We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Ruth Gregory

Gregory, Ruth , Marshall, Katie M. Florent, Michel & Moss, Ian G. (2018). Negative modes of Coleman–De Luccia and black hole bubbles. Physical Review D 98(8): 085017.

Author(s) from Durham


We study the negative modes of gravitational instantons representing vacuum decay in asymptotically flat space-time. We consider two different vacuum decay scenarios: the Coleman-de Luccia O(4)-symmetric bubble, and
instantons with a static black hole. In spite of the similarities between the models, we find qualitatively different behaviors. In the O(4)-symmetric case, the number of negative modes is known to be either one or infinite, depending on the sign of the kinetic term in the quadratic action. In contrast, solving the mode equation numerically for the static black hole instanton, we find only one negative mode with the kinetic term always positive outside the event horizon. The absence of additional negative modes supports the interpretation of these solutions as giving the tunneling rate for false vacuum decay seeded by microscopic black holes.