Three-Dimensional Metrics as Deformations of a Constant Curvature Metric

Coll, Bartolomé; Llosa, Josep; Soler, D.

doi:10.1023/a:1015391411214

Cited by 22 publications

(37 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In thermodynamic language this is a special case of isothermal Carnot's path, 19 known as Moutier's [37], which produces no work and has zero thermodynamic efficiency. 20 Carnot's evolution is reversible and this does not contradict anything here, as the origin of irreversibility for the described phenomenon is purely geometrical.…”

Section: The Entropy Current and Its Conservationsupporting

confidence: 51%

The Robinson–Trautman spacetime and its holographic fluid

Ciambelli¹,

Petkou²,

Petropoulos³

et al. 2017

Proceedings of Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2016)

View full text Add to dashboard Cite

We discuss the holographic reconstruction of four-dimensional asymptotically anti-de Sitter Robinson-Trautman spacetime from boundary data. We use for that a resummed version of the derivative expansion. The latter involves a vector field, which is interpreted as the dualholographic-fluid velocity field and is naturally defined in the Eckart frame. In this frame the analysis of the non-perfect holographic energy-momentum tensor is considerably simplified. The Robinson-Trautman fluid is at rest and its time evolution is a heat-diffusion kind of phenomenon: the Robinson-Trautman equation plays the rôle of heat equation, and the heat current is identified with the gradient of the extrinsic curvature of the two-dimensional boundary spatial section hosting the conformal fluid, interpreted as an out-of-equilibrium kinematical temperature. The hydrodynamic-frame-independent entropy current is conserved for vanishing chemical potential, and the evolution of the fluid resembles a Moutier thermodynamic path. We finally comment on the general transformation rules for moving to the Landau-Lifshitz frame, and on possible drawbacks of this option.

show abstract

Section: The Entropy Current and Its Conservationsupporting

confidence: 51%

The Robinson–Trautman spacetime and its holographic fluid

Ciambelli¹,

Petkou²,

Petropoulos³

et al. 2017

Proceedings of Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2016)

View full text Add to dashboard Cite

show abstract

“…They generalize the Minkowski matrix η AB with constant elements in the definition of the metric. A further restriction on the matrices Φ A C comes from the theorem proved by Riemann by which an n-dimensional metric has n(n− 1)/2 degrees of freedom (see [5] for details). With this definitions in mind, let us consider the main properties of deforming matrices.…”

Section: Generalities On Space-time Deformationsmentioning

confidence: 99%

“…We have to remember that all these quantities are not independent as, by the theorem mentioned in [5], they have to form at most six independent functions in a four dimensional space-time.…”

Section: Properties Of Deforming Matricesmentioning

confidence: 99%

Space-Time Deformations as Extended Conformal Transformations

Capozziello

Stornaiolo

2008

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

A definition of space-time metric deformations on an n-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation theory giving a natural picture by which gravitational waves are described by small deformations of the metric. As further result, deformations can be related to approximate Killing vectors (approximate symmetries) by which it is possible to parameterize the deformed region of a given manifold. The perspectives and some possible physical applications of such an approach are discussed.

show abstract

“…Now, as an apllication of the results in ref. [23], 3 g can be transformed by constriction into a constant curvature metric on the space. Finally, g is obtained by pulling the latter bcak to V 4 .…”

Section: Discussionmentioning

confidence: 99%