Constraints on the effective fluid theory of stationary branes

TL;DR

This paper advances the effective fluid theory for stationary branes, including finite-thickness and spin effects, and applies it to blackfold examples like black tori and charged black rings.

Contribution

It introduces higher-derivative corrections and constraints for the effective fluid theory of stationary branes, including transverse spin effects, and applies the formalism to specific blackfold solutions.

Findings

Derived thermodynamic constraints from the Lagrangian

Fixed the coupling of transverse spin to background space-time

Compared theoretical predictions with numerical solutions for black rings

Abstract

We develop further the effective fluid theory of stationary branes. This formalism applies to stationary blackfolds as well as to other equilibrium brane systems at finite temperature. The effective theory is described by a Lagrangian containing the information about the elastic dynamics of the brane embedding as well as the hydrodynamics of the effective fluid living on the brane. The Lagrangian is corrected order-by-order in a derivative expansion, where we take into account the dipole moment of the brane which encompasses finite-thickness corrections, including transverse spin. We describe how to extract the thermodynamics from the Lagrangian and we obtain constraints on the higher-derivative terms with one and two derivatives. These constraints follow by comparing the brane thermodynamics with the conserved currents associated with background Killing vector fields. In particular, we fix uniquely the one- and two-derivative terms describing the coupling of the transverse spin to the background space-time. Finally, we apply our formalism to two blackfold examples, the black tori and charged black rings and compare the latter to a numerically generated solution.