Lagrangian perfect fluids and black hole mechanics

Iyer, Vivek

doi:10.1103/physrevd.55.3411

Cited by 36 publications

(99 citation statements)

References 15 publications

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“…Aided by this observation, we tentatively forward the following hypothesis: in the absence of anomalies the Schwinger-Keldysh sources can be identified with {g 98 Accordingly, (15.22) suggests that the currents map as {T…”

Section: Jhep05(2015)060mentioning

confidence: 99%

“…Modulo a sensible extension to the new fields {A This close analogy to the Schwinger-Keldysh doubled formalism then suggests that in the hydrodynamic limit, where we want to consider only the fully retarded correlators, we should be working to leading order in the difference fields which are now {g µν ,Ã µ } for 98 In the present context we view this identification as heuristic. Studying anomalies as in section 17.3 shows that the identification of Schwinger-Keldysh fields should actually be twisted to involve the field A …”

Section: Jhep05(2015)060mentioning

confidence: 99%

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Adiabatic hydrodynamics: the eightfold way to dissipation

Haehl

Loganayagam

Rangamani

2015

J. High Energ. Phys.

131

373

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Hydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs density matrix. Conventionally, one views the effective dynamics in terms of the conserved currents, which should be expressed via the constitutive relations in terms of the fluid velocity and the intensive parameters such as the temperature, chemical potential, etc. . . However, not all constitutive relations are acceptable; one has to ensure that the second law of thermodynamics is satisfied on all physical configurations. In this paper, we provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint.The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids is quite rich, and admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law. While this completes a transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics. We suggest that this symmetry is the macroscopic manifestation of the microscopic KMS invariance. We demonstrate its utility by explicitly constructing effective actions for adiabatic transport. The theory of adiabatic fluids, we speculate, provides a useful starting point for a new framework to describe non-equilibrium dynamics, wherein dissipative effects arise by Higgsing the Abelian symmetry.

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Section: Jhep05(2015)060mentioning

confidence: 99%

Section: Jhep05(2015)060mentioning

confidence: 99%

Adiabatic hydrodynamics: the eightfold way to dissipation

Haehl

Loganayagam

Rangamani

2015

J. High Energ. Phys.

131

373

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“…We give a precise definition in II and discuss its relation to a previous definition by Bonazzola et al [3] for example, Refs. [10][11][12][13][14][15].) Despite the lack of asymptotic flatness one can choose the current to make Q finite, and it Q is independent of the 2-surface S on which it is evaluated, as long as S lies outside the matter and all black holes.…”

Section: Introductionmentioning

confidence: 99%

Erratum: Thermodynamics of binary black holes and neutron stars [Phys. Rev. D65, 064035 (2002)]

Friedman¹,

Uryū²,

Shibata³

2004

Phys. Rev. D

170

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We consider compact binary systems, modeled in general relativity as vacuum or perfect-fluid spacetimes with a helical Killing vector k α , heuristically, the generator of time-translations in a corotating frame. Systems that are stationary in this sense are not asymptotically flat, but have asymptotic behavior corresponding to equal amounts of ingoing and outgoing radiation. For blackhole binaries, a rigidity theorem implies that the Killing vector lies along the horizon's generators, and from this one can deduce the zeroth law (constant surface gravity of the horizon). Remarkably, although the mass and angular momentum of such a system are not defined, there is an exact first law, relating the change in the asymptotic Noether charge to the changes in the vorticity, baryon mass, and entropy of the fluid, and in the area of black holes.Binary systems with M Ω small have an approximate asymptopia in which one can write the first law in terms of the asymptotic mass and angular momentum. Asymptotic flatness is precise in two classes of solutions used to model binary systems: spacetimes satisfying the post-Newtonian equations, and solutions to a modified set of field equations that have a spatially conformally flat metric. (The spatial conformal flatness formalism with helical symmetry, however, is consistent with maximal slicing only if replaces the extrinsic curvature in the field equations by an artificially tracefree expression in terms of the shift vector.) For these spacetimes, nearby equilibria whose stars have the same vorticity obey the relation δM = ΩδJ, from which one can obtain a turning point criterion that governs the stability of orbits.

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“…[15]- [18], while the higher curvature terms and higher derivative terms in the metric were considered in [19]. The case when the Lagrangian is an arbitrary function of metric, Ricci tensor and a scalar field…”

Section: Introductionmentioning

confidence: 99%

First law of black ring thermodynamics in higher dimensional dilaton gravity withp+1strength forms

Rogatko

2006

Phys. Rev. D

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04.50.+h, 98.80.Cq.We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p + 1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface. I. INTRODUCTIONRecently there has been a great resurgence of interests in n-dimensional generalization of black holes motivated by various attempts of constructing the unified theories. As far as the static n-dimensional black holes is concerned the uniqueness theorem for them is quite well established [1]. But for stationary axisymmetric ones the problem is much more complicated. In Ref.[2] it was shown that even in five-dimensional spacetime there is the so-called black ring solution possessing S 2 × S 1 topology of the event horizon and having the same mass and angular momentum as spherical five-dimensional stationary axisymmetric black hole. On the contrary, when one assumes the spherical topology of the horizon S 3 the uniqueness proof can be conducted (see Ref.[3] for the vacuum case and Ref.[4] for the stationary axisymmetric self-gravitating σ-model). As was remarked in [5] due to the vast number of the ways of forming of these objects, one can take the view that the spirit of no-hair theorem is preserved.The black ring solution was vastly treated in literature, i.e., the solution possessing the electric and magnetic dipole charge was found [6,7], static black ring solution in five-dimensional Einstein-Maxwell-dilaton gravity was presented in [8] and systematically derived in [9] both in asymptotically flat and non-asymptotically flat case. Recently, the rotating non-asymptotically flat black ring solution in charged dilaton gravity was given [10]. Also the supersymmetric black ring solutions were discovered [11].As far as the black hole thermodynamics is concerned, Wald [12] referred two versions of the black hole thermodynamics. The first one, the so-called equilibrium state version was treated for the first time in the seminal paper of Bardeen, Carter and Hawking [13]. In this attitude the linear perturbations of a stationary electrovac black hole to another stationary black hole were taken into account. In Ref.[14] arbitrary asymptotically flat perturbations of a stationary black hole were considered. The first law of black hole thermodynamics valid for an arbitrary diffeomorphism invariant Lagrangian with metric and matter fields possessing stationary and axisymmetric black hole solutions was given in Refs.[15]- [18], while the higher curvature terms and higher derivative terms in the metric were considered in [19]. The case when the Lagrangian is an arbitrary function of metric, Ricci tensor and a scalar field

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Lagrangian perfect fluids and black hole mechanics

Cited by 36 publications

References 15 publications

Adiabatic hydrodynamics: the eightfold way to dissipation

Adiabatic hydrodynamics: the eightfold way to dissipation

Erratum: Thermodynamics of binary black holes and neutron stars [Phys. Rev. D65, 064035 (2002)]

First law of black ring thermodynamics in higher dimensional dilaton gravity withp+1strength forms

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