I was recently going through Einstein's 'The Meaning of Relativity', where in chapter 4, he describes:
To the second approximation we must then put $g_{\mu\nu} = -\delta_{\mu\nu} + \gamma_{\mu\nu}$ where $\gamma_{\mu\nu}$ are to be regarded as small of the first order.
At first I thought that $\gamma_{\mu\nu}$ is just any other addition to the metric, but as I read along, I found that $\gamma_{\mu\nu}$ is used plenty of times, even while discussing the cosmological problem. Einstein, at one point also says that $\frac{\gamma_{44}}{2}$ can be identified as the gravitational potential.
My question is this: Is there a physical and/or mathematical meaning for $\gamma_{\mu\nu}$. And what is it's connection with the metric, and how can it be derived. Basically I want to know what $\gamma_{\mu\nu}$ means in the real world and how it is obtained mathematically. And I think mathematical rigour would be preferable for me to grasp the concept more fundamentally.