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arXiv · 1707.02995

The Robinson-Trautman spacetime and its holographic fluid

Luca Ciambelli·Anastasios C. Petkou·P. Marios Petropoulos·Konstantinos Siampos
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Abstract

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 dual-holographic-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 r\^ole 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.

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Luca Ciambelli, Anastasios C. Petkou, P. Marios Petropoulos, Konstantinos Siampos. 2017-07-10. The Robinson-Trautman spacetime and its holographic fluid. https://arxiv.org/abs/1707.02995

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