Niky Kamran

Separation of variables and symmetry operators for the neutrino and Dirac equations in the space‐times admitting a two‐parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences

We show that there exist a coordinate system and null tetrad for the space‐times admitting a two‐parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences in which the neutrino equation is solvable by separation of variables if and only if the Weyl tensor is Petrov type D. The massive Dirac equation is separable if in addition the conformal factor satisfies a certain functional equation. As a corollary, we deduce that the neutrino equation is separable in a canonical system of coordinates and tetrad for the solution of Einstein’s type D vacuum or electrovac field equations with cosmological constant admitting a nonsingular aligned Maxwell field and that the Dirac equation is separable only in the subclass of Carter’s [A] solutions and the Debever–McLenaghan null orbit solution A0. We also compute the symmetry operators which arise from the above separability properties.

Exhaustive integration and a single expression for the general solution of the type D vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field

We present an exhaustive integration of the type D vacuum and electrovac field equations with cosmological constant admitting a nonsingular aligned Maxwell field satisfying the generalized Goldberg–Sachs theorem. We derive a single expression for the general solution from which one may obtain all particular cases known until now in partial versions. We also investigate in detail the separability properties of the Hamilton–Jacobi equation for the charged particle orbits and of the Klein–Gordon equation for a massive charged spin‐zero test particle and their corresponding Killing tensors.

A single expression for the general solution of Einstein's vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field

Abstract We present a single expression for the general solution of Einsteins vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field satisfying the generalized Goldberg-Sachs theorem from which all the particular cases until the present known in partial versions may be deduced.

Separation of variables for the Rarita–Schwinger equation on all type D vacuum backgrounds

We present a separable master equation governing Rarita–Schwinger spin‐ (3)/(2) fields, valid in the whole class of type D vacuum backgrounds.

Equivalence of Higher Order Lagrangians II. The Cartan Form for Particle Lagrangians

It is shown how Cartan’s method of equivalence may be used to obtain the Cartan form for an r th‐order particle Lagrangian on the line by solving the standard equivalence problem under contact transformations on the jet bundle J r+k for k≥r−1.

The classification of complete sets of operators commuting with the Dirac operator in Minkowski space‐time

Under the action of the Poincare group P(1,3) the three‐, four‐, and five‐dimensional vector spaces of formally self‐adjoint first‐order matrix differential operators commuting among themselves and with the Dirac operator are classified. This gives a complete classification of the maximal subspaces of the vector space of first‐order formally self‐adjoint matrix differential operators commuting with the Dirac operator, which form an Abelian Lie algebra under the commutator.

Empty spaces and perfect fluids with homothetic transformation

A class of Lorentzian metrics in one variable that admits homothetic transformation is introduced. Solutions of Einsteins empty space equations are presented. The case of perfect fluids is discussed.

Real structures in asymptotically flat ℋ spaces

A real structure is defined in asymptotically flat ℋ spaces and investigated in connection with the equations of motion in ℋ space.