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Time and a Light Sphere

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The metric in Anti de Sitter space can be written as: (see attachment)

(a) Find the time it takes a radially directed light to travel from R = 0 to R = infinity.

(b) A bubble of vanishing size forms at (t=0, R=0) in Anti de Sitter space. Assuming that the bubble is spherically symmetric and expands at the speed of light, what is the surface area of the bubble as a function of time? Is the surface area larger or smaller than it would have in flat space?

(See attached file additional information)

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This solution contains detailed steps to calculate the relation between time and the radius and area of a light sphere in Anti de Sitter space.

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