Paper preprint:

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Keywords:

general relativity, quantum gravity, quantum cosmology, tunnelling, Israel junction conditions, relativistic shells, WKB (semiclassical) approximation, conjugate mommentum, Euclidean quantumgravity, inflation.

Project goals:

to present a problem with the semiclassical quantum tunnelling process for general relativistic shells and to propose a possible solution.

Project results:

identification of a method to solve the continuity problem of the momentum in the tunnelling process of a relativistic shell.

Short Description.

The system under consideration is constituted by a relativistic shell (described using Israel's junction conditions). The classical dynamics of the system is known and many models for cosmological and astrophysical exploit the intuitive and synthetic description of this system provided by Israel junction conditions. Works on shell quantization also exist in the literature. We are here interested in the tunnelling process between two different solutions of the spherical shell equation of motions: this process can be described using the Euclidean version of the shell momentum. But in this formulation there are some cases in which an apparent inconsistency appears. We present here the problem and an intuition about a possible solution. A more detailed analysis is presently under development.

Additional material: