Deciphering the Christoffel Symbol and Potential in Shutz's Relativity Book"

[alejandrito29]

Hello,

i have learning the boock of Shutz , and i not understand why the Christoffel symbol for the potential
$$\phi$$ with $$|\phi |<<1$$ .

$$\Gamma^0_{00}= \frac{\phi,_0}{1+2\phi}$$ is written as

$$\Gamma^0_{00}= \phi,_0 + 0( \phi^2)$$

I don't see the quadratic term $$0( \phi^2)$$ . I tried with Taylor, but i don't understand

 

[Popper]

Hello,

i have learning the boock of Shutz , and i not understand why the Christoffel symbol for the potential
$$\phi$$ with $$|\phi |<<1$$ .

$$\Gamma^0_{00}= \frac{\phi,_0}{1+2\phi}$$ is written as

$$\Gamma^0_{00}= \phi,_0 + 0( \phi^2)$$

I don't see the quadratic term $$0( \phi^2)$$ . I tried with Taylor, but i don't understand

Which edition of Schutz do you have, the first or second? What page is it on?

 

[alejandrito29]

Which edition of Schutz do you have, the first or second? What page is it on?

pg 186, equation 7.13

i know the firtz edition

 

[WannabeNewton]

$\frac{\partial _{t}\phi}{1 + 2\phi}\simeq \partial _{t}\phi(1 - 2\phi) = \partial _{t}\phi - \partial _{t}(\phi^{2})$. $|\phi| << 1$ and $\phi$ varies smoothly so the derivatives of the second order terms should also be negligible.