Kerr-Gauss-Bonnet Black Holes: An Analytical Approximation

Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.Comment: 5 pages, 1 figur

Slow-roll inflation with a Gauss-Bonnet correction

We consider slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave Anisotropy Probe data. The Gauss-Bonnet term with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio and hence may revive the quartic potential ruled out by recent cosmological data.Comment: 7 pages, 2 figures, RevTeX, references added, published versio

Discussion of "Second order topological sensitivity analysis" by J. Rocha de Faria et al

The article by J. Rocha de Faria et al. under discussion is concerned with the evaluation of the perturbation undergone by the potential energy of a domain $\Omega$ (in a 2-D, scalar Laplace equation setting) when a disk $B_{\epsilon}$ of small radius $\epsilon$ centered at a given location \hat{\boldsymbol{x}\in\Omega is removed from $\Omega$, assuming either Neumann or Dirichlet conditions on the boundary of the small `hole' thus created. In each case, the potential energy $\psi(\Omega_{\epsilon})$ of the punctured domain \Omega_{\epsilon}=\Omega\setminus\B_{\epsilon} is expanded about $\epsilon=0$ so that the first two terms of the perturbation are given. The first (leading) term is the well-documented topological derivative of $\psi$. The article under discussion places, logically, its main focus on the next term of the expansion. However, it contains incorrrect results, as shown in this discussion. In what follows, equations referenced with Arabic numbers refer to those of the article under discussion.Comment: International Journal of Solids and Structures (2007) to appea

Power spectra from an inflaton coupled to the Gauss-Bonnet term

We consider power-law inflation with a Gauss-Bonnet correction inspired by string theory. We analyze the stability of cosmological perturbations and obtain the allowed parameter space. We find that for GB-dominated inflation ultra-violet instabilities of either scalar or tensor perturbations show up on small scales. The Gauss-Bonnet correction with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio in the potential-dominated case. We place tight constraints on the model parameters by making use of the WMAP 5-year data.Comment: 5 pages, 4 figures, RevTeX, references added, published versio

A Quantum Gauss-Bonnet Theorem

In [4], Lanzat and Polyak introduced a polynomial invariant of generic curves in the plane as a quantization of Hopf’s Umlaufsatz, and showed that Arnold’s J+ invariant could be derived from their polynomial, leading to an integral formula for J+. Here we extend their invariant to the case of ho- mologically trivial generic curves in closed oriented surfaces with Riemannian metric. The resulting invariant turns out to be a quantization of a new formula for the rotation number, which can be viewed as a form of the Gauss-Bonnet Theorem. We show that J+ can be calculated from the generalized invariant when the Euler characteristic of the surface is nonzero, thereby obtaining an integral formula for J+ for homologically trivial curves in oriented surfaces with nonzero Euler characteristic.No embargoAcademic Major: Mathematic

Finite element modelling of an energy–storing prosthetic foot during the stance phase of transtibial amputee gait

Energy-storing prosthetic feet are designed to store energy during mid-stance motion and to recover it during latestance motion. Gait analysis is the most commonly used method to characterize prosthetic foot behaviour during walking. In using this method, however, the foot is generally modelled as a rigid body. Therefore, it does not take into account the ability of the foot to deform. However, the way this deformation occurs is a key parameter of various foot properties under gait conditions. The purpose of this study is to combine finite element modelling and gait analysis in order to calculate the strain, stress and energy stored in the foot along the stance phase for self-selected and fast walking speeds. A finite element model, validated using mechanical testing, is used with boundary conditions collected experimentally from the gait analysis of a single transtibial amputee. The stress, strain and energy stored in the foot are assessed throughout the stance phase for two walking speed conditions: a self-selected walking speed (SSWS), and a fast walking speed (FWS). The first maximum in the strain energy occurs during heel loading and reaches 3 J for SSWS and 7 J for FWS at the end of the first double support phase. The second maximum appears at the end of the single support phase, reaching 15 J for SSWS and 18 J for FWS. Finite element modelling combined with gait analysis allows the calculation of parameters that are not obtainable using gait analysis alone. This modelling can be used in the process of prosthetic feet design to assess the behaviour of a prosthetic foot under specific gait conditions