Question A5 State the value of the Ricci tensor R on the event horizon of a Schwarzschild black hole, and justify your answer.
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Q: State the value of the Ricci tensor R on the event horizon of a Schwarzschild black hole, and…
A: Required: The value of the Ricci tensor on the event horizon of a Schwarzschild black hole.
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- A spacecraft is in a 300 km circular parking orbit. It is desired to increase the altitude to 600 km and change the inclination by 20°. Find the total ΔV required if: Part A The plane change is made after insertion into the 600 km orbit (so there is a total of three ΔV burns).Suppose an alien race on a distant planet tries to send a message to us, with a laser (light). However, we were unaware that there is a stellar-mass black hole almost directly between us and them. How would this complicate our attempts to locate their position in the Galaxy? O Gravitational lensing would make the signal appear to be coming from a different location O The information carried by the laser (light) would be altered O It would not matter The black hole absorbs all of the lightTwo distant galaxies are observed to have redshifts z1 = 0.05 and z2 = 0.15, and distances d1 = 220.60 Mpc and d2 = 661.75 Mpc, respectively. Assuming the motion of the galaxies is due to the Hubble flow, determine the value of the Hubble constant, H0. Show how the value of H0 can be used to estimate the age of the Universe, describing any assumptions that you make. Use the value of H0 you have obtained to estimate the age of the Universe, expressing your answer in Gyr.
- An accretion disc may form around a black hole. This is a thin disc of orbiting matter spanning radii r = Rin to Rout around the black hole. We assume that Rout » Rin and so we make the simplifying approximation that Rout → +∞o. The disc radiates according to the following equation 3 GM D(r, 0) = 1 CM (1-[B]"). 4 3 Here, r and are the usual polar coordinates with the origin at the centre of the disc. G is the gravitational constant, M is the mass of the black hole, Rin is the disc inner radius, M is the accretion rate - all these are constants. (a) Integrate D(r, 0) over the surface of the disc to find the total radiation output of the disc. (b) Find the total radiation in the case of Rin = 6GM/c².Stephen Hawking’s derivation of the black hole temperature used the fact that the black hole’s entropy is given by S = 8π2GM2k/hc. Complete the derivation using the thermodynamic defi nition of temperature 1/T = δS/δU. Assume that the black hole’s energy is entirely mass-energy, that is, U = Mc2.In some experiment, we found the fast meson’s velocity is vf=0.9999c while the slow meson’s velocity is vs=0.9955c. Using unit of c in this problem. (leave two decimal places of your result, i.e. like 1.23) (a) Calculate the ratio of the fast meson's lifetime in the laboratory frame to the slow meson's lifetime in the laboratory frame. (b) Calculate the ratio of the fast meson's decay length to the slow meson's decay length.