Related papers: Killing spinor-valued forms and their integrabilit…
We construct, for spin $0,1,2$ tensor fields on S$^d$, a set of ladder operators that connect the distinct UIRs of SO$(d+1)$. This is achieved by relying on the conformal Killing vectors of S$^d$. For the case of spinning fields, the ladder…
The presence of Killing-Yano tensors implies the existence of non-standard supersymmetries in point particle theories on curved backgrounds. In a string theoretical context these are symmetries of the modes describing the particle-like…
We introduce and carefully define an entire class of field theories based on non-standard spinors. Their dominant interaction is via the gravitational field which makes them naturally dark; we refer to them as Dark Spinors. We provide a…
We determine the Killing spinors for a class of magnetic brane solutions with Minkowski worldvolume of the theory of AdS Einstein Maxwell theories in d dimensions. We also obtain curved magnetic brane solutions with Ricci-flat worldvolumes.…
We construct the Killing spinors for a class of supersymmetric solutions of type IIB supergravity that are invariant under the non-relativistic Schrodinger algebra. The solutions depend on a five-dimensional Sasaki-Einstein space and it has…
Symmetry operators of twistor spinors and harmonic spinors can be constructed from conformal Killing-Yano forms. Transformation operators relating twistors to harmonic spinors are found in terms of potential forms. These constructions are…
We study Killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the Hamilton-Jacobi equation. This work is motivated primarily by the case of spaces of constant curvature where…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by…
In this article, we will discuss the smooth $(X_{M}+\sqrt{-1}Y_{M})$-invariant forms on $M$ and to establish a localization formulas. As an application, we get a localization formulas for characteristic numbers.
We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for $G= U(n), SU(n), Sp(n), Sp(n)\cdot…
This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set…
We study solutions to the eleven-dimensional supergravity action, including terms quartic and cubic in the Riemann curvature, that admit an eight-dimensional compact space. The internal background is found to be a conformally Kahler…
We make use of the black hole holograph construction of [I. R\'acz, Stationary black holes as holographs, Class. Quantum Grav. 31, 035006 (2014)] to analyse the existence of Killing spinors in the domain of dependence of the horizons of…
We study the spinorial Killing equation of supergravity involving a torsion 3-form $\T$ as well as a flux 4-form $\F$. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel…
Spinorial geometry techniques have recently been used to classify all half supersymmetric solutions in gauged five dimensional supergravity with vector multiplets. In this paper we consider solutions for which at least one of the Killing…
In this paper we will review some facts, both classical and recent, concerning the geometry and analysis of the Kerr and related black hole spacetimes. This includes the analysis of test fields on these spacetimes. Central to our analysis…
We present two complex scalar gauge invariants for perturbations of the Kerr spacetime defined covariantly in terms of the Killing vectors and the conformal Killing-Yano tensor of the background together with the linearized curvature and…
We discuss the pairs of quadratic integrals of motion belonging to the $n$-dimensional space of independent integrals of motion in involution, that provide integrability of the corresponding Hamiltonian equations of motion by quadratures.…
In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes is potentially computationally difficult or not at…