🚀 go-pugleaf

>From: matmcinn@nuscc.nus.sg (Mcinnes B T (Dr))
>Subject: Re: An easy problem in general relativity
>Date: 10 Aug 92 06:05:05 GMT
>
>Of all these replies I like those of Joe Voros and John Baez the best.
>But I can put all your perplexities to rest.
>I f you want to find out how much matter [you know, matter: this stuff
>here, not that interesting but irrelevant [here] parameter with which
>Schoen and Yau concerned themselves] there is in a region, you just
>integrate the appropriate component of the stress-energy tensor over the
>appropriate spacelike hypersurface. In the Schwarzschild case, the
>answer is zero.
>    [deleted]

    This works only in a (nearly) flat space-time. The problem is that
to add stuff here to stuff over there in any meaningful way, you have
to have a notion of transport.  This is formalized in the covariant
derivative or connection -- i.e., to add stuff here and stuff there,
bring the stuff over from there with zero covariant derivative (or
parallel transport it or so on), and add it to the stuff here. Now,
in a curved spacetime, there is no unique path-independent answer of
how vectors or tensors parallel-transport. In fact, if you transport
a tensor around a closed curve, you don't recover the same tensor:
that's how you know there is curvature !

-arun gupta
ag3L@andrew.cmu.edu