A pulsar model from an oscillating black hole

Abstract

The first part of this paper examines conditions in accord with Einstein's criterion of regularity on the field solutions everywhere that would correspond to the existence of a black hole star, following from solutions of his (nonvacuum) field equations. ‘Black hole’ is defined here as a star whose matter is so condensed as to correspond to a complete family of spatially closed geodesics. The condition imposed is that the angular momentum of a test body in each of the closed geodesics is a constant of the motion. The second part of the paper examines the implications in the problem of the condensed star of a generalized (factorized) version of the metrical field equations, discovered earlier by the author. It is found that in general relativity stars should naturally pulsate, and in its succeeding cycles the gravitational radius of the star is attenuated by a factor exp(−0.349T), where T is the pulsation period. Conditions are discussed for the possibility that the (relatively) regular emissions of radiation from a pulsar may be dynamically rooted in a (smaller) part of the pulsation cycle when the star is out of the black hole state (less dense → open geodesics)—when radiation would be emitted to the outside world—and the (greater) part of the cycle when it is in the black hole state (more dense → closed geodesics)—when radiation would not be emitted.