Question

Metric: $ds^2 = - \Big(1-\frac{r^2}{R^2}\Big)du^2 -2dudr+r^2(d\theta ^2+ \sin^2\theta d\phi^2)$

slopes of light in u,r plane: or $\frac{dr}{du} = \frac{1}{2}\Big(\frac{r^2}{R^2}-1 \Big)$

Question : In the u,r plane, show that r=R is a horizon with opposite characteristics. i.e. light rays starting at r > R cannot enter the r < R region. (This is because of the accelerating expansion of the universe)

COnstant

Answer 1

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