Re: Gravity on a torus

This discussion is funny to me because apparently all the
string theory guys have solved this already---since they
speak of the description of gravity in an alternative world
say 2 space dimensions,
where one dimension is compactified and they claim to know
what the gravitational potential would be in such a case.


I don't think string theory is meant to work as a gravity theory in
2-d. One is instead building a gravity theory, say, in ten dimensions
using
(quantum) fields in 2-d.

I think you must try to solve Poisson equation on the torus.

This would seem to be exactly what is needed. A complication is that
a necessary condition for the Poisson equation (with a well-behaved,
non-negative mass density) to have a solution on the torus is that
the mass density vanishes everywhere!

To see this, just integrate the equation over the torus and use the
divergence theorem. This implies the total mass vanishes. Since the
mass density is non-negative, it must vanish everywhere.

charlie torre

.

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