Related papers: The Cartan Algorithm in Five Dimensions
A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a non-flat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find…
Gell-Mann and Hartle have proposed a significant generalisation of quantum theory with a scheme whose basic ingredients are `histories' and decoherence functionals. Within this scheme it is natural to identify the space $\UP$ of…
We investigate general properties of Kerr-Schild (KS) metrics in n>4 spacetime dimensions. First, we show that the Weyl tensor is of type II or more special if the null KS vector k is geodetic (or, equivalently, if T_{ab}k^ak^b=0). We…
We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for…
There are various types of global and local spacetime invariant in general relativity. Here I focus on the local invariants obtainable from the curvature tensor and its derivatives. The number of such invariants at each order of…
The rotation of multi-dimensional arrays, or tensors, is a fundamental operation in computer science with applications ranging from data processing to scientific computing. While various methods exist, achieving this rotation in-place…
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in…
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
Elie Cartan's general equivalence problem is recast in the language of Lie algebroids. The resulting formalism, being coordinate and model-free, allows for a full geometric interpretation of Cartan's method of equivalence via reduction and…
We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the…
Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras,…
We present an exact five-dimensional ($5D$) rotating regular black hole metric, with a deviation parameter $k\geq 0$, that interpolates between the $5D$ Kerr black hole ($k=0$) and $5D$ Kerr-Newman ($r \gg k$). This $5D$ rotating regular…
The necessary and sufficient conditions for a spacetime with an invariant frame to admit a group of isometries of dimension $r$ are given in terms of the connection tensor $H$ associated with this frame. In Petrov-Bel types I, II and III,…
We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any…
The Kerr-type solutions of the five-dimensional Einstein and Einstein-Gauss-Bonnet equations look pretty similar when written in Kerr-Schild form. However the Myers-Perry spacetime is circular whereas the rotating solution of the…
Recently, Peter Doyle and Curt McMullen devised an iterative solution to the fifth degree polynomial. At the method's core is a rational mapping of the Riemann sphere with the icosahedral symmetry of a general quintic. Moreover, this map…
This article is dedicated to solve the equivalence problem for two third order differential operators on the line under general fiber--preserving transformation using the Cartan method of equivalence. We will do three versions of the…
Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalization of the vector-field method, which allows the use of higher-order symmetry operators.…
Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of $D\rightarrow\infty$. Similar to classification of any arbitrary dimension $D>4$, this spacetime is…
The calculation of loop amplitudes with parity violation or spin effects within dimensional regularization needs a consistent definition of gamma5. Also loop calculations in supersymmetric theories need a consistent definition of gamma5. In…