- #1
maxverywell
- 197
- 2
I read that the number of Einstein equations is 10 and because of Bianchi identity, it reduces to 6. This is true because we have totally 16 components, but they are symmetric, so there are 10 independent components. However in four dimensional space-time, the number of second order partial differential equations for the metric tensor is 40, because, each component [itex]g_{\mu\nu}[/itex] is a function of [itex]x^{\alpha}, \alpha=0,1,2,3[/itex]. So finally we have a system of 24 independent second order partial differential equations for the metric tensor. Is that correct?