Zerilli-type perturbation of traversable wormhole

Abstract

The perturbation problems of four types of gravitational waves under the traversable Lorentzian wormhole geometry, are studied in this paper. The axial tensor perturbation with odd parity is similar to the Regge-Wheeler equation for the black hole, and the polar tensor perturbation with even parity is similar to the Zerilli equation for the black hole. The general form of the potentials for the Schrödinger-type one-dimensional wave equation in terms of spin is found.