, if this time is less than the scrambling time. If we believe that the Schwarzschild geometry exterior to the horizon is a robust thermodynamic feature of the quantum black hole, independent of whether it is newly formed, or has…
We consider the membrane viewpoint a là Parikh-Wilczek on the Kerr solution for a rotating black hole. Computing the stress-energy tensor of a close-to-the-horizon stretched membrane and comparing it to the stress-tensor of a viscous fluid, we recover transport coefficients in terms of the Kerr geometry. Viscosities of the dual fluid remain constant, while the rest of the transport coefficients become complex functions of radial and angle coordinates. We study the qualitative behavior of the pressure, expansion, and energy/momentum densities for two specific black holes: the slowly rotating bl…
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. The fluid dynamics of the membrane is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same.…
We show that at the level of linear response the low frequency limit of a strongly coupled field theory at finite temperature is determined by the horizon geometry of its gravity dual, i.e. by the "membrane paradigm" fluid of classical black hole mechanics. Thus generic boundary theory transport coefficients can be expressed in terms of geometric quantities evaluated at the horizon. When applied to the stress tensor this gives a simple, general proof of the universality of the shear viscosity in terms of the universality of gravitational couplings, and when applied to a conserved current it gi…
The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm appr…
In the membrane paradigm of black holes, it is usually assumed that the normal vector of the stretched horizon has a vanishing acceleration. This assumption breaks down for black bottles, a class of solutions discovered recently in the asymptotically anti-de Sitter spacetime. In this paper, the membrane paradigm is generalized to the stretched horizon with a nonvanishing acceleration of normal vector, and then it is applied to the static black bottle. In this example, the membrane stress tensor and the fluid quantities are similar to those of black holes, while the fluid continuity equation an…
The membrane paradigm approach adopts a timelike surface, stretched out off the null event horizon, to study several important black hole properties. We use this powerful tool to give a direct derivation of the black hole mass formula in the static and stationary cases without and with electric field. Since here the membrane is a self-gravitating material system we go beyond the usual applicability on test particles and test fields of the paradigm.
The membrane paradigm is the remarkable view that, to an external observer, a black hole appears to behave exactly like a dynamical fluid membrane, obeying such pre-relativistic equations as Ohm's law and the Navier-Stokes equation. It has traditionally been derived by manipulating the equations of motion. Here we provide an action formulation of this picture, clarifying what underlies the paradigm, and simplifying the derivations. Within this framework, we derive previous membrane results, and extend them to dyonic black hole solutions. We discuss how it is that an action can produce dissipat…
We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients ηand ζof the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associat…
The asymptotic symmetry group of three-dimensional (anti) de Sitter space is the two dimensional conformal group with central charge $c=3\ell/2G$. Usually the asymptotic charge algebra is derived using the symplectic structure of the bulk Einstein equations. Here, we derive the asymptotic charge algebra by a different route. First, we formulate the dynamics of the boundary as a 1+1-dimensional dynamical system. Then we realize the boundary equations of motion as a Hamiltonian system on the dual Lie algebra, $\mathfrak{g}^*$, of the two-dimensional conformal group. Finally, we use the Lie-Poiss…
PT-symmetry in one-way wormholes
本文研究修正版爱因斯坦-罗森桥中粒子穿越喉部时的PT对称性，并提出双度量模型实现两页全等点的认同，从而可能产生可观测效应。
We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions $ \ge 5$. As in the case of general relativity, the horizon can be modeled as a membrane endowed with fluidlike properties. We derive the stress tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross section, for which the stress tensor can be regularized with the usual redshift factor, and expressed in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. We evaluate the transport coe…
We use the membrane paradigm to analyze the horizon dynamics of a uniformly boosted black brane in a (d+2)-dimensional asymptotically Anti-de-Sitter space-time and a Rindler acceleration horizon in (d+2)-dimensional Minkowski space-time. We show that in these cases the horizon dynamics is governed by the relativistic CFT hydrodynamics equations. The fluid velocity and temperature correspond to the normal to the horizon and to the surface gravity, respectively. The second law of thermodynamics for the fluid is mapped into the area increase theorem of General Relativity. The analysis is applicab…
We study the effective geometry felt by the fluctuations of open strings living on the worldvolume of probe D-branes in the presence of background electromagnetic fields. This is captured by an effective action consisting of a Maxwell term and a topological term, with the role of the metric played by the open string metric. Studying generalized Eddington-Finkelstein coordinates for stationary but non-static manifolds, we consider an open string membrane paradigm to obtain a generic formula for the DC transport coefficients, including the effect of external electromagnetic fields present on the…
Cosmological hysteresis is a purely thermodynamical phenomenon caused by the gradient in pressure, hence the characteristic equation of state during the expansion and contraction phases of the universe are different, provided that the universe bounces and recollapses. During hysteresis pressure asymmetry is created due to the presence of a single scalar field in the dynamical process. Also such an interesting scenario has vivid implications in cosmology when applied to variants of modified gravity models described within the framework of membrane paradigm. Cyclic universe along with scalar fie…
Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions
本文从量子混沌视角出发，证明高维双曲流形上的测地运动具有Schwarzian能级密度和量子混沌普适特征，从而提出单系统层面与Jackiw-Teitelboim引力的可能对偶，并展示虫洞几何如何从周期轨道离散性中涌现。
We study the relations between two different approaches to the holographic Renormalization Group (RG) flow at the dual gravity level: One is the radial evolution of the classical equation of motion and the other is the flow equation given by the holographic Wilsonian RG coming from the cut off independence. Apparently, the two flows look different. We give general proofs that the two flows are actually equivalent. The role of the momentum continuity (MC) is essential. We show that MC together with cutoff independence gives the evolution equation of the boundary values. Equivalence of conductiv…
One Membrane to Love them all: Tidal deformations of compact objects from the membrane paradigm
本文基于膜范式开发了与模型无关的框架，用粘性系数描述致密天体潮汐性质，推导了非旋转球对称天体潮汐Love数的一般结果，并发现中子星膜剪切粘性系数的准普适关系。
Following the membrane paradigm, we explore the effect of the gravitational $Θ$-term on the behavior of the stretched horizon of a black hole in (3+1)-dimensions. We reformulate the membrane paradigm from a quantum path-integral point of view where we interpret the macroscopic properties of the horizon as effects of integrating out the region inside the horizon. The gravitational $Θ$-term is a total derivative, however, using our framework we show that this term affects the transport properties of the horizon. In particular, the horizon acquires a third order parity violating, dimensionless tr…
This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in d+1 dimensions capture the (generalized) Navier-Stokes equations in d dimensions. Given an arbitrary fluid dynamical solution, we can systematically construct a corresponding asymptotically AdS black hole spacetime with a regular horizon whose properties mimic that of the fluid flow. Apart from an overview of this construction, we describe some of its applica…
This thesis addresses some classical and semi-classical aspects of black holes using an effective membrane representation of the event horizon. The classical "membrane paradigm" equations are derived from an underlying action formulation, even though the equations are dissipative. It is shown how the membrane action can also account for the hole's entropy, including the numerical factor. Two short derivations of Hawking radiation are then presented, the first based on particles in a dynamical geometry and the second on the membrane. The calculations obey conservation laws and lead to a correct…
Although the black holes are an integral part of the standard model of astrophysics and cosmology, their existence poses some serious fundamental problems. In recent years, several horizonless compact object models were proposed to address those issues. As the gravitational wave detectors started to observe more and more merger events with a large signal-to-noise ratio, gravitational wave spectroscopy could hold the key to uncover the existence of these objects. This is because the late time ringdown signals of horizonless compact objects differ from that of the black holes. In this paper, we …
Quantum Horizon and Quantum Membrane Paradigm from Black Hole Quantum Mechanics
该研究从黑洞矩阵量子力学发展微观量子膜范式，由模糊球拓扑诱导贝里单极子，部分子形成LLL态产生相关电流，通过特定矩阵配置耦合电流与外场，给出量子修正，为探测视界微观量子结构提供可能。
Characterization of exotic matter in PT-symmetric wormholes
本文扩展PT对称双度量虫洞模型的分析至喉部零超曲面，用Barrabes-Israel形式主义揭示稳定喉部的负能奇异类光膜，提出引力波回波等4类观测特征，为可穿越性提供新途径并阐明CTCs自洽出现条件。
Several general arguments indicate that the event horizon behaves as a stretched membrane. We propose using this relation to understand gravity and dynamics of black objects in higher dimensions. We provide evidence that (i) the gravitational Gregory-Laflamme instability has a classical counterpart in the Rayleigh-Plateau instability of fluids. Each known feature of the gravitational instability can be accounted for in the fluid model. These features include threshold mode, dispersion relation, time evolution and critical dimension of certain phase transitions. Thus, we argue that black string…
In this article, we have studied the cosmological and particle physics constraints on dark matter relic abundance from effective field theory of inflation using tensor-to-scalar ratio ($r$), in case of Randall-Sundrum single membrane (RSII) paradigm. Using semi-analytical approach we establish a direct connection between the dark matter relic abundance ($Ω_{DM}h^2$) and primordial gravity waves ($r$), which establishes a precise connection between inflation and generation of dark matter within the framework of effective field theory in RSII membrane. Further assuming the UV completeness of the…
Fluid-membrane Descriptions of Various Black Holes
本文利用黑洞膜范式研究不同维度下多种黑洞的性质，发现BTZ黑洞具有物理体粘度，Lorentz违反参数在范式中表现为移动能层的毛发，并验证了该范式对量子修正和stringy黑洞的预测能力。
Membrane Paradigm Approach to the Johannsen-Psaltis Black Hole
本文用膜范式将JP黑洞描述为热流体，推导输运系数并约束额外毛发，发现压力在能层发散，支持喷流源于能层的观点。
We consider the dynamics of a d+1 space-time dimensional membrane defined by the event horizon of a black brane in (d+2)-dimensional asymptotically Anti-de-Sitter space-time and show that it is described by the d-dimensional incompressible Navier-Stokes equations of non-relativistic fluids. The fluid velocity corresponds to the normal to the horizon while the rate of change in the fluid energy is equal to minus the rate of change in the horizon cross-sectional area. The analysis is performed in the Membrane Paradigm approach to black holes and it holds for a general non-singular null hypersurf…
Quasinormal modes of slowly-spinning horizonless compact objects
本研究将膜范式推广到自旋一阶近似，分析慢自旋无视界致密天体的拟正模与相关参数的关系，发现自旋会增大其与黑洞拟正模谱的偏离，更易在铃宕阶段被区分。
We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D=4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism i…
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