New Solutions of the Einstein-dirac Equation in Dimension

Consider a Riemannian spin manifold of dimension n ≥ 3 and denote by D the Dirac operator acting on spinor fields. A solution of the Einstein-Dirac equation is a spinor field ψ solving the equations Ric − 1 2 S · g = ± 1 4 T ψ , D(ψ) = λψ. Here S denotes the scalar curvature of the space, λ is a real constant and T ψ is the energy-momentum tensor of the spinor field ψ defined by the formula