Integrability, Einstein spaces and holographic fluids

Understand

Using holographic-fluid techniques, we discuss some aspects of the integrability properties of Einstein's equations in asymptotically anti-de Sitter spacetimes.

• We review and we amend the results of 1506.04813 on how exact four-dimensional Einstein spacetimes, which are algebraically special with respect to Petrov's classification, can be reconstructed from boundary data: this is possible if the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless.
• We illustrate the method when the hydrodynamic congruence has vorticity and the boundary metric has two commuting isometries.
• This leads to the complete Plebanski-Demianski family.