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Related Links
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Keywords:
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general relativity, quantum gravity, quantum
mechanics, vacuum decay, Israel junction conditions, relativistic
shells, WKB (semiclassical) approximation, quantum tunneling.
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Project goals:
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to give an effective Lagrangian description
for the dynamics of spherically symmetric shells in general
relativity that recovers the description in terms of Israel's
junction conditions; to apply the above formalism to the problem
of vacuum decay.
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Project results:
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determination of the dynamical quantities for
a Lagrangian description of vacuum bubbles; computation of the
limit of vanishing gravitational constant and of two cases of
gravitational vacuum decay.
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Short Description.
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We propose an effective Lagrangian description for
the dynamics of spherically symmetric shells in general
relativity. The description is effective in the sense
that it reproduces Israel's junction conditions in the spherically
symmetric case. As shown in more detail elsewhere,
the only remaining junction condition in the spherically symmetric
case can be related with the superhamiltonian constraint of
the system.
To test the above formulation we apply it to three specific
cases. In particular:
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we compute the flat spacetime limit,  ,
and show that we can reproduce the false vacuum decay amplitude
in ordinary quantum field theory;
- we analyse the simplest example of gravitational vacuum
fluctuation, computing the probability for the spontaneous
nucleation in Minkowski spacetime;
- we compute a more complex example of gravitational vacuum
fluctuation, namely the amplitude for inflationary bubble
nucleation.
In our formalism and under the WKB approximation, all the above
results can be obtained as the integral of the Euclidean momentum
describing a tunneling process through an effective potential
barrier that links two alllowed classical configurations.
As shown in all examples, the results obtained with our method
are consistent with those obtained by other procedures in the
literature.
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Additional material:
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