Consider the following spacetime: ds² - (½ 7 - M) di² dr² dt² + +1² do². -M where > 0 and M > 0 are constants. (a) Find the effective potential governing the trajectories of timelike and null geodesics. (b) Sketch the effective potential and describe the possible trajectories of the radial null geodesics. (c) Does this spacetime contain a black hole? Reason your answer. (d) Find coordinates such that the metric (2) is regular at r = M.

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