85,740 research outputs found
Non-extremal black holes from the generalised r-map
We review the timelike dimensional reduction of a class of five-dimensional
theories that generalises 5D, N = 2 supergravity coupled to vector multiplets.
As an application we construct instanton solutions to the four-dimensional
Euclidean theory, and investigate the criteria for solutions to lift to static
non-extremal black holes in five dimensions.
We focus specifically on two classes of models: STU-like models, and models
with a block diagonal target space metric. For STU-like models the second order
equations of motion of the four-dimensional theory can be solved explicitly,
and we obtain the general solution. For block diagonal models we find a
restricted class of solutions, where the number of independent scalar fields
depends on the number of blocks. When lifting these solutions to five
dimensions we show, by explicit calculation, that one obtains static
non-extremal black holes with scalar fields that take finite values on the
horizon only if the number of integration constants reduces by exactly half.Comment: 22 pages. Based on talk by OV at "Black Objects in Supergravity
School" (BOSS2011), INFN, Frascati, Italy, 9-13 May, 201
Mixed superposition rules and the Riccati hierarchy
Mixed superposition rules, i.e., functions describing the general solution of
a system of first-order differential equations in terms of a generic family of
particular solutions of first-order systems and some constants, are studied.
The main achievement is a generalization of the celebrated Lie-Scheffers
Theorem, characterizing systems admitting a mixed superposition rule. This
somehow unexpected result says that such systems are exactly Lie systems, i.e.,
they admit a standard superposition rule. This provides a new and powerful tool
for finding Lie systems, which is applied here to studying the Riccati
hierarchy and to retrieving some known results in a more efficient and simpler
way.Comment: 20 page
Marginal States in Mean Field Glasses
We study mean field systems whose free energy landscape is dominated by
marginally stable states. We review and develop various techniques to describe
such states, elucidating their physical meaning and the interrelation between
them. In particular, we give a physical interpretation of the two-group replica
symmetry breaking scheme and confirm it by establishing the relation to the
cavity method and to the counting of solutions of the Thouless-Anderson-Palmer
equations. We show how these methods all incorporate the presence of a soft
mode in the free energy landscape and interpret the occurring order parameter
functions in terms of correlations between the soft mode and the local
magnetizations. The general formalism is applied to the prototypical case of
the Sherrington-Kirkpatrick-model where we re-examine the physical properties
of marginal states under a new perspective.Comment: 27 pages, 8 figure
Non-extremal and non-BPS extremal five-dimensional black strings from generalized special real geometry
We construct non-extremal as well as extremal black string solutions in
minimal five-dimensional supergravity coupled to vector multiplets using
dimensional reduction to three Euclidean dimensions. Our method does not assume
that the scalar manifold is a symmetric space, and applies as well to a class
of non-supersymmetric theories governed by a generalization of special real
geometry. We find that five-dimensional black string solutions correspond to
geodesics in a specific totally geodesic para-K\"ahler submanifold of the
scalar manifold of the dimensionally reduced theory, and identify the subset of
geodesics that corresponds to regular black string solutions in five
dimensions. BPS and non-BPS extremal solutions are distinguished by whether the
corresponding geodesics are along the eigendirections of the para-complex
structure or not, a characterization which carries over to non-supersymmetric
theories. For non-extremal black strings the values of the scalars at the outer
and inner horizon are not independent integration constants but determined by
certain functions of the charges and moduli. By lifting solutions from three to
four dimensions we obtain non-extremal versions of small black holes, and find
that while the outer horizon takes finite size, the inner horizon is still
degenerate.Comment: 46 page
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