24 research outputs found
Ricci flow and black holes
Gradient flow in a potential energy (or Euclidean action) landscape provides
a natural set of paths connecting different saddle points. We apply this method
to General Relativity, where gradient flow is Ricci flow, and focus on the
example of 4-dimensional Euclidean gravity with boundary S^1 x S^2,
representing the canonical ensemble for gravity in a box. At high temperature
the action has three saddle points: hot flat space and a large and small black
hole. Adding a time direction, these also give static 5-dimensional
Kaluza-Klein solutions, whose potential energy equals the 4-dimensional action.
The small black hole has a Gross-Perry-Yaffe-type negative mode, and is
therefore unstable under Ricci flow. We numerically simulate the two flows
seeded by this mode, finding that they lead to the large black hole and to hot
flat space respectively, in the latter case via a topology-changing
singularity. In the context of string theory these flows are world-sheet
renormalization group trajectories. We also use them to construct a novel free
energy diagram for the canonical ensemble.Comment: 31 pages, 14 color figures. v2: Discussion of the metric on the space
of metrics corrected and expanded, references adde
Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity
We consider spatially homogeneous Lifshitz black hole solutions in five
dimensional higher derivative gravity theories, which can be possible near
horizon geometries of some systems that are interesting in the framework of
gauge/gravity duality. We show the solutions belonging to the nine Bianchi
classes in the pure R^2 gravity. We find that these black holes have zero
entropy at non-zero temperatures and this property is the same as the case of
BTZ black holes in new massive gravity at the critical point. In the most
general quadratic curvature gravity theories, we find new solutions in Bianchi
Type I and Type IX cases.Comment: 15 pages, no figure; v2, refs added, version to appear in JHE
On the uniqueness and global dynamics of AdS spacetimes
We study global aspects of complete, non-singular asymptotically locally AdS
spacetimes solving the vacuum Einstein equations whose conformal infinity is an
arbitrary globally stationary spacetime. It is proved that any such solution
which is asymptotically stationary to the past and future is itself globally
stationary.
This gives certain rigidity or uniqueness results for exact AdS and related
spacetimes.Comment: 18pp, significant revision of v
Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes
We study the effect of an order N^2 density of heavy quarks in strongly
coupled N=4 SUSY Yang-Mills theory in the large N limit. This is achieved in
the type IIB supergravity dual by introducing a uniformly smeared density of
macroscopic string sources stretching to the boundary of AdS_5 x S^5. The
backreacted system exhibits a flow from an AdS_5 "hedgehog" geometry to a
scaling Lifshitz-like solution Lif_5 x S^5 with dynamical critical exponent
z=7, wherein the scaling symmetry is broken by a logarithmic running dilaton.
We find an exact black brane solution within the scaling regime which describes
the low temperature thermodynamics of the system.Comment: 20 pages, 2 figures, references adde
New AdS solitons and brane worlds with compact extra-dimensions
We construct new static, asymptotically AdS solutions where the conformal
infinity is the product of Minkowski spacetime and a sphere . Both
globally regular, soliton-type solutions and black hole solutions are
considered. The black holes can be viewed as natural AdS generalizations of the
Schwarzschild black branes in Kaluza-Klein theory. The solitons provide new
brane-world models with compact extra-dimensions. Different from the
Randall-Sundrum single-brane scenario, a Schwarzschild black hole on the Ricci
flat part of these branes does not lead to a naked singularity in the bulk.Comment: 28 pages, 4 figure
Luttinger's theorem, superfluid vortices, and holography
Strongly coupled field theories with gravity duals can be placed at finite
density in two ways: electric field flux emanating from behind a horizon, or
bulk charged fields outside of the horizon that explicitly source the density.
We discuss field-theoretical observables that are sensitive to this
distinction. If the charged fields are fermionic, we discuss a modified
Luttinger's theorem that holds for holographic systems, in which the sum of
boundary theory Fermi surfaces counts only the charge outside of the horizon.
If the charged fields are bosonic, we show that the the resulting superfluid
phase may be characterized by the coefficient of the transverse Magnus force on
a moving superfluid vortex, which again is sensitive only to the charge outside
of the horizon. For holographic systems these observables provide a
field-theoretical way to distinguish how much charge is held by a dual horizon,
but they may be useful in more general contexts as measures of deconfined (i.e.
"fractionalized") charge degrees of freedom.Comment: 21 pages; version 2: minor changes, version to be published in CQG;
version 3: minor change
A General Black String and its Microscopics
Using G2(2) dualities we construct the most general black string solution of
minimal five-dimensional ungauged supergravity. The black string has five
independent parameters, namely, the magnetic one-brane charge, smeared electric
zero-brane charge, boost along the string direction, energy above the BPS
bound, and rotation in the transverse space. In one extremal limit it reduces
to the three parameter supersymmetric string of five-dimensional minimal
supergravity; in another extremal limit it reduces to the three parameter
non-supersymmetric extremal string of five-dimensional minimal supergravity. It
also admits an extremal limit when it has maximal rotation in the
four-dimensional transverse space. The decoupling limit of our general black
string is a BTZ black hole times a two sphere. The macroscopic entropy of the
string is reproduced by the Maldacena-Strominger-Witten CFT in appropriate
ranges of the parameters. When the pressureless condition is imposed, our
string describes the infinite radius limit of the most general class of black
rings of minimal supergravity. We discuss implications our solution has for
extremal and non-extremal black rings of minimal supergravity.Comment: 35 pages; 3 figures; v2 section 4.1.1 rewritten + minor changes + ref
adde
Instabilities of Black Strings and Branes
We review recent progress on the instabilities of black strings and branes
both for pure Einstein gravity as well as supergravity theories which are
relevant for string theory. We focus mainly on Gregory-Laflamme instabilities.
In the first part of the review we provide a detailed discussion of the
classical gravitational instability of the neutral uniform black string in
higher dimensional gravity. The uniform black string is part of a larger phase
diagram of Kaluza-Klein black holes which will be discussed thoroughly. This
phase diagram exhibits many interesting features including new phases,
non-uniqueness and horizon-topology changing transitions. In the second part,
we turn to charged black branes in supergravity and show how the
Gregory-Laflamme instability of the neutral black string implies via a
boost/U-duality map similar instabilities for non- and near-extremal smeared
branes in string theory. We also comment on instabilities of D-brane bound
states. The connection between classical and thermodynamic stability, known as
the correlated stability conjecture, is also reviewed and illustrated with
examples. Finally, we examine the holographic implications of the
Gregory-Laflamme instability for a number of non-gravitational theories
including Yang-Mills theories and Little String Theory.Comment: 119 pages, 16 figures. Invited review for Classical and Quantum
Gravit