Roldao da Rocha

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 Čech 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

FROM DIRAC ACTION TO ELKO ACTION

{H^1}\left( {M,{\mathbb{Z}_2}} \right)

Flag-dipole spinor fields in ESK gravities

. 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.

Dynamical dispersion relation for ELKO dark spinor fields

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that defines and introduces such a mapping, is shown to be a composition of the Dirac operator and the non-unitary transformation that maps Dirac spinor fields into ELKO spinor fields, defined in a previous paper. This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

ELKO SPINOR FIELDS: LAGRANGIANS FOR GRAVITY DERIVED FROM SUPERGRAVITY

We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on

Stability of the graviton Bose–Einstein condensate in the brane-world

f(R)

Unfolding physics from the algebraic classification of spinor fields

and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given for instance by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle.

Black string corrections in variable tension braneworld scenarios

An intrinsic mass generation mechanism for exotic ELKO dark matter fields is scrutinized, in the context of the very special relativity (VSR). Our results are reported on unraveling inequivalent spin structures that educe an additional term on the associated Dirac operator. Contrary to the spinor fields of mass dimension 3/2, this term is precluded to be absorbed as a shift of some gauge vector potential, regarding the equations for the dark spinor fields. It leads to some dynamical constraints that can be intrinsically converted into a dark spinor mass generation mechanism, with the encoded symmetries maintained by the VSR. The dynamical mass is embedded in the VSR framework through a natural coupling to the kink solution of a λϕ4 theory for a scalar field ϕ. Our results evince the possibility of novel effective scenarios, derived from exotic couplings among dark spinor fields and scalar field topological solutions.

The Minimal Geometric Deformation Approach Extended

Dual-helicity eigenspinors of the charge conjugation operator (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. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein–Hilbert, the Einstein–Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekars quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that — in particular — the Einstein–Hilbert, Einstein–Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator — leading ELKO Lagrangian into the Dirac Lagrangian — is also pointed out, together with its relationship to the instanton Hopf fibration.

A de Sitter tachyon thick braneworld

Abstract We consider a solution of the effective four-dimensional Einstein equations, obtained from the general relativistic Schwarzschild metric through the principle of Minimal Geometric Deformation (MGD). Since the brane tension can, in general, introduce new singularities on a relativistic Eotvos brane model in the MGD framework, we require the absence of observed singularities, in order to constrain the brane tension. We then study the corresponding Bose–Einstein condensate (BEC) gravitational system and determine the critical stability region of BEC MGD stellar configurations. Finally, the critical stellar densities are shown to be related with critical points of the information entropy.