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### Velocity of massless particles in $\mathrm{AdS}_4$ space-time

In spherical coordinates in a $(1+3)$-dimensional space-time one has the $\mathrm{AdS}_4$ metric $$ds^{2}=-\left(1+k^{2}r^{2}\right)dt^{2}+\left(1+k^{2}r^{2}\right)^{-1}dr^{2}+r^{2}d\Omega ^{2}.$$ ...
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### Speed of light in a perfect vacuum

Lets' say that something is in a universe with a perfect vacuum, where nothing exists but that object. This universe has an infinite amount of space and time. Now that object emits a single photon. ...
In the case of spherical symmetry you can say that the velocity of light (in coordinate time) goes as: $v_{light}=c(1-\frac{2GM}{rc^2})$ in the radial direction and as: \$v_{light}=c\sqrt{(1-\frac{...