4. [24 marks] Consider the following wormhole metric ds² = −dt² + dr² + (b² +r²) (do² + sin² Ody²) (9) with b > 0. Alice

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4 24 Marks Consider The Following Wormhole Metric Ds Dt Dr B R Do Sin Ody 9 With B 0 Alice 1 (234.2 KiB) Viewed 12 times

4. [24 marks] Consider the following wormhole metric ds² = −dt² + dr² + (b² +r²) (do² + sin² Ody²) (9) with b > 0. Alice is located at the radial coordinate r = R. At time t = = 0, she throws a clock into the wormhole, with a speed v. The clock follows a radial trajectory from = R to r - R. r = = (a) [4 marks] What is the metric tensor guy for this spacetime? (b) [4 marks] What is the four-velocity u of the clock at t = 0? ry rr (c) [4 marks] Calculate the Christoffel symbols I and I for the wormhole metric. (d) [4 marks] How much time has passed on the clock, when it arrives at r = - R? (e) [4 marks] Alice orbits in a circle around the wormhole, at a radial coordinate r = R. What is the distance she travels while making one full orbit? (f) [4 marks] For safety reasons, Alice decides to build a spherical fence around the wormhole, at radial coordinate r = = R (where R > 0). What is the surface area of this fence?