614 research outputs found
Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution
The double cone, a cone over a product of a pair of spheres, is known to play
a role in the black-hole black-string phase diagram, and like all cones it is
continuously self similar (CSS). Its zero modes spectrum (in a certain sector)
is determined in detail, and it implies that the double cone is a co-dimension
1 attractor in the space of those perturbations which are smooth at the tip.
This is interpreted as strong evidence for the double cone being the critical
merger solution. For the non-symmetry-breaking perturbations we proceed to
perform a fully non-linear analysis of the dynamical system. The scaling
symmetry is used to reduce the dynamical system from a 3d phase space to 2d,
and obtain the qualitative form of the phase space, including a
non-perturbative confirmation of the existence of the "smoothed cone".Comment: 25 pages, 4 figure
Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black Hole
The auxiliary/dynamic decoupling method of hep-th/0609001 applies to
perturbations of any co-homogeneity 1 background (such as a spherically
symmetric space-time or a homogeneous cosmology). Here it is applied to compute
the perturbations around a Schwarzschild black hole in an arbitrary dimension.
The method provides a clear insight for the existence of master equations. The
computation is straightforward, coincides with previous results of
Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity
in either the definition of variables or in fixing the gauge. We note that the
method's emergent master fields are canonically conjugate to the standard ones.
In addition, our action approach yields the auxiliary sectors.Comment: 26 page
High and Low Dimensions in The Black Hole Negative Mode
The negative mode of the Schwarzschild black hole is central to Euclidean
quantum gravity around hot flat space and for the Gregory-Laflamme black string
instability. We analyze the eigenvalue as a function of space-time dimension by
constructing two perturbative expansions: one for large d and the other for
small d-3, and determining as many coefficients as we are able to compute
analytically. Joining the two expansions we obtain an interpolating rational
function accurate to better than 2% through the whole range of dimensions
including d=4.Comment: 17 pages, 4 figures. v2: added reference. v3: published versio
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
The Delocalized Effective Degrees of Freedom of a Black Hole at Low Frequencies
Identifying the fundamental degrees of freedom of a black hole poses a
long-standing puzzle. In hep-th/0511133 Goldberger and Rothstein forwarded a
theory of the low frequency degrees of freedom within the effective field
theory approach, where they are relevancy-ordered but of unclear physical
origin. Here these degrees of freedom are identified with near-horizon but
non-compact gravitational perturbations which are decomposed into delocalized
multipoles. Their world-line (kinetic) action is determined within the
classical effective field theory (CLEFT) approach and their interactions are
discussed. The case of the long-wavelength scattering of a scalar wave off a
Schwarzschild black hole is treated in some detail, interpreting within the
CLEFT approach the equality of the leading absorption cross section with the
horizon area.Comment: 8 pages. Awarded fifth prize in the 2008 Gravity Research Foundation
essay contest. v2: minor change
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
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