A curious variant of Bronnikov-Ellis spacetime

Abstract

We explore a curious but simple variant of the Bronnikov-Ellis (BE) wormhole spacetime with a specific `red-shift function' (i.e. $g_{00}$) in the line element. The matter required to support such a geometry violates the local Null Energy Condition (NEC) only around the throat and the global Averaged Null Energy Condition (ANEC) integral along radial null geodesics may be adjusted to arbitrarily small negative values, using metric parameters. Properties of the line element manifest in the metric functions, curvature and the required matter stress energy are delineated. Further, exact null and timelike geodesics are found and generic features of periodic/non-periodic motion (closed, bounded or open) are presented. Scalar wave propagation is also solved analytically, thereby providing a partial check on the stability of the geometry under scalar perturbations. Interestingly, we note that this BE variant may be viewed as a four dimensional, timelike section of a five dimensional, static, non-vacuum, Witten bubble--like geometry which, with an extra dimension, also has wormhole features and is threaded by matter satisfying the NEC.