Moduli vacuum bubbles produced by evaporating black holes

We consider a model with a toroidally compactified extra dimension giving rise to a temperature-dependent 4D effective potential with one-loop contributions due to the Casimir effect, along with a 5D cosmological constant. The forms of the effective potential at low and high temperatures indicate a possibility for the formation of a domain wall bubble, formed by the modulus scalar field, surrounding an evaporating black hole. This is viewed as an example of a recently proposed black hole vacuum bubble arising from matter-sourced moduli fields in the vicinity of an evaporating black hole [D. Green, E. Silverstein, and D. Starr, Phys. Rev. D 74, 024004 (2006)]. The black hole bubble can be highly opaque to lower-energy particles and photons, and thereby entrap them within. For high-temperature black holes, there may also be a symmetry-breaking black hole bubble of false vacuum of the type previously conjectured by Moss [I. G. Moss, Phys. Rev. D 32, 1333 (1985)], tending to reflect low-energy particles from its wall. A double bubble composed of these two different types of bubble may form around the black hole, altering the hole's emission spectrum that reaches outside observers. Smaller mass black holes that have already evaporated away could have left vacuum bubbles behind that contribute to the dark matter