Related papers: Refinements of the Weyl tensor classification in f…
We consider the nonstandard inclusion of SO(3) in SO(5) associated with a 5-dimensional irreducible representation. The tensor $\Upsilon$ representing this reduction is found to be given by a ternary symmetric form with special properties.…
Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of…
We present a new class of expanding and twisting solutions to the Einstein-Maxwell equations of algebraic type D, where the null eigendirections of the Faraday tensor are not aligned with PNDs of the Weyl tensor. After deriving this novel…
We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild-Tangherlini solution. We find a particular gauge invariant component of the Weyl tensor…
It is shown that the equations of motion of eleven-dimensional supergravity follow from setting the dimension zero components of the superspace torsion tensor equal to the Dirac matrices. The proof of this assertion is facilitated by the…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the…
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the…
The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst Potential is considered. The…
Energy momentum tensors of higher-derivative free scalar conformal field theories in flat spacetime are discussed. Two algorithms for the computation of energy momentum tensors are described, which accomplish different goals: the first is…
Weyl's conformal theory of gravity is an extension of Einstein's theory of general relativity which associates metrics with 1-forms . In the case of locally integrable (closed non-exact) 1-forms the spacetime manifolds are no more simply…
Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4d algebraically special spacetimes. We investigate the 5d analogues of such solutions: vacuum spacetimes admitting a…
We discuss the generalisation of the Weyl double copy to higher spin "multi-copies", showing how the natural linearised higher spin field strengths can be related to sums of powers of the Maxwell tensor. The tracelessness of the field…
Five-dimensional gauge and gravity theories are known to exhibit striking properties. D=5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor…
We show that a spacetime satisfying the linearized vacuum Einstein equations around a type D background is generically of type I, and that the splittings of the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the Weyl…
A new effective approach to the algebraic classification of geometries in 2+1 gravity is presented. It uses five real Cotton scalars $\Psi_A$ of distinct boost weights, which are 3D analogues of the Newman-Penrose scalars representing the…
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…
In this paper we study the spectrum of all conformal, ${\cal N}$-extended supergravities (${\cal N}=1,2,3,4$) in four space-time dimensions. When these theories are obtained as massless limit of Einstein plus Weyl$^2$supergravity, the…
We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…
This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…