729 research outputs found
Matched Asymptotic Expansion for Caged Black Holes - Regularization of the Post-Newtonian Order
The "dialogue of multipoles" matched asymptotic expansion for small black
holes in the presence of compact dimensions is extended to the Post-Newtonian
order for arbitrary dimensions. Divergences are identified and are regularized
through the matching constants, a method valid to all orders and known as
Hadamard's partie finie. It is closely related to "subtraction of
self-interaction" and shows similarities with the regularization of quantum
field theories. The black hole's mass and tension (and the "black hole
Archimedes effect") are obtained explicitly at this order, and a Newtonian
derivation for the leading term in the tension is demonstrated. Implications
for the phase diagram are analyzed, finding agreement with numerical results
and extrapolation shows hints for Sorkin's critical dimension - a dimension
where the transition turns second order.Comment: 28 pages, 5 figures. v2:published versio
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
No analytic solution is known to date for a black hole in a compact
dimension. We develop an analytic perturbation theory where the small parameter
is the size of the black hole relative to the size of the compact dimension. We
set up a general procedure for an arbitrary order in the perturbation series
based on an asymptotic matched expansion between two coordinate patches: the
near horizon zone and the asymptotic zone. The procedure is ordinary
perturbation expansion in each zone, where additionally some boundary data
comes from the other zone, and so the procedure alternates between the zones.
It can be viewed as a dialogue of multipoles where the black hole changes its
shape (mass multipoles) in response to the field (multipoles) created by its
periodic "mirrors", and that in turn changes its field and so on. We present
the leading correction to the full metric including the first correction to the
area-temperature relation, the leading term for black hole eccentricity and the
"Archimedes effect". The next order corrections will appear in a sequel. On the
way we determine independently the static perturbations of the Schwarzschild
black hole in dimension d>=5, where the system of equations can be reduced to
"a master equation" - a single ordinary differential equation. The solutions
are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the
introductio
The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability
It is shown that the usual entropy argument for the Gregory-Laflamme (GL)
instability for appropriate black strings and -branes gives
surprising agreement up to a few percent. This may provide a strong support to
the GL's horizon fragmentation, which would produce the array of
higher-dimensional Schwarzschild-type's black holes finally. On the other hand,
another estimator for the size of the black hole end-state relative to the
compact dimension indicates a second order (i.e., smooth) phase transition for
some appropriate compactifications and total dimension of spacetime
wherein the entropy argument is not appropriate. In this case,
Horowitz-Maeda-type's non-uniform black strings or -branes can be the final
state of the GL instability.Comment: More emphasis on a second order phase transition. The computation
result is unchange
On Black-Brane Instability In an Arbitrary Dimension
The black-hole black-string system is known to exhibit critical dimensions
and therefore it is interesting to vary the spacetime dimension , treating
it as a parameter of the system. We derive the large asymptotics of the
critical, i.e. marginally stable, string following an earlier numerical
analysis. For a background with an arbitrary compactification manifold we give
an expression for the critical mass of a corresponding black brane. This
expression is completely explicit for , the dimensional torus of
an arbitrary shape. An indication is given that by employing a higher
dimensional torus, rather than a single compact dimension, the total critical
dimension above which the nature of the black-brane black-hole phase transition
changes from sudden to smooth could be as low as .Comment: 1+14 pages, 2 eps figures. Replaced with the published versio
Holographic repulsion and confinement in gauge theory
We show that for asymptotically anti-deSitter backgrounds with negative
energy, such as the AdS soliton and regulated negative mass AdS-Schwarzshild
metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a
Coulomb to confinement transition. We also show that the quark-antiquark () potential can be interpreted as affine time along null geodesics on
the minimal string world sheet,and that its intrinsic curvature provides a
signature of transition to confinement phase. The result demonstrates a UV/IR
relation in that the boundary separation of the pair exhibits an
inverse relationship with the radial descent of the world sheet into the bulk.
Our results suggest a generic (holographic) relationship between confinement in
gauge theory and repulsive gravity, which in turn is connected with singularity
avoidance in quantum gravity.Comment: 8 pages, 4 figure
Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
We describe the first convergent numerical method to determine static black
hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a
family of solutions parametrized by the ratio of the black hole size and the
size of the compact extra dimension. The solutions satisfy the demanding
integrated first law. For small black holes our solutions approach the 5d
Schwarzschild solution and agree very well with new theoretical predictions for
the small corrections to thermodynamics and geometry. The existence of such
black holes is thus established. We report on thermodynamical (temperature,
entropy, mass and tension along the compact dimension) and geometrical
measurements. Most interestingly, for large masses (close to the
Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as
evidence for an approach to a physical tachyonic instability. Using
extrapolation we speculate that the system undergoes a first order phase
transition.Comment: 42 pages, 19 eps figures; v2: 3 references added, version to appear
in Phys.Rev.
Network synchronization of groups
In this paper we study synchronized motions in complex networks in which
there are distinct groups of nodes where the dynamical systems on each node
within a group are the same but are different for nodes in different groups.
Both continuous time and discrete time systems are considered. We initially
focus on the case where two groups are present and the network has bipartite
topology (i.e., links exist between nodes in different groups but not between
nodes in the same group). We also show that group synchronous motions are
compatible with more general network topologies, where there are also
connections within the groups
Stable non-uniform black strings below the critical dimension
The higher-dimensional vacuum Einstein equation admits translationally
non-uniform black string solutions. It has been argued that infinitesimally
non-uniform black strings should be unstable in 13 or fewer dimensions and
otherwise stable. We construct numerically non-uniform black string solutions
in 11, 12, 13, 14 and 15 dimensions. Their stability is investigated using
local Penrose inequalities. Weakly non-uniform solutions behave as expected.
However, in 12 and 13 dimensions, strongly non-uniform solutions appear to be
stable and can have greater horizon area than a uniform string of the same
mass. In 14 and 15 dimensions all non-uniform black strings appear to be
stable.Comment: 26 pages, 11 figures. V2: reference added, matches published versio
Hall effect and geometric phases in Josephson junction arrays
Since effectively the local contact vortex velocity dependent part of the Magnus force in a Josephson junction array is zero in the classical limit, we predict zero classical Hall effect. In the quantum limit because of the geometric phases due to the finite superfluid density at superconductor grains, rich and complex Hall effect is found in this quantum regime due to the Thouless-Kohmoto-Nightingale-den-Nijs effect
Post-ISCO Ringdown Amplitudes in Extreme Mass Ratio Inspiral
An extreme mass ratio inspiral consists of two parts: adiabatic inspiral and
plunge. The plunge trajectory from the innermost stable circular orbit (ISCO)
is special (somewhat independent of initial conditions). We write an expression
for its solution in closed-form and for the emitted waveform. In particular we
extract an expression for the associated black-hole ringdown amplitudes, and
evaluate them numerically.Comment: 21 pages, 5 figures. v4: added section with numerical evaluation of
the ringdown amplitude
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