- #1
simoncks
- 29
- 0
Mathematically,
##T_{\mu_\nu} = 0##
##\Rightarrow~R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 0##
Now multiply both sides by ##g_{\mu\nu}##
with definition of ##R = g^{\mu\nu} R_{\mu\nu}##
##R - \frac{1}{2} R = 0##
##R = 0##
Is that my imagination wrong? I thought 'empty space' might not be flat in general, like the Schwarzschild metric. And, I thought ##R = 0## meant 'the spacetime is flat.
What is the point I missed? Thanks.
##T_{\mu_\nu} = 0##
##\Rightarrow~R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 0##
Now multiply both sides by ##g_{\mu\nu}##
with definition of ##R = g^{\mu\nu} R_{\mu\nu}##
##R - \frac{1}{2} R = 0##
##R = 0##
Is that my imagination wrong? I thought 'empty space' might not be flat in general, like the Schwarzschild metric. And, I thought ##R = 0## meant 'the spacetime is flat.
What is the point I missed? Thanks.