show that the proper time delta tau for a radial infall from rr to r0 is finite for a timelike g

Name: show that the proper time delta tau for a radial infall from rr to r0 is finite for a timelike geodesic assume that the particle is released at rr thus its conserved energy can be written by 31494
Uploaded: 2022-11-25T16:51:19-08:00
Duration: 1 min 35 s
Channel: Sri K
Description: show that the proper time delta tau for a radial infall from rr to r0 is finite for a timelike geodesic assume that the particle is released at rr thus its conserved energy can be written by 31494

Step 1: Given the conserved energy for radial motion, u_a u^a = -1, we can write the energy as E

Question

Show that the proper time, Delta au , for a radial infall from r=R to r=0 is finite for a timelike geodesic. Assume that the particle is "released" at r=R, thus its conserved energy can be written by using the relation u_(a)u^(a)=-1 for radial motion only. Use this result to then obtain d(r)/(d) au . Solve this for d au and finally integrate from r=R ro r=0 to obtain Delta au =(pi R^((3)/(2)))/(2sqrt(2M)) Then compute the infall time in seconds for R=10M where M=M_(o.). 2. Show that the proper time, , for a radial infall from r = R to r = 0 is finite for a timelike geodesic. Assume that the particle is "released" at r = R, thus its conserved energy can be written by using the relation uu = -1 for radial motion only. Use this result to then obtain dr/d. Solve this for d and finally integrate from r = R ro r = 0 to obtain T =TTR3/2 2V2M Then compute the infall time in seconds for R = 10M where M = Mo

          Show that the proper time, Delta 	au , for a radial infall from r=R to r=0 is finite for a timelike geodesic. Assume that the particle is "released" at r=R, thus its conserved energy can be written by using the relation u_(a)u^(a)=-1 for radial motion only. Use this result to then obtain d(r)/(d)	au . Solve this for d	au  and finally integrate from r=R ro r=0 to obtain
Delta 	au =(pi R^((3)/(2)))/(2sqrt(2M))
Then compute the infall time in seconds for R=10M where M=M_(o.).
2. Show that the proper time, , for a radial infall from r = R to r = 0 is finite for a
timelike geodesic. Assume that the particle is "released" at r = R, thus its conserved
energy can be written by using the relation uu = -1 for radial motion only. Use this
result to then obtain dr/d. Solve this for d and finally integrate from r = R ro r = 0
to obtain
T =TTR3/2 2V2M
Then compute the infall time in seconds for R = 10M where M = Mo

show that the proper time delta tau for a radial infall from rr to r0 is finite for a timelike geodesic assume that the particle is released at rr thus its conserved energy can be written by 31494

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