Question A7 Consider the following line element, ds² = - dt² + a² (t) (da² + dy²) + b² (t) dz², where a(t) and b(t) are distinct functions. State whether or not this line element obeys the Cosmological Principle, if applied to describe the universe on large scales. Justify your answer.
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- 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.Please answer within 90 minutes.P2 X The image to the left is a Feynman diagram with time increasing upward. P1 (a) If p1 is an electron and X is a W+ what must p2 be? Why? (b) If p1 is a μ+ and p2 is a different flavor of lepton, what must p2 be? Why? (c) In the last question, what must X be? Why? (d) If p1 and p2 are both electron neutrinos, what must X be? Why? (e) If p1 and p2 are both the same flavor of charged lepton, what might X be? (There are two possibilities.) Why?
- Suppose that the universe were full of spherical objects, each of mass m and radius r, with the objects distributed uniformly throughout the universe as in the previous problem. (Assume nonrelativistic objects.) Given the density of these spherical objects (as you would have found in the previous problem), how far would you be able to see in meters, on average, before your line of sight intersected one of them? Values (note, different from the above problem): m = 3 kg r = 0.03 m Answer must be in scientific notation and include zero decimal places (1 sig fig).There are two parts to this question. I need to know the years for both. I have tried 14,000,000,000, 17,908,900,000, 17.29 x 10^9, and 17.9089 x 10^9 for the hubble time and all those are wrong. I have tried 17,908,900,000, 17.29 x 10^9, and 17.9089 x 10^9 for the second question and those are wrong too.Please answer within 90 minutes.
- Briefly explain what is meant by “particle horizon” and “event horizon” in cosmology. Calculate the physical particle horizon, RH(t), at time t. Assume a flat FRW universe whichis dominated by a fluid that gives rise to scale factor evolution where n is a constant with 0 < n < 1, and a(t0) = a0.Subject: physicsWhat magnetic field B is needed to keep 943-GeV protons revolving in a circle of radius 1.0 km ? Use the relativistic mass. The proton's "rest mass" is 0.938 GeV/c². (1 GeV = 10⁹ eV) [Hint: In relativity, mrelv²/r = quB in still valid in a magnetic field, mrel = ym.] Express your answer to two significant figures and include the appropriate units B = μA Value Units ?