Black holes and biophysical (mem)-branes

Abstract

We argue that the effective theory describing the long-wavelength dynamics of black branes is the same effective theory that describes the dynamics of biophysical membranes. We improve the phase structure of higher-dimensional black rings by considering finite thickness corrections in this effective theory, showing a striking agreement between our analytical results and recent numerical constructions while simultaneously drawing a parallel between gravity and the effective theory of biophysical membranes.Introduction. In the past three years many remarkable properties of higher-dimensional black holes were uncovered, leading to a new perspective on black holes as materials describable by effective theories of continuous media. In particular, in a long-wavelength regime, besides having fluid-like properties, they can behave as elastic (mem)-branes if bent and exhibit piezoelectric behaviour if charged and flexed. In this regime they are characterised by a set of transport coefficients such as shear and bulk viscosities [1,2], the Young modulus [3] and the piezoelectric moduli [4], which can be directly measured from gravity.Fluid and (mem)-brane elastic behaviour of a physical system can be described by a single unified framework of hydrodynamics on embedded surfaces [5,6]. When applied to black holes and black branes, this framework is commonly known as the blackfold approach [7,8], which has enabled a systematic scan of new horizon topologies in higher-dimensions [9] and the construction of new approximate solutions, such as black rings in arbitrary space-time dimensions [10].The blackfold approach, as originally developed in [7,8], consists in applying generic long wavelength perturbations of neutral asymptotically flat black p-brane metrics and describing its dynamics via an effective theory. In this case, to leading order in the perturbation, the black branes are described by a set of world volume fields composed of the induced metric γ ab , the local boost velocity u a and the brane thickness r 0 . Focusing on the stationary sector, the dynamics of these branes can be described by the free energy functional of a fluid living on an elastic brane. To next order in the perturbation, the black brane metric is corrected by terms proportional to derivatives of the fields γ ab , u a , r 0 which include, as we will explain shortly, terms proportional to the extrinsic curvature tensor K ab i , the Riemann curvature tensor of the world volume, or the vorticity of the fluid. [11] The dynamics of elastic membranes has also taken an important role in the context of biophysics, beginning with the early work of Helfrich [12] and Canham [13] in the 60's. They showed that the bending deformations of elastic membranes played a crucial role in the

Rings, ripples, and rotation: connecting black holes to black rings

“…We thank Jay Armas and Troels Harmark for kindly sharing their unpublished result (3) [33]. BW thanks Joan Camps for helpful discussions and for bringing to our attention the work of [33].…”

“…BW thanks Joan Camps for helpful discussions and for bringing to our attention the work of [33]. OJCD was supported in part by the ERC Starting Grant 240210 -String-QCD-BH.…”

“…In d > 6, one can also include finite-size corrections to the blackfold approximation (which only become dominant over self-gravitational effects in d > 6 [32]). For d = 7, these are given by [33] This is illustrated for d = 7 in figure 5 and figure 6, where the dashed red line is the leading order blackfold result and the solid red line includes finite-size corrections. With the corrections, the agreement is impressive, even giving a H to ∼ 1% when j ∼ O(1).…”

Blackfolds, plane waves and minimal surfaces

“…It would be very interesting to understand how these geometries are modified when second order corrections given in (2.12) are taken into account using the tools available in [6][7][8][9].…”

“…One of these effective theories, known as the blackfold approach [3,4], describing the long wavelength dynamics of black branes in a derivative expansion including hydrodynamic and elastic degrees of freedom [5][6][7][8][9], has allowed to scan for non-trivial black hole horizon topologies in asymptotically flat and (Anti)-de Sitter space-times [10][11][12][13]. These new black hole topologies include black rings in higher-dimensions, black odd-spheres and black cylinders, some of which have been constructed numerically [14][15][16][17].…”