Related papers: The Kretschmann scalar for 5D Vacua
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.
The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial _{\overline{z}}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
The decay rate of a metastable vacuum is usually calculated using a semiclassical approximation to the Euclidean path integral. The extension to a complete Euclidean lattice Monte Carlo computation, however, is hampered by analytic…
We look for critical points with U(2) residual symmetry in 5-dimensional maximally supersymmetric gauged supergravity, by varying the embedding tensor, rather than directly minimizing the scalar potential. We recover all previously known…
In this paper, we establish the curvature estimates for a class of Hessian type equations. Some applications are also discussed.
Two-point functions of the scalar curvature for metric fluctuations on the four-sphere are analysed. The two-point function for points separated by a fixed distance and for metrics of fixed volume is calculated using spacetime foam methods.…
The regularized vacuum fluctuation related to a conformally coupled massless scalar field defined on a space-time with dynamical horizon is computed with respect a radially moving observer in a generic flat Friedmann-Robertson-Walker…
We develop an stochastic approach to study gravitational waves produced during the inflationary epoch under the presence of a decaying cosmological parameter, on a 5D geometrical background which is Riemann flat. We obtain that the squared…
Simple cosmological models based upon five-dimensional Kaluza-Klein relativity are re-examined and interesting properties are indicated. These models are special cases of those obtained by Davidson et al. and Mann and Vincent, specifically,…
We calculate the vacuum fluctuation of the stress tensor of a higher-derivative theory around a thin cosmic string. To this end, we adopt the method to obtain the stress tensor from the effective action developed by Gibbons et al. By their…
A short review of scalar curvature invariants in gravity theories is presented. We introduce how these invariants are constructed and discuss the minimal number of invariants required for a given spacetime. We then discuss applications of…
A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to…
In 2005, A. Knutson--R. Vakil conjectured a puzzle rule for equivariant K-theory of Grassmannians. We resolve this conjecture. After giving a correction, we establish a modified rule by combinatorially connecting it to the authors' recently…
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
In this paper, we derive certain curvature estimates for 4-dimensional gradient steady Ricci solitons either with positive Ricci curvature or with scalar curvature decay.
A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality $d$ of space and the degree of compressibility of the smooth advecting velocity field, the cascade of…
Spherically symmetric, vacuum solutions in 5D and 7D Kaluza-Klein theory are obtained. These solutions are flux tubes with constant cross-sectional size, located between (+) and (-) Kaluza-Klein's ``electrical'' and ``magnetic'' charges…
Some multidimensional generalizations of the Fokker-Planck equation used by R. Friedrich and J. Peinke for the description of a turbulent cascade as a stochastic process of Markovian type, are considered. The exact solutions of the Cauchy…
We present SimpleBounce, a C++ package for finding the bounce solution for the false vacuum decay. This package is based on a flow equation which is proposed by the author and solves Coleman-Glaser-Martin's reduced problem: the minimization…