# Incorporation of special relativity into general relativity

...Yes very, very much so. There are quite a few misconceptions hiding in there that only a good textbook can eradicate...

"Flat" means "not curved", which is to say free of significant gravitational influences. This is different from"inertial". ...

... but there has been some confusion over (B). The modern consensus among professional relativists is that (B) is part of special relativity, but I don't think that was always the case historically, and I think many beginners in relativity today still think that (B) is part of general relativity...

Thanks a lot.

A cute example pointed out by Ohanian is the ratio of longer to shorter axis of a free falling drop of perfect fluid. In tidal gravity, this ratio is constant in the limit as drop size goes to zero, and measures one particular curvature scalar.

Wikipedia states a perfect fluid has no shear stresses, viscosity, or heat conduction.
It does not mention surface tension (is that derived or emergent from the others above?).
I'm thinking that surface tension will overcome and result in approaching a 1:1 ratio as the drop size goes to zero...?

Doesn't "local" in relativity mean a distance approaching 0?

PAllen
Wikipedia states a perfect fluid has no shear stresses, viscosity, or heat conduction.
It does not mention surface tension (is that derived or emergent from the others above?).
I'm thinking that surface tension will overcome and result in approaching a 1:1 ratio as the drop size goes to zero...?

Doesn't "local" in relativity mean a distance approaching 0?

You can assume any surface tension you want for perfect fluid. The measurement I described was "in principle", and assumed a fluid with no surface tension, so that the shape is purely determined by gravity. In this case, the shape is independent of size, for size approaching zero.

I have a copy of Ohanian's original paper on this (which I can't find, so far, on the internet). However, here is link inside his book presenting a simplified derivation. Hopefully the link works for you: