Hi. I can't find a source that shows how to superpose two metrics.(adsbygoogle = window.adsbygoogle || []).push({});

For example, superposing Schwarzchild metric

[itex]ds^2=\left(1-\frac{2M}{r}\right)dt^2-\frac{dr^2}{1-\frac{2M}{r}}-r^2d\Omega^2[/itex]

with de Sitter metric

[itex]ds^2=\left(1-\frac{r^2}{\alpha^2}\right)dt^2-\frac{dr^2}{1-\frac{r^2}{\alpha^2}}-r^2d\Omega^2[/itex]

yields de Sitter-Schwarzchild metric

[itex]ds^2=\left(1-\frac{2M}{r}-\frac{r^2}{\alpha^2}\right)dt^2-\frac{dr^2}{1-\frac{2M}{r}-\frac{r^2}{\alpha^2}}-r^2d\Omega^2[/itex]

I've tried letting

[itex]g_{\mu\nu}=g_{\mu\nu}\left(Schwarzchild\right)+g_{\mu\nu}\left(de Sitter\right)-\eta_{\mu\nu}[/itex]

which works for the time component of the metric but not the radial. Any ideas?

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# Superposing two metrics

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