- #1

unscientific

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## Homework Statement

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(a) Find christoffel symbols and ricci tensor

(b) Find the transformation to the usual flat space form ## g_{\mu v} = diag (-1,1,1,1)##.

## Homework Equations

## The Attempt at a Solution

__Part(a)__

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I have found the metric to be ## g_{tt} = g^{tt} = -1, g_{xt} = g_{tx} = 2c, g_{xx} = g^{xx} = 0, g_{yy} = g^{yy} = 1, g_{zz} = g^{zz} = 1##.

The christoffel symbols can be calculated by:

[tex] \Gamma_{\alpha \beta}^{\mu} = \frac{1}{2} g^{\mu v} \left( \frac{\partial g_{\alpha v}}{\partial x^{\beta}} + \frac{\partial g_{v \beta}}{\partial x^{\alpha}} - \frac{\partial g_{\alpha \beta}}{\partial x^{v}} \right) [/tex]

Since all components of the metric are constants, it means ##\Gamma_{\alpha \beta}^{\mu} = 0## and ##R_{\alpha \beta}^{\mu} = 0##.

__Part (b)__

I'm not sure how to approach this question. I know I have to find the Jacobian ##\frac{\partial \tilde{x^{\mu}}}{\partial x^{v}}##. I also know the transformation is ##\tilde{g_{\alpha \beta}} = \frac{\partial x^{\mu}}{\partial \tilde{x^{\alpha}}} \frac{\partial x^v}{\partial \tilde{x^{\beta}}} g_{\mu v}##.