Dual-helicity eigenspinors of the charge conjugation operator [eigenspinoren des ladungskonjugationsoperators (ELKO) spinor fields] belong—together with Majorana spinor fields—to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three, respectively, corresponding to flagpole, flag-dipole, and Weyl spinor fields. This paper is devoted to investigate and provide the necessary and sufficient conditions to map Dirac spinor fields to ELKO, in order to naturally extend the standard model to spinor fields possessing mass dimension 1. As ELKO is a prime candidate to describe dark matter, an adequate and necessary formalism is introduced and developed here, to better understand the algebraic, geometric, and physical propert...

From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators

Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Cech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group \( {H^1}\left( {M,{\mathbb{Z}_2}} \right) \). The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender — from the dynamics of dark spinor fields — constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as probe the spacetime metric structure.

Exotic dark spinor fields

Exotic dark spinor fields are introduced and investigated in the context of inequivalent spin structures on arbitrary curved spacetimes, which induces an additional term on the associated Dirac operator, related to a Cech cohomology class. For the most kinds of spinor fields, any exotic term in the Dirac operator can be absorbed and encoded as a shift of the electromagnetic vector potential representing an element of the cohomology group H^1(M, Z_2). The possibility of concealing such an exotic term does not exist in case of dark (ELKO) spinor fields, as they cannot carry electromagnetic charge, so that the full topological analysis must be evaluated. Since exotic dark spinor fields also satisfy Klein-Gordon propagators, the dynamical constraints related to the exotic term in the Dirac equation can be explicitly calculated. It forthwith implies that the non-trivial topology associated to the spacetime can drastically engender --- from the dynamics of dark spinor fields --- constraints in the spacetime metric structure. Meanwhile, such constraints may be alleviated, at the cost of constraining the exotic spacetime topology. Besides being prime candidates to the dark matter problem, dark spinor fields are shown to be potential candidates to probe non-trivial topologies in spacetime, as well as probe the spacetime metric structure.

Exotic Dark Spinor Fields

Cylindrical spacetimes with rotation are studied using the Newmann–Penrose formulas. By studying null geodesic deviations, the physical meaning of each component of the Riemann tensor is given. These spacetimes are further extended to include rotating dynamic shells, and the general expression of the surface energy-momentum tensor of the shells is given in terms of the discontinuity of the first derivatives of the metric coefficients. As an application of the developed formulas, a stationary shell that generates the Lewis solutions, which represent the most general vacuum cylindrical solutions of the Einstein field equations with rotation, is studied by assuming that the spacetime inside the shell is flat. It is shown that the shell can satisfy all the energy conditions by properly choosing the parameters appearing in the model, provided that 0 ≤ σ ≤ 1, where σ is related to the mass per unit length of the shell. PACS numbers: 04.20Cv, 04.30.+x, 97.60.Sm, 97.60.Lf.

Dynamics of Rotating Cylindrical Shells in General Relativity

Nakedly Singular Solutions of Einstein's Equations (K Lake) Clifford Algebras, Relativity and Quantum Mechanics (P Lounesto) Numerical Relativity and Dynamical Evolution of Black Hole Spacetimes (R Matzner) Soliton and Vacua in Relativity Theory Revisited (G W Gibbons) Cosmic Strings and Their Observational Consequences (E P S Shellard) and 77 research papers by Latin American scientists.

Gravitation : the spacetime structure : SILARG VIII : proceedings of the 8th Latin American Symposium on Relativity and Gravitation, Águas de Lindóia, Brazil, 25-30 July 1993

W. A. Rodrigues

Papers

Gravitation : the spacetime structure : SILARG VIII : proceedings of the 8th Latin American Symposium on Relativity and Gravitation, Águas de Lindóia, Brazil, 25-30 July 1993