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Integrability and Einstein's equations

N. Woodhouse (1997)

Banach Center Publications

1. Introduction. In recent years, there has been considerable interest in Oxford and elsewhere in the connections between Einstein's equations, the (anti-) self-dual Yang-Mills (SDYM) equations, and the theory of integrable systems. The common theme running through this work is that, to a greater or lesser extent, all three areas involve questions that can be addressed by twistor methods. In this paper, I shall review progress, with particular emphasis on the known and potential applications in...

New Vacuum Solutions for Quadratic Metric-Affine Gravity - a Metric Affine Model for the Massless Neutrino?

Pasic, Vedad (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 83C15, 83C35In this paper we present an overview of our research that was presented at theMASSEE International Congress on Mathematics MICOM 2009 in Ohrid, Macedonia. We deal with quadratic metric–affine gravity, which is an alternative theory of gravity. We present new vacuum solutions for this theory and an attempt to give their physical interpretation on the basis of comparison with existing classical models. These new explicit vacuum solutions of quadratic metric–affine...

Quasi-local energy-momentum and the Sen geometry of two-surfaces

László Szabados (1997)

Banach Center Publications

We review the main ideas of the two dimensional Sen geometry and apply these concepts i. in finding the `most natural' quasi-local energy-momentum, ii. in characterizing the zero energy-momentum and zero mass configurations and iii. in finding the quasi-local radiative modes of general relativity.

Théorie de la diffusion pour l’équation de Dirac sans masse dans la métrique de Kerr

Dietrich Häfner, Jean-Philippe Nicolas (2002/2003)

Séminaire Équations aux dérivées partielles

Pour l’équation de Dirac sans masse à l’extérieur d’un trou noir de Kerr lent nous démontrons la complétude asymptotique. Nous introduisons une nouvelle tétrade de Newman-Penrose pour laquelle l’expression de l’équation ne contient pas de termes à longue portée artificiels. La technique principale utilisée est une estimation de Mourre. La géométrie proche de l’horizon exige d’appliquer une transformation unitaire avant de se retrouver dans une situation dans laquelle le générateur de dilatations...

Two new estimates for eigenvalues of Dirac operators

Wenmin Gong, Guangcun Lu (2016)

Annales Polonici Mathematici

We establish lower and upper eigenvalue estimates for Dirac operators in different settings, a new Kirchberg type estimate for the first eigenvalue of the Dirac operator on a compact Kähler spin manifold in terms of the energy momentum tensor, and an upper bound for the smallest eigenvalues of the twisted Dirac operator on Legendrian submanifolds of Sasakian manifolds. The sharpness of those estimates is also discussed.

Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

Daniel Canarutto (2018)

Archivum Mathematicum

An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle S M with 2-dimensional fibers, called a 2 -spinor bundle. Any further considered object is assumed to...

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