Nonlinear integro-differential Einstein’s field equations from nonstandard Lagrangians

Abstract

Given a manifold [Formula: see text] described by coordinates {xμ} and a space–time metric gμν on [Formula: see text] describing the gravitational field whose standard action is the Einstein–Hilbert action, we observe that if the action functional of spinor fields {Ψ(S)(x)}, S = 1, 2, …, N representing the matter and gauge fields holds a nonstandard exponential Lagrangian, the modified Einstein field equations acquire nonlinear partial integro-differential forms where both spinor and gravitational fields come out together.