Related papers: Maxwell, Yang-Mills, Weyl and eikonal fields defin…
Properties of (skew-symmetric) conformal Yano--Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano--Killing tensor. The relation between spin-2 fields and…
The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher…
A recent complete, explicit classification of all locally constructed symmetries and currents for free spinorial massless spin s fields on Minkowski space is summarized and extended to give a classification of all covariant symmetry…
The generalized Cauchy-Riemann equations (GCRE) in biquaternion algebra appear to be Lorentz-invariant. The Laplace equation is in this case replaced by a nonlinear (complexified) eikonal equation. GCRE contain the 2-spinor and the gauge…
We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null…
A complete and explicit classification of all independent local conservation laws of Maxwell's equations in four dimensional Minkowski space is given. Besides the elementary linear conservation laws, and the well-known quadratic…
The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the…
We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not…
The generic null geodesic of the Schwarzschild--Kruskal--Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity. To realize that complexification as a Riemann surface without a cusp, and also to…
We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and…
We develop a four-dimensional gauge-gravity unification based on the $% SL(2N,C)$ gauge theory taken in a universal Yang--Mills type setting. The accompanying tetrads are promoted to dynamical fields whose length, when projected onto the…
We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which…
The properties of Dirac gamma matrices in a four-dimensional space-time with the $(2,2)$ signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in $2 + 2$ dimensions 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…
The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate…
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein-Gordon equation called Fackerell-Ipser equation. Our model is based on conformal Yano-Kiling…
We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the…
A new, conserved, symmetric tensor field for a source-free Maxwell test field on a four-dimensional spacetime with a conformal Killing-Yano tensor, satisfying a certain compatibility condition, is introduced. In particular, this…
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…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…