Nonperfect Carrollian Fluids Through Holography

TL;DR

This work develops a covariant, gauge-invariant radiation criterion for spacetimes with negative cosmological constant by embedding the Fernández-Álvarez–Senovilla framework in the AdS/CFT fluid/gravity setting, using the Bel-Robinson tensor ${\cal D}_{\mu\nu\rho\sigma}$ and conformal geometry to relate bulk gravitational waves to boundary dissipation and an emergent entropy current. It shows that bulk radiation translates into Carrollian boundary data after a controlled flat limit, with Carroll-covariant quantities $(\hat{\varrho}, \hat{\Upsilon}^A)$ governed by Carroll data $(\Sigma_{AB}, Q_A)$ and a radiative vector that encodes energy flux to the boundary; the boundary entropy production law ties bulk dynamics to boundary thermodynamics. The Robinson–Trautman spacetimes provide a concrete anchor: for $\Lambda<0$ the boundary is non-conformally flat and radiation can occur without violating a conserved boundary entropy current, while in the Carrollian limit the radiative data persist only for time-dependent RT fields, signaling nonperfect Carrollian fluids. The paper outlines promising extensions to broader bulk solutions, higher-spin holography, and second-order Carrollian transport to further elucidate how bulk waves sculpt boundary symmetries and thermodynamics.

Abstract

We embed the covariant, gauge-invariant gravitational radiation criteria of Fernández-Álvarez and Senovilla, based in terms of conformal geometry and the Bel-Robinson tensor, into the hydrodynamic framework of gauge/gravity duality. This construction uncovers a direct correspondence between bulk gravitational waves and dissipative processes in the boundary theory, from which a natural notion of entropy production emerges. We further analyze a smooth flat limit in which the dual fluid becomes Carrollian, with dissipation governed by Carroll-covariant tensors. As an example, we apply our framework to the Robinson-Trautman family of solutions.