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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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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