An action for black hole membranes

Parikh, Maulik; Wilczek, Frank

doi:10.1103/physrevd.58.064011

Cited by 177 publications

(302 citation statements)

References 20 publications

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“…This gives an Israel matching condition, with the only difference being that the extrinsic curvature term for the ''exterior'' region vanishes in this case-the physics of the exterior region is encoded in the boundary action. A similar Israel condition arises in the action description of the membrane paradigm for black holes, this time with the region interior to the black hole horizon replaced by boundary matter [10,11]. The upshot is that (23) fixes the canonical momentum K À Kh and hence half of the boundary conditions for the gravitational field.…”

Section: B Gravitymentioning

confidence: 99%

“…An example that immediately springs to mind is the method of image charges in electrostatics in which conducting boundary conditions are replaced by fictitious charges. A closer analogue to our proposal is the membrane description of black hole horizons [10,11]. The membrane paradigm is the remarkable notion that, from the perspective of an outside observer, a black hole behaves precisely as if it were cloaked in a fluid membrane living at the event horizon.…”

Section: Mach's Principlementioning

confidence: 99%

“…1(b). This is in precise analogy with the membrane paradigm for black holes [11]. (We continue to refer to this timelike surrogate horizon as the stretched horizon even though in de Sitter space, it should probably be called a shrunken horizon.)…”

Section: B De Sitter Spacementioning

confidence: 99%

“…Following the action formulation of the membrane paradigm [11], one deals with this leftover variation by adding and subtracting a boundary action on AE,…”

Section: A Electromagnetic Analogymentioning

confidence: 99%

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Mach’s holographic principle

Khoury

Parikh

2009

Phys. Rev. D

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Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. Einstein's equations are not modified and no selection principle is applied to their solutions; Mach's principle is realized wholly within Einstein's general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Specification of both boundary and bulk stress tensors uniquely specifies the geometry and thereby the inertial frames. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically AdS space-times, is consistent with holographic duality. I. MACH'S PRINCIPLEAcceleration appears absolute. A snapshot of a rotating bucket of water reveals, through the gentle curve in the water's surface, that the bucket was rotating. Two rocks tied with a rope and set spinning about an axis perpendicular to the rope are measurably distinct from the same two rocks undergoing linear motion: the rope becomes tense. A passenger in an elevator or a windowless spaceship is aware of starts and stops even though the vehicle is a closed system.With his principle of equivalence, Einstein recognized that gravity was simply acceleration in disguise. Moreover, Einstein's equations, like Newton's law of gravitation, indicate that matter is the source for gravity. But if acceleration and gravity are linked, and if gravity

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Section: B Gravitymentioning

confidence: 99%

Section: Mach's Principlementioning

confidence: 99%

Section: B De Sitter Spacementioning

confidence: 99%

“…Following the action formulation of the membrane paradigm [11], one deals with this leftover variation by adding and subtracting a boundary action on AE,…”

Section: A Electromagnetic Analogymentioning

confidence: 99%

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Mach’s holographic principle

Khoury

Parikh

2009

Phys. Rev. D

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“…To our knowledge, the precise procedure has yet not been completely worked out. We mention here the recent works [31,32,33] in which generalized definitions of horizon have been proposed, mainly to allow for evolution. However, in what follows, we shall not need an action governing continuous changes in area.…”

Section: Boundary Terms In the Einstein-hilbert Actionmentioning

confidence: 99%

How the change in horizon area drives black hole evaporation

2000

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We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon which must be added to the canonical action of general relativity in order to obtain a well defined action principle when the area varies. These coordinates have already been used by Teitelboim and collaborators to compute the partition function of a black hole. We use them to show that the probability to emit a particle is given by e −∆A/4 where ∆A is the decrease in horizon area induced by the emission. This expression improves Hawking result which is governed by a temperature (given by the surface gravity) in that the specific heat of the black hole is no longer neglected. The present derivation of quantum black hole radiation is based on the same principles which are used to derive the first law of classical black hole thermodynamics. Moreover it also applies to quantum processes associated with cosmological or acceleration horizons. These two results indicate that not only black holes but all event horizons possess an entropy which governs processes according to quantum statistical thermodynamics.

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Effects of porosity, fiber size, and layering sequence on sound absorption performance of needle‐punched nonwovens

Yılmaz

Banks‐Lee

Powell

et al. 2011

J of Applied Polymer Sci

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The relationships between the material parameters, i.e., the fiber fineness, porosity, areal density, layering sequence, and airflow resistivity with the normalincidence sound absorption coefficient of nonwoven composites consisting of three layers have been studied. The monofiber or multifiber needle-punched nonwovens included poly(lactic acid) (PLA), polypropylene (PP), glass fiber, and hemp fibers. Air flow resistivity was statistically modeled and was found to increase with decreasing fiber size and nonwoven porosity. The former models developed for glass fiber mats in the literature were found to be inconsistent with the air flow resistance of the nonwovens reported below. The effects of the layering sequence on air flow resistivity and sound absorption were obtained. It was found that when the layer including reinforcement fibers, i.e., hemp or glass fiber, faced the air flow/sound source, the air flow resistance and the absorption coefficient were higher than the case when the layer including reinforcement fibers was farthest from the air flow/sound source. The difference was more pronounced if there was a greater difference between the resistivity values of the constituent layers of the nonwoven composite. Sound absorption coefficient was statistically modeled in terms of air flow resistivity and frequency.

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An action for black hole membranes

Cited by 177 publications

References 20 publications

Mach’s holographic principle

Mach’s holographic principle

How the change in horizon area drives black hole evaporation

Effects of porosity, fiber size, and layering sequence on sound absorption performance of needle‐punched nonwovens

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