2,158 research outputs found
Stability and Thermodynamics of AdS Black Holes with Scalar Hair
Recently a class of static spherical black hole solutions with scalar hair
was found in four and five dimensional gauged supergravity with modified, but
AdS invariant boundary conditions. These black holes are fully specified by a
single conserved charge, namely their mass, which acquires a contribution from
the scalar field. Here we report on a more detailed study of some of the
properties of these solutions. A thermodynamic analysis shows that in the
canonical ensemble the standard Schwarzschild-AdS black hole is stable against
decay into a hairy black hole. We also study the stability of the hairy black
holes and find there always exists an unstable radial fluctuation, in both four
and five dimensions. We argue, however, that Schwarzschild-AdS is probably not
the endstate of evolution under this instability.Comment: 18 pages, 4 figure
Violation of Energy Bounds in Designer Gravity
We continue our study of the stability of designer gravity theories, where
one considers anti-de Sitter gravity coupled to certain tachyonic scalars with
boundary conditions defined by a smooth function W. It has recently been argued
there is a lower bound on the conserved energy in terms of the global minimum
of W, if the scalar potential arises from a superpotential P and the scalar
reaches an extremum of P at infinity. We show, however, there are
superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos
corrected, reference adde
Particle Production near an AdS Crunch
We numerically study the dual field theory evolution of five-dimensional
asymptotically anti-de Sitter solutions of supergravity that develop
cosmological singularities. The dual theory is an unstable deformation of the N
= 4 gauge theory on R S3, and the big crunch singularity in the bulk
occurs when a boundary scalar field runs to infinity. Consistent quantum
evolution requires one imposes boundary conditions at infinity. Modeling these
by a steep regularization of the scalar potential, we find that when an
initially nearly homogeneous wavepacket rolls down the potential, most of the
potential energy of the initial configuration is converted into gradient energy
during the first oscillation of the field. This indicates there is no
transition from a big crunch to a big bang in the bulk for dual boundary
conditions of this kind.Comment: 20 pages, 6 figure
Numerical simulation of a possible counterexample to cosmic censorship
A numerical simulation is presented here of the evolution of initial data of
the kind that was conjectured by Hertog, Horowitz and Maeda to be a violation
of cosmic censorship. That initial data is essentially a thick domain wall
connecting two regions of anti-deSitter space. The initial data has a free
parameter that is the initial size of the wall. The simulation shows no
violation of cosmic censorship, but rather the formation of a small black hole.
The simulation described here is for a moderate wall size and leaves open the
possibility that cosmic censorship might be violated for larger walls.Comment: discussion clarifie
Towards a Novel no-hair Theorem for Black Holes
We provide strong numerical evidence for a new no-scalar-hair theorem for
black holes in general relativity, which rules out spherical scalar hair of
static four dimensional black holes if the scalar field theory, when coupled to
gravity, satisfies the Positive Energy Theorem. This sheds light on the
no-scalar-hair conjecture for Calabi-Yau compactifications of string theory,
where the effective potential typically has negative regions but where
supersymmetry ensures the total energy is always positive. In theories where
the scalar tends to a negative local maximum of the potential at infinity, we
find the no-scalar-hair theorem holds provided the asymptotic conditions are
invariant under the full anti-de Sitter symmetry group.Comment: 25 pages, 11 figure
Towards a Big Crunch Dual
We show there exist smooth asymptotically anti-de Sitter initial data which
evolve to a big crunch singularity in a low energy supergravity limit of string
theory. This opens up the possibility of using the dual conformal field theory
to obtain a fully quantum description of the cosmological singularity. A
preliminary study of this dual theory suggests that the big crunch is an
endpoint of evolution even in the full string theory. We also show that any
theory with scalar solitons must have negative energy solutions. The results
presented here clarify our earlier work on cosmic censorship violation in N=8
supergravity.Comment: 27 pages, 3 figures;v2:minor correction
Stability in Designer Gravity
We study the stability of designer gravity theories, in which one considers
gravity coupled to a tachyonic scalar with anti-de Sitter boundary conditions
defined by a smooth function W. We construct Hamiltonian generators of the
asymptotic symmetries using the covariant phase space method of Wald et al.and
find they differ from the spinor charges except when W=0. The positivity of the
spinor charge is used to establish a lower bound on the conserved energy of any
solution that satisfies boundary conditions for which has a global minimum.
A large class of designer gravity theories therefore have a stable ground
state, which the AdS/CFT correspondence indicates should be the lowest energy
soliton. We make progress towards proving this, by showing that minimum energy
solutions are static. The generalization of our results to designer gravity
theories in higher dimensions involving several tachyonic scalars is discussed.Comment: 29 page
Holographic Description of AdS Cosmologies
To gain insight in the quantum nature of the big bang, we study the dual
field theory description of asymptotically anti-de Sitter solutions of
supergravity that have cosmological singularities. The dual theories do not
appear to have a stable ground state. One regularization of the theory causes
the cosmological singularities in the bulk to turn into giant black holes with
scalar hair. We interpret these hairy black holes in the dual field theory and
use them to compute a finite temperature effective potential. In our study of
the field theory evolution, we find no evidence for a "bounce" from a big
crunch to a big bang. Instead, it appears that the big bang is a rare
fluctuation from a generic equilibrium quantum gravity state.Comment: 34 pages, 8 figures, v2: minor changes, references adde
Hidden Convexity in Partially Separable Optimization
The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization
Is It Really Naked? On Cosmic Censorship in String Theory
We investigate the possibility of cosmic censorship violation in string
theory using a characteristic double-null code, which penetrates horizons and
is capable of resolving the spacetime all the way to the singularity. We
perform high-resolution numerical simulations of the evolution of negative mass
initial scalar field profiles, which were argued to provide a counterexample to
cosmic censorship conjecture for AdS-asymptotic spacetimes in five-dimensional
supergravity. In no instances formation of naked singularity is seen. Instead,
numerical evidence indicates that black holes form in the collapse. Our results
are consistent with earlier numerical studies, and explicitly show where the
`no black hole' argument breaks.Comment: 8 pages, 5 figures, 1 table; REVTeX 4.
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