🚀 go-pugleaf

matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
> Question: what is the mass of the object represented by the
> Schwarzschild solution?
> Answer: Zero. Exactly zero. It's a vacuum solution, remember?
> Comments? [Please don't tell me that the mass is all squashed up "inside
> the singularity".]

We spent the whole of last year's seminar series in the Relativity Group
here trying to understand this.  I mean, *understand*, not mouth out all
the standard disclaimers.  The conclusion:

No one has the faintest idea.  

The only way to operationally define mass is to take the far-field limit
--- the ``stuff'' inside an infintely large two-surface.  This means
being able to handle asymptotically-flat spacetimes, the latter concept
being fairly ill-defined, despite many (!) elegant definitions offered
in the literature.  At some point it becomes necessary to throw away the
non-linearity of the Einstein equations, either directly (Fierz-Pauli
spin 2 gravity, for example), or by a mathematical trick which brings
infinity ``over here where I can deal with it without getting the
screaming heebie-geebies.''  

The ``linearization'' of the equations is trickier than you might think. 
Think about it for a while and you'll agree.  

-- 
Joe Voros
Department of Physics, Monash University, Clayton, VIC, 3168, Australia.

Quantum Mechanics is God's way of telling you to mind your P_i's and Q_j's.