The Robinson-Trautman spacetime and its holographic fluid
Résumé
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.
Mots clés
fluid: holography
fluid: conformal
fluid: velocity
duality: holography
current: conservation law
tensor: energy-momentum
expansion: derivative
potential: chemical
entropy: current
field theory: vector
dimension: 4
dimension: 2
space-time
thermodynamical
anti-de Sitter
temperature
kinematics
curvature
at rest