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## Main Question or Discussion Point

I have a doubt since I see the next equation and the corresponding matrix:

$$ ds^2 = \Bigg( \frac{1-\frac{r_s}{4\rho}}{1+\frac{r_s}{4\rho}}\Bigg)^2 dt^2 - \Big(1+\frac{r_s}{4\rho}\Big)^4 (d\rho^2 + p^2 d\Omega_2^2) $$

$$ g_{\mu\nu} =

\left( \begin{array}{ccc}

\Bigg( \frac{1-\frac{r_s}{4\rho}}{1+\frac{r_s}{4\rho}}\Bigg)^2 & 0 & 0 & 0 \\

0 & -\Big(1+\frac{r_s}{4\rho}\Big)^2 & 0 & 0 \\

0 & 0 & -\rho^2 & 0 \\

0 & 0 & 0 & -sin^2 \theta \end{array} \right) $$

My doubt comes because I see a quadratic term in the matrix: $$ g_{11} = -\Big(1+\frac{r_s}{4\rho}\Big)^2 $$ however, a power 4 term in the ds² equation. Why?

$$ ds^2 = \Bigg( \frac{1-\frac{r_s}{4\rho}}{1+\frac{r_s}{4\rho}}\Bigg)^2 dt^2 - \Big(1+\frac{r_s}{4\rho}\Big)^4 (d\rho^2 + p^2 d\Omega_2^2) $$

$$ g_{\mu\nu} =

\left( \begin{array}{ccc}

\Bigg( \frac{1-\frac{r_s}{4\rho}}{1+\frac{r_s}{4\rho}}\Bigg)^2 & 0 & 0 & 0 \\

0 & -\Big(1+\frac{r_s}{4\rho}\Big)^2 & 0 & 0 \\

0 & 0 & -\rho^2 & 0 \\

0 & 0 & 0 & -sin^2 \theta \end{array} \right) $$

My doubt comes because I see a quadratic term in the matrix: $$ g_{11} = -\Big(1+\frac{r_s}{4\rho}\Big)^2 $$ however, a power 4 term in the ds² equation. Why?

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