Ghost neutrinos and radiative Kerr metric in Einstein-Cartan gravity

Ghost neutrino solution in radiative Kerr spacetime endowed with totally skew-symmetric Cartan contortion is presented. The computations are made by using the Newman-Penrose (NP) calculus. The model discussed here maybe useful in several astrophysical applications specially in black hole astrophysics. PACS number(s): 0420, 0450 Departamento de F́ısica Teorica-UERJ. Rua São Fco. Xavier 524, Rio de Janeiro, RJ Maracanã, CEP:20550-003 , Brasil. E-Mail.: [email protected] Earlier Audretsch [1] have presented two interesting types of ghost neutrino solutions in Riemannian spacetime having as its carachteristic the fact that the the energy-momentum tensor was null while the neutrino current vector did not vanish. In this paper he showed that the Scharzschild and Kerr-Newman metric were not able to support ghost neutrinos. Besides he presented a solution of the Weyl neutrino equation in General Relativity (GR) which represented a pp gravitational wave coupled with a ghost neutrino. More recently Griffiths [2] presented a ghost neutrino solution in Einstein-Cartan (EC) Weyl equation which generalized the Collinson-Morris [3] ghost neutrino in GR. In the present letter we show that is possible to have a new solution of ECWeyl equation representing a ghost neutrino in Kerr radiative spacetime with torsion. Despite of several ghostness conditions proposed earlier by Letelier [4] we addopt here the same one as given in Griffiths which is the vanishing of the Riemann-Cartan U4 Ricci tensor where Rμν(Γ) = 0 (1) where Γ is the U4 connection (μ = 0, 1, 2, 3). The J μ is the neutrino current vector given by J = φ(u)l (2) where φ is the neutrino field. The Ricci tensor in U4 can be expressed in terms of the Ricci tensor in the Riemannian manifold V4 as R(μν)(Γ) = R 0 μν +∇αKμν −KαμKβν (3) where the round brackets indicate the symmetrization and the zero superscript indicates the Riemannian quantities. Thus the symmetric part of the Ricci-Cartan tensor is given by R(μν)(Γ) = R 0 μν + 2k JμJν (4) which can be expressed in therms of the neutrino current scalar field φ as R(μν)(Γ) = R 0 μν + 2k φ(u)lμlν (5) Here the vector l represents one of the four legs of the tetrad of null vectors defined by e μ i = (l , n, m, m̄μ) (6)