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Berezin87: Dynamics of bubbles in GR (Phys. Rev. D 36, 2919)

In section III/A above the equation (3.1) there is the following statement:

"Thus, for given inner and outer metrics sigma determine the global geometry

(i.e. how the inner geometry is stuck together to the outer one)"

Sigma is a sign +1 or -1, see for example in the master equation

(Schwarzschild-Schwarzschild thin shell):

sigma_in*sqrt(1-2mc/r+v^2) - sigma_out*sqrt(1-2(mc+mg)/r+v^2) = mr/r

where r is the circumferential radius;

v = dr/dtau, and tau is the proper time of the shell;

mc is the central Schwarzschild mass parameter;

mg is the gravitational mass of the shell, this means

that the outer Schwarzschild mass parameter is mc+mg;

and mr is the rest mass of the shell, mr > 0;

It can be shown for all four possibilities of the signs that

the following equation of motion

can be derived independent of the signs:

(dr/dtau)^2 = (mg/mr)^2 - 1 + (2mc+mg)/r + (mr/2r)^2

This coincide with the above statement,

because he signs do not influence the local motion.

But in another paper of Goldwirth & Katz:

http://arxiv.org/abs/gr-qc/9408034

they have a nice illustration of gluing manifolds together:

http://arxiv.org/PS_cache/gr-qc/ps/9408/9408034v3.fig1-1.png [Broken]

They suggest that the signs comes from the four possibilities:

witch half of the manifolds is chosen.

But if we have already chosen the half, we also fix the metric.

I think Berezin's statement means that the signs comes from

how to join chosen metrics together, and not how to chose the metrics!

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# Dynamics of thin shells in GR

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