Gauge theory in Riem(M)

I am writing my views on a transportation of gauge theory (a sort of generalized framework for electromagnetism and the weak and strong nuclear forces) to Riem(M), which is a space whose points are "instantaneous" configuration of the Universe (in a given time-like foliation) .
Here is the abstract:
In this paper we restrict our attention to an open subset $\mathcal{M}'$ of $\riem=\mathcal{M}$, consisting solely of metrics with no global symmetry beyond the identity. Therein we have a natural principal fiber bundle (PFB) structure $\diff\hookrightarrow \M \overset{\pi}{\ra}\M/\DD$ in which we input the connection form $\omega$ implicitly defined in \cite{Ba.1}. We work out the implications of this connection in the associated bundle with typical fiber the complex line bundle over $M$.
It is at http://arxiv.org/abs/math-ph/0702061

Goldilocks

Many times after I have mentioned that the conditions on Earth are very precisely tuned to allow complex life, specially intelligent life, to flourish, I hear the rebuke: "life as we know it, perhaps life in other parts of the Universe can thrive in very different conditions than it does here. Perhaps it doesn't need a liquid (or dense) medium where heavier, complex molecules can be suspended and interact more easily, exploring the infinite possibilities of chemical reactions. Perhaps it doesn't need a relatively stable environment (among other things), where, if mildly complex life evolves at all, it has the possibility and time to grow variants and become evolutionary more robust. "

Perhaps, but the fact of the matter is physical conditions are alike all around. The same elements we have here on Earth will be those available to a planet at the other side of the galaxy, since the processes of its formation inside a star are the same. So there are no magical elements. The physical fundamental forces are the same, and so on and so forth, so there is no magical possibility of escaping certain physical facts that are crucial to life. In some senses, conditions over planets vary a lot, but on another scale, they are pretty much the same, so there apparently is no room for interventions of exotic elements, fields or other esoteric contraptions.

Links explained

Links (besides the ones whose titles are self-explanatory):

• MIT opencourseware: MIT is making available gratuitously online the material for its courses, so you can have a look at the homework, tests, and class material and try to follow it yourelf.
• Huygens'-Fresnel Principle in Superspace: is a paper I wrote on the transposition to superspace (the configuration space for a dynamical setting of G.R.) of a principle that better accounts for light diffraction and interference than Fraunhofer diffraction (which is valid for large relative distances between aperture and screen).
• Edge: is a site where leading intellectuals from many areas try to explain accessibly to each other their current work. Very recommended.
• Beyond Belief: Was a conference held in 2006, held to discuss the interaction between science and religion. Attended by such figures as Steven Weinberg and Richard Dawkins, the site holds videos of all the sessions. Truly interesting.

Isochronous Brachistochrones

In spite of the heavy name, the concept of isochronicity in curves of shortest time is a very acessible one. Let us suppose we are in a constant gravitational field, and we have a bead, which we are to slide along a maleable piece of wire connecting two points, a and b. The shape over which the bead takes the least amount of time to descend to point b is a cycloid, which in this case is also a brachistochrone (curve of least time). But the cycloid has another interesting property, that of isochronicity. If you release the bead from any point along the cycloid, it will also take the same amount of time as if eleased from a.
Now, is this a generic property, reflecting a principle of nature? If we considered more general gravitational fields would a brachistochrone retain this property? The best way to describe this property is to forget about Newtonian kinematics altogheter and utilize semi-riemannian geometry.
However, to model a time-independent gravitational field we must restrict our attention to a stationary space-time, i.e. a smooth Lorentzian manifold (M,g) with a timelike Killing vector field W (defines the direction in space-time over which the metric doesn't change) . This will define such a thing as constant energy along a curve and will make the analogy with classical concepts possible. There are two possible brachistochrone problems in the context of stationary space-times:

1. To minimize the travel time measured in terms of a global coordiante time defined by the timelike irrotational Killing field W. Irrotational means that the field perpendicular to W will be consistently tangent to spatial hypersurfaces. It foliates space-time with these constant time surfaces.
2. Minimize the travel time in terms of the proper time

We are at the moment defining the conditions for isochronicity, and will give out the link for the results soon.