67 research outputs found
How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
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. 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.Comment: v3: 50pp; minor corrections in Sec. 3.2; typos fixed; published in
JHE
Instabilities of Thin Black Rings: Closing the Gap
We initiate the study of dynamical instabilities of higher-dimensional black
holes using the blackfold approach, focusing on asymptotically flat boosted
black strings and singly-spinning black rings in . We derive novel
analytic expressions for the growth rate of the Gregory-Laflamme instability
for boosted black strings and its onset for arbitrary boost parameter. In the
case of black rings, we study their stability properties in the region of
parameter space that has so far remained inaccessible to numerical approaches.
In particular, we show that very thin (ultraspinning) black rings exhibit a
Gregory-Laflamme instability, giving strong evidence that black rings are
unstable in the entire range of parameter space. For very thin rings, we show
that the growth rate of the instability increases with increasing
non-axisymmetric mode while for thicker rings, there is competition between
the different modes. However, up to second order in the blackfold
approximation, we do not observe an elastic instability, in particular for
large modes , where this approximation has higher accuracy. This
suggests that the Gregory-Laflamme instability is the dominant instability for
very thin black rings. Additionally, we find a long-lived mode that describes a
wiggly time-dependent deformation of a black ring. We comment on disagreements
between our results and corresponding ones obtained from a large analysis
of black ring instabilities.Comment: v3: 31pp, 7figs; clarifications added, typos fixe
Constraints on the effective fluid theory of stationary branes
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.Comment: v2: 26pp, 3 figures, minor clarifications, presentation improved, to
be published in JHE
Blackfolds, Plane Waves and Minimal Surfaces
Minimal surfaces in Euclidean space provide examples of possible non-compact
horizon geometries and topologies in asymptotically flat space-time. On the
other hand, the existence of limiting surfaces in the space-time provides a
simple mechanism for making these configurations compact. Limiting surfaces
appear naturally in a given space-time by making minimal surfaces rotate but
they are also inherent to plane wave or de Sitter space-times in which case
minimal surfaces can be static and compact. We use the blackfold approach in
order to scan for possible black hole horizon geometries and topologies in
asymptotically flat, plane wave and de Sitter space-times. In the process we
uncover several new configurations, such as black helicoids and catenoids, some
of which have an asymptotically flat counterpart. In particular, we find that
the ultraspinning regime of singly-spinning Myers-Perry black holes, described
in terms of the simplest minimal surface (the plane), can be obtained as a
limit of a black helicoid, suggesting that these two families of black holes
are connected. We also show that minimal surfaces embedded in spheres rather
than Euclidean space can be used to construct static compact horizons in
asymptotically de Sitter space-times.Comment: v2: 67pp, 7figures, typos fixed, matches published versio
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.Comment: v2: 5pp, 3 figures, improved introduction, to be published in PR
One-form superfluids and magnetohydrodynamics
We use the framework of generalised global symmetries to study various
hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic
theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The
latter of these describes a one-form superfluid, which is characterised by a
vector Goldstone mode and a two-form superfluid velocity. Two special limits of
this theory have been studied in detail: the string fluid limit where the U(1)
one-form symmetry is partly restored, and the electric limit in which the
symmetry is completely broken. The transport properties of these theories are
investigated in depth by studying the constraints arising from the second law
of thermodynamics and Onsager's relations at first order in derivatives. We
also construct a hydrostatic effective action for the Goldstone modes in these
theories and use it to characterise the space of all equilibrium
configurations. To make explicit contact with hot electromagnetism, the
traditional treatment of magnetohydrodynamics, where the electromagnetic photon
is incorporated as dynamical degrees of freedom, is extended to include
parity-violating contributions. We argue that the chemical potential and
electric fields are not independently dynamical in magnetohydrodynamics, and
illustrate how to eliminate these within the hydrodynamic derivative expansion
using Maxwell's equations. Additionally, a new hydrodynamic theory of
non-conducting, but polarised, plasmas is formulated, focusing primarily on the
magnetically dominated sector. Finally, it is shown that the different limits
of one-form superfluids formulated in terms of generalised global symmetries
are exactly equivalent to magnetohydrodynamics and the hydrodynamics of
non-conducting plasmas at the non-linear level.Comment: v3: 69 + 1 pages, 1 figure, added clarifications and appendix with
discrete symmetries, to be published in JHE
On actions for (entangling) surfaces and DCFTs
The dynamics of surfaces and interfaces describe many physical systems,
including fluid membranes, entanglement entropy and the coupling of defects to
quantum field theories. Based on the formulation of submanifold calculus
developed by Carter, we introduce a new variational principle for (entangling)
surfaces. This principle captures all diffeomorphism constraints on
surface/interface actions and their associated spacetime stress tensor. The
different couplings to the geometric tensors appearing in the surface action
are interpreted in terms of response coefficients within elasticity theory. An
example of a surface action with edges at the two-derivative level is studied,
including both the parity-even and parity-odd sectors. Its conformally
invariant counterpart restricts the type of conformal anomalies that can appear
in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics,
it is shown that classification methods can be used to constrain the stress
tensor of (entangling) surfaces at a given order in derivatives. This analysis
reveals a purely geometric parity-odd contribution to the Young modulus of a
thin elastic membrane. Extending this novel variational principle to BCFTs and
DCFTs in curved spacetimes allows to obtain the Ward identities for
diffeomorphism and Weyl transformations. In this context, we provide a formal
derivation of the contact terms in the stress tensor and of the displacement
operator for a broad class of actions.Comment: v2: 71pp, 1fig, comments and references added, typos fixed, to be
published in JHE
New Geometries for Black Hole Horizons
We 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 -branes
as well as helicoidal black rings and helicoidal black tori in .Comment: v2: 37pp, 5figures, typos fixed, matches published versio
Electroelasticity of Charged Black Branes
We 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. 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.Comment: v2: 40pp; typos fixe
- …