How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes

Understand

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes.

• When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane.
• Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion.
• This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating.