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4Problem 4. Stephen Hawking is orbiting the Earth in Virgin Galactic’s first commercialspace voyage. To be on the safe side, Richard Branson has chosen the orbit to be perfectlycircular and ensured that the clock on-board the spaceship is ticking at the same rate as aclock at rest on the surface of the Earth. Calculate the altitude of Stephen Hawking (youmay neglect the rotation of the Earth).(7p)Problem 5. Derive the following formulas:(2)D µ V µ = ∂ µ V µ + Γ µ µλ V λΓ µ µλ= 1 √ g∂ µ√ g(3)D µ V µ = 1(4)(5)√ g∂ µ ( √ gV µ )D µ D µ φ = 1 √ g∂ µ(√ g ∂ µ φ ) .(7p)
5Problem 6. Something goes wrong with the navigation system in Virgin Galactic’s spacevoyage and the spaceship carries Stephen Hawking out of the solar system toward the centerof the Milky Way. Stephen quickly realizes that he must avoid the supermassive black holeand boldly takes the spaceship to manual drive and performs an emergency landing on abig neutron star inside the globular custer Terzan 5, close to the heart of the galaxy. Beingthe fearless scientist that he is, Stephen gets out of the spaceship to take a tour on thesurface of the neutron star with his motorized wheel chair (don’t worry, he has a suit thatprotects him from being crushed by the gravitational force). How far can Stephen drivefrom his spaceship and still see it? Assume that the spaceship is 20 meters in height andthat the height of Stephen in a wheel chair is 1 meter. The mass of the neutron star is 3solar masses and its radius is 5 km.(12p)
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Page 3: 3Problem 2. Consider a torus T 2 wi
Page 7 and 8: 7Problem 9. A rotating black hole i

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