Related papers: Algebraic classification of higher dimensional spa…
We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl's geometry. We show that some of the known…
In this paper we study the possibility of assigning a geometric structure to the Lie groups. It is shown the Poincar\'{e} and Weyl groups have geometrical structure of the Riemann-Cartan and Weyl space-time respectively. The geometric…
Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and…
A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed…
We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes…
The spacetime Ehlers group, which is a symmetry of the Einstein vacuum field equations for strictly stationary spacetimes, is defined and analyzed in a purely spacetime context (without invoking the projection formalism). In this setting,…
We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…
This paper derives new identities for the Weyl tensor on a gradient Ricci soliton, particularly in dimension four. First, we prove a Bochner-Weitzenb\"ock type formula for the norm of the self-dual Weyl tensor and discuss its applications,…
We study the particle spectrum and the unitarity of the generic n-dimensional Weyl-invariant quadratic curvature gravity theories around their (anti-)de Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS and…
The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
The Weyl geometric gravity theory, in which the gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a…
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…
We study the class of six-dimensional $\Lambda$-vacuum spacetimes which admit a non-degenerate multiple Weyl aligned null direction l (thus being of Weyl type~II or more special) with a ``generic'' optical matrix. Subject to an additional…
The BRST transformations for gravity with torsion including Weyl symmetry are discussed by using the so-called Maurer-Cartan horizontality conditions. Also the coupling of scalar matter fields to gravity is incorporated in this analysis.…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…
We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and…
Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl…
Following Geroch, Traschen, Mars and Senovilla, we consider Lorentzian manifolds with distributional curvature tensor. Such manifolds represent spacetimes of general relativity that possibly contain gravitational waves, shock waves, and…
We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and…