Jay Armas

Blackfolds in (anti)-de Sitter backgrounds

We construct different neutral blackfold solutions in Anti-de Sitter and de Sitter background spacetimes in the limit where the cosmological constant is taken to be much smaller than the horizon size. This includes a class of blackfolds with horizons that are products of odd-spheres times a transverse sphere, for which the thermodynamic stability is also studied. Moreover, we exhibit a specific case in which the same blackfold solution can describe different limiting black hole spacetimes therefore illustrating the geometric character of the blackfold approach. Furthermore, we show that the higher-dimensional Kerr-(Anti)-de Sitter black hole allows for ultraspinning regimes in the same limit under consideration and demonstrate that this is correctly described by a pancaked blackfold geometry. We also give evidence for the possibility of saturating the rigidity theorem in these backgrounds.

The Young modulus of black strings and the fine structure of blackfolds

A bstractWe explore corrections in the blackfold approach, which is a worldvolume theory capturing the dynamics of thin black branes. The corrections probe the fine structure of the branes, going beyond the approximation in which they are infinitely thin, and account for the dipole moment of worldvolume stress-energy as well as the internal spin degrees of freedom. We show that the dipole correction is induced elastically by bending a black brane. We argue that the long-wavelength linear response coefficient capturing this effect is a relativistic generalization of the Young modulus of elastic materials and we compute it analytically. Using this we draw predictions for black rings in dimensions greater than six. Furthermore, we apply our corrected blackfold equations to various multi-spinning black hole configurations in the blackfold limit, finding perfect agreement with known analytic solutions.

How fluids bend: the elastic expansion for higher-dimensional black holes

A bstractHydrodynamics 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. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.

Black Branes as Piezoelectrics

We find a realization of linear electroelasticity theory in gravitational physics by uncovering a new response coefficient of charged black branes, exhibiting their piezoelectric behavior. Taking charged dilatonic black strings as an example and using the blackfold approach we measure their elastic and piezolectric moduli. We also use our results to draw predictions about the equilibrium condition of charged dilatonic black rings in dimensions higher than six.

Thermal Giant Gravitons

A bstractWe study the giant graviton solution as the AdS5 × S5 background is heated up to finite temperature. The analysis employs the thermal brane probe technique based on the blackfold approach. We focus mainly on the thermal giant graviton corresponding to a thermal D3-brane probe wrapped on an S3 moving on the S5 of the background at finite temperature. We find several interesting new effects, including that the thermal giant graviton has a minimal possible value for the angular momentum and correspondingly also a minimal possible radius of the S3. We compute the free energy of the thermal giant graviton in the low temperature regime, which potentially could be compared to that of a thermal state on the gauge theory side. Moreover, we analyze the space of solutions and stability of the thermal giant graviton and find that, in parallel with the extremal case, there are two available solutions for a given temperature and angular momentum, one stable and one unstable. In order to write down the equations of motion, action and conserved charges for the thermal giant graviton we present a slight generalization of the blackfold formalism for charged black branes. Finally, we also briefly consider the thermal giant graviton moving in the AdS5 part.

Constraints on the effective fluid theory of stationary branes

A bstractWe 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.

Black Holes and Biophysical (Mem)-branes

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.

(Non)-dissipative hydrodynamics on embedded surfaces

A bstractWe construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of non-dissipative hydrodynamics to second order in a derivative expansion in the case of codimension higher than one under the assumption of no angular momenta in transverse directions to the surface. This construction includes the elastic degrees of freedom, and hence the corresponding transport coefficients, that take into account transverse fluctuations of the geometry where the fluid lives. Requiring the second law of thermodynamics to be satisfied leads us to conclude that in the case of codimension-1 surfaces the stress-energy tensor is characterized by 2 hydrodynamic and 1 elastic independent transport coefficient to first order in the expansion while for codimension higher than one, and for non-dissipative flows, the stress-energy tensor is characterized by 7 hydrodynamic and 3 elastic independent transport coefficients to second order in the expansion. Furthermore, the constraints imposed between the stress-energy tensor, the bending moment and the entropy current of the fluid by these extra non-dissipative contributions are fully captured by equilibrium partition functions. This analysis constrains the Young modulus which can be measured from gravity by elastically perturbing black branes.

Electroelasticity of charged black branes

A bstractWe present the first-order corrected dynamics of fluid branes carrying higher-form charge by obtaining the general form of their equations of motion to pole-dipole order in the absence of external forces. Assuming linear response theory, we characterize the corresponding effective theory of stationary bent charged (an)isotropic fluid branes in terms of two sets of response coefficients, the Young modulus and the piezoelectric moduli. We subsequently find large classes of examples in gravity of this effective theory, by constructing stationary strained charged black brane solutions to first order in a derivative expansion. Using solution generating techniques and bent neutral black branes as a seed solution, we obtain a class of charged black brane geometries carrying smeared Maxwell charge in Einstein-Maxwell-dilaton gravity. In the specific case of ten-dimensional space-time we furthermore use T-duality to generate bent black branes with higher-form charge, including smeared D-branes of type II string theory. By subsequently measuring the bending moment and the electric dipole moment which these geometries acquire due to the strain, we uncover that their form is captured by classical electroelasticity theory. In particular, we find that the Young modulus and the piezoelectric moduli of our strained charged black brane solutions are parameterized by a total of 4 response coefficients, both for the isotropic as well as anisotropic cases.

New geometries for black hole horizons

A bstractWe construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.