1. (a) Consider the following line element of a (1 + 1)-dimensional space-time: ds - dt...

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1. (a) Consider the following line element of a (1 + 1)-dimensional space-time: ds - dt + eat dx, where is a constant. = Determine the Christoffel symbols and hence the geodesic equations. Solve these equations to obtain the time-like geodesics t(s) and x(s) explicitly, for the initial conditions t(0) = to and x(0) = x. (b) In the Pound-Rebka experiment, a 7-ray from a 14.4 KeV, 57Co - 57Fe transition was allowed to fall vertically (from an adjustable height h) in the earth's gravitational field. At h 22.6 m, resonant absorption in the terrestrial 57Fe target was found to occur, as the gravitational frequency shift z got cancelled by the relativistic Doppler shift. The experiment gave the value: z =( = (2.57 +0.26) 10-15. (i) What was the predicted value of z? Determine this, by first deriving the general expression of the gravitational frequency shift (in terms of the radii of the source and the orbit of the observer), and then making the approximation h < Re, where R = 6371 Km is the radius of the earth. (ii) Estimate the value of the relative speed of the 57 Co emitter and the 57Fe receiver for which the resonance occurs. 1. (a) Consider the following line element of a (1 + 1)-dimensional space-time: ds - dt + eat dx, where is a constant. = Determine the Christoffel symbols and hence the geodesic equations. Solve these equations to obtain the time-like geodesics t(s) and x(s) explicitly, for the initial conditions t(0) = to and x(0) = x. (b) In the Pound-Rebka experiment, a 7-ray from a 14.4 KeV, 57Co - 57Fe transition was allowed to fall vertically (from an adjustable height h) in the earth's gravitational field. At h 22.6 m, resonant absorption in the terrestrial 57Fe target was found to occur, as the gravitational frequency shift z got cancelled by the relativistic Doppler shift. The experiment gave the value: z =( = (2.57 +0.26) 10-15. (i) What was the predicted value of z? Determine this, by first deriving the general expression of the gravitational frequency shift (in terms of the radii of the source and the orbit of the observer), and then making the approximation h < Re, where R = 6371 Km is the radius of the earth. (ii) Estimate the value of the relative speed of the 57 Co emitter and the 57Fe receiver for which the resonance occurs.

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The image shows a physics problem divided into two parts a and b Lets address part a first Part a presents a 1 1dimensional spacetime with the line element given by ds2 dt2 ealpha t dx2 where is a con... View the full answer