Gravitational Tunnelling of Relativistic
Shells
In Print
[Proceedings of the 6th International Symposium on Frontiers
in Fundamental and Computational Physics]
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.