On El Naschieʹs complex time and gravitation

El Naschie proposed in Chaos, Solitons & Fractals, 5, 1551–1555, 1995 [1], a complex time measure and demonstrated in this connection that massless particles may, under such conditions, achieve an infinite velocity whilst adhering to all prerequisites of the special theory of relativity. The aim of the present paper is to generalize this result in the presence of a relativistic gravitational field. The method is based on Einsteinʹs equivalence principle whereby the action of a gravitational field on a test particle is locally compensated by a suitable choice of the acceleration of the particle.