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

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

On the Complexity of Optimization over the Standard Simplex

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]global optimization;standard simplex;PTAS;multivariate Bernstein approximation;semidefinite programming

Environmental sensitivity of n-i-n and undoped single GaN nanowire photodetectors

In this work, we compare the photodetector performance of single defect-free undoped and n-in GaN nanowires (NWs). In vacuum, undoped NWs present a responsivity increment, nonlinearities and persistent photoconductivity effects (~ 100 s). Their unpinned Fermi level at the m-plane NW sidewalls enhances the surface states role in the photodetection dynamics. Air adsorbed oxygen accelerates the carrier dynamics at the price of reducing the photoresponse. In contrast, in n-i-n NWs, the Fermi level pinning at the contact regions limits the photoinduced sweep of the surface band bending, and hence reduces the environment sensitivity and prevents persistent effects even in vacuum

Discrete Least-norm Approximation by Nonnegative (Trigonomtric) Polynomials and Rational Functions

Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However, the approximation may not inherit these properties automatically.We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials and rational functions that preserve nonnegativity.(trigonometric) polynomials;rational functions;semidefinite programming;regression;(Chebyshev) approximation

Robust Optimization Using Computer Experiments

During metamodel-based optimization three types of implicit errors are typically made.The first error is the simulation-model error, which is defined by the difference between reality and the computer model.The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel.The third is the implementation error.This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors.We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models.The methods proposed are applied to the design of two parts of the TV tube.The simulationmodel errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors