Waves in the Witten Bubble of Nothing and the Hawking Wormhole

Abstract

Abstract. We investigate the propagation of the scalar waves in the Witten space-time called "bubble of nothing" and in its remarkable sub-manifold, the Lorentzian Hawking wormhole. Due to the global hyperbolicity, the global Cauchy problem is well-posed in the functional framework associated with the energy. We perform a complete spectral analysis that allows to get an explicit form of the solutions in terms of special functions. If the effective mass is non zero, the profile of the waves is asymptotically almost periodic in time. In contrast, the massless case is dispersive. We develop the scattering theory, classical as well as quantum. The quantized scattering operator leaves invariant the Fock vacuum: there is no creation of particles. The resonances can be defined in the massless case and they are purely imaginary.

Global existence of the self-interacting scalar field in the de Sitter universe

“…For the case of large mass, that is m 2 ≥ n 2 /4, and for the brief review of the bibliography related to that case, one can consult [20,28,37] and for the results on the equation in the asymptotically de Sitter spaces see [4,5,25,26,30]. The waves in spacetimes with a nonvanishing cosmological constant are studied in [3,12,27].…”

A curious variant of Bronnikov-Ellis spacetime

“…About four decades ago, Witten [27] found a vacuum bubble spacetime in five dimensional Kaluza-Klein theory by performing a double Wick rotation [27], [41] of five dimensional Schwarzschild geometry ( T = iχ and Θ = it + π 2 , where T, r, Θ, Φ, ξ are coordinates in the 5D Schwarzschild). The idea there was to demonstrate an instability in the Kaluza-Klein vacuum via this construction.…”