Related papers: The geometry of null-like disformal transformation…

In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric…

We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned…

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schr\"odinger equation. In particular we discuss the algebra $\mathfrak{sch}(d)$ of vector fields conformally-preserving…

We study optical metrics via null geodesics as a central force system, deduce the related Binet equation and apply the analysis to certain solutions of Einstein's equations with and without spherical symmetry. A general formula for the…

We study the symmetries of the Lorentz violating Randers-Finsler spacetime. The privileged frame defined by the background vector diagonalises the deformed mass-shell and provides an anisotropic observer transformations. The particle…

We investigate the tidal response of Kerr black holes in four-dimensional space-times subjected to external gravitational fields. Using the Ernst formalism and Weyl coordinates, we analyze the non-linear tidal deformation of rotating black…

It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if…

We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra…

The Horndeski action is the most general one involving a metric and a scalar field that leads to second-order field equations in four dimensions. Being the natural extension of the well-known scalar-tensor theories, its structure and…

We study interacting massive N=(2,2) supersymmetric field theories in two dimensions which arise from deforming conformal field theories with a continuous spectrum. Firstly, we deform N=2 superconformal Liouville theory with relevant…

This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the…

We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely…

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional \Lambda-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double…

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…

We show that existing decay results for scalar fields on the Schwarzschild metric are sufficient to obtain a conformal scattering theory. Then we re-interpret this as an analytic scattering theory defined in terms of wave operators, with an…

The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are…

In quantum gravity, physically meaningful operator is required to be invariant under the diffeomorphisms. Such gauge invariant operator is typically given by the relational observable, the operator localized in relation to some background…

This elementary discussion generalizes a Weyl geometry to allow quaternion valued gauge transformations and classical Yang-Mills geometric fields. This development will assume that the symmetric metric tensor is real in some gauge, and will…

The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…

A special subclass of shear-free null congruences (SFC) is studied, with tangent vector field being a repeated principal null direction of the Weyl tensor. We demonstrate that this field is parallel with respect to an effective affine…