<i>Black Holes: The Membrane Paradigm</i>

Thorne, Kip S.; Price, Richard H.; MacDonald, Douglas; Detweiler, Steven

doi:10.1063/1.2811504

Cited by 794 publications

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“…In particular, an effective spatial dimension of black holes is obtained as two. Further he insisted that his result agrees with the membrane picture of black holes [11]. Later on, it turns out that his calculation is wrong and the effective spatial dimension of black holes is not two.…”

Section: Introductionsupporting

confidence: 54%

Critical behavior for the dilaton black holes

Cai

Myung

1997

Nuclear Physics B

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We study the critical behavior in the black p-branes and four dimensional charged dilaton black holes. We calculate the thermodynamic fluctuations in the various (microcanonical, canonical, and grandcanonical) ensembles. It is found that the extremal limit of some black configurations has a critical point and a phase transition takes place from the extremal to nonextremal black configurations. Some critical exponents are obtained, which satisfy the scaling laws. This is related to the fact that the entropy of these black configurations is a homogeneous function.

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Section: Introductionsupporting

confidence: 54%

Critical behavior for the dilaton black holes

Cai

Myung

1997

Nuclear Physics B

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“…These results agree with our 3 The Ricci scalar of the induced horizon geometry approaches O(10 4 ) in mass units. 4 Such solutions were found in d = 5, but these conical singularities [36]. numerics for large j.…”

Section: Jhep07(2014)045mentioning

confidence: 93%

“…According to the membrane paradigm [4], external observers will find that BH horizons behave like fluid membranes, endowed with a viscosity, conductivity, temperature, entropy, etc. Moreover, in certain circumstances there are formal mappings between solutions of general relativity and solutions of Navier-Stokes [5,6].…”

Section: Jhep07(2014)045mentioning

confidence: 99%

Rings, ripples, and rotation: connecting black holes to black rings

Dias

Santos

Way

2014

J. High Energ. Phys.

105

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Singly-spinning Myers-Perry black holes in d ≥ 6 spacetime dimensions are unstable for sufficiently large angular momentum. We numerically construct (in d = 6 and d = 7) two new stationary branches of lumpy (rippled) black hole solutions which bifurcate from the onset of this ultraspinning instability. We give evidence that one of these branches connects through a topology-changing merger to black ring solutions which we also construct numerically. The other branch approaches a solution with large curvature invariants. We are also able to compare the d = 7 ring solutions with results from finite-size corrections to the blackfold approach, finding excellent agreement. JHEP07(2014)045Introduction. As expressed by John Wheeler's statement, "Black holes have no hair" [1], black holes (BHs) in four spacetime dimensions are remarkably simple objects. The topology, rigidity, uniqueness, and no-hair theorems ensure that Kerr BHs are the only stationary, vacuum, and asymptotically flat solutions to general relativity, and that they are uniquely specified by their mass M and angular momentum J [2]. Because Kerr BHs are also linear mode stable [3], any stellar object undergoing gravitational collapse towards a BH is expected to settle to the Kerr solution.Yet, the uniqueness of the Kerr BH may seem surprising given the close connection between gravity and fluids. According to the membrane paradigm [4], external observers will find that BH horizons behave like fluid membranes, endowed with a viscosity, conductivity, temperature, entropy, etc. Moreover, in certain circumstances there are formal mappings between solutions of general relativity and solutions of Navier-Stokes [5,6]. Fluids, however, lack strong uniqueness theorems and admit a rich structure of solutions. Indeed, rotational instabilities appear in fluid droplets and non-spherical solutions develop [7]. In particular, a ring configuration is preferred for high spin. Therefore, it may be natural to suspect that BHs behave like fluid droplets and have a greater diversity of solutions. This is the emerging picture in d > 4 spacetime dimensions.In higher dimensions, gravity becomes weaker as it spreads out over extra dimensions. Horizons are therefore more flexible, creating new gravitational phenomena with no fourdimensional counterparts. For example, in d ≥ 5 black strings exist and suffer from the Gregory-Laflamme instability [8]. This instability leads to a fractal-like array of spherical BHs and cosmic censorship violation [9,10]. This behaviour is similar to the RayleighPlateau instability, where a fluid jet breaks into an array of spherical droplets [11].In addition, there are black rings with horizon topology S 1 × S d−3 . These have been constructed in closed analytic form in d = 5 [12] and numerically in d = 6 [13]. (The list of other BH horizon topologies that are allowed in d > 4 were discussed in [14]). In any d ≥ 5, black rings can be found perturbatively using the blackfold approach if the S 1 radius is much larger than the S d−3 radius [15]...

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“…For this relatively simple, but nondiagonal, two-dimensional spacetime we can develop the "1 + 1" formalism. Doing so we follow as a blueprint the well-known "3+1 formalism, widely used in the physics of black holes [27][28][29]. Namely, we introduce definitions of the lapse function:…”

Section: Rf Treatmentmentioning

confidence: 99%

Centrifugally Driven Relativistic Dynamics on Curved Trajectories

Rogava

Dalakishvili

Osmanov

2003

General Relativity and Gravitation

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Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity ω = const. The solutions are found and analyzed for the case when the form of the trajectory is given by an Archimedes spiral. It is found that particles can reach infinity while they move along these trajectories and the physical interpretation of their behaviour is given. The analogy of this idealized study with the motion of particles along the curved rotating magnetic field lines in the pulsar magnetosphere is pointed out. We discuss further physical development (the conserved total energy case, when ω = const) and astrophysical applications (the acceleration of particles in active galactic nuclei) of this theory.

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Black Holes: The Membrane Paradigm

Cited by 794 publications

References 0 publications

Critical behavior for the dilaton black holes

Critical behavior for the dilaton black holes

Rings, ripples, and rotation: connecting black holes to black rings

Centrifugally Driven Relativistic Dynamics on Curved Trajectories

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