Re: the basis of relativity

Ken S. Tucker <dynamics@xxxxxxxxxxxx> wrote:

> Tom Roberts wrote:

[...]
>> Aparently you have not been paying attention.
>> As I have said before: If R^a_bcd is nonzero in a region, then there are
>> no coordianates for which the {g_uv} are constant. And yet if this is a
>> vacuum region then necessarily both R_uv and R are zero.

> Please provide a ref where R^a_bcd >0 but R=0 to
> support you point.

Schwarzschild solution
Kerr solution
Reissner-Nordstrom solution
Kerr-Newman solution
Vaidya solution
Any of a huge number of vacuum gravitational plane wave solutions
The electrovac solutions
Weyl's stationary axisymmetric vacuum solutions

Get the book Exact Solutions to Einstein's Field Equations, second
edition, by Stephani et al. -- you'll find *hundreds* of metrics
for which R=0 but the full curvature tensor is nonzero.

Steve Carlip
.

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