Propagation of gravitational waves in a dynamical wormhole background for two-scalar Einstein–Gauss–Bonnet theory

Abstract

In this work, we propose a model of Einstein–Gauss–Bonnet gravity coupled with two scalar fields. The two scalar fields are considered to be “frozen” or they become non-dynamical by employing appropriate constraints in terms of Lagrange multiplier fields. We show that, even in the case that the arbitrary spherically symmetric spacetime is dynamical, we can construct a model where the wormhole spacetime is a stable solution in this framework. We especially concentrate on the model reproducing the dynamical wormhole, where the wormhole appears in a finite-time interval. We investigate the propagation of the gravitational wave in the wormhole spacetime background and we show that the propagation speed is different from that of light in general, and there is a difference in the speeds between the incoming propagating wave and the outgoing propagating gravitational wave. We need to stress that the wormhole model used for exploring gravitational wave propagation is not obtained by solving any equations but is essentially constructed by hand.