UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #5
Due Wednesday, Feb. 11 at 5pm (in Broida 6239)
1. Show that
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #6
Due Wednesday, Feb. 25 at 5pm (in Broida 6239)
1. Show that
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #2
Due Wednesday, Jan. 21 at 5pm (in Broida 6239)
1. Show that
Phys 231B Winter 2015
Assignment 5 Solutions
2
2
1. Using r+ 2M r+ + a2 = 0 and H = a/(r+ + a2 ), the norm of
= /t + H /
on the horizon (r = r+ ) is
g = gtt + 2H gt + 2 g
H
2M r+
4H M ar+ sin2 a2
= 1
Phys 231B Winter 2015
Assignment 3 Solutions
1. The Reissner-Nordstrom metric is
ds2 = 1
2M
Q2
+ 2
r
r
dt2 + 1
2M
Q2
+ 2
r
r
1
dr2 + r2 d2 .
(1)
The acceleration of an observer with 4-velocity ua is
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #4
Due Wednesday, Feb. 4 at 5pm (in Broida 6239)
1. Practice w
Physics 231B Winter 2014
Prof. Gary Horowitz
Assignment 4 Solutions '
1. Here are the Penrose diagrams 2. The metric of the hypersurface t : constant, 7' = r+ 2 M + \/ M 2 a2 is given by
setting dt 2
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #3
Due Wednesday, Jan. 28 at 5pm (in Broida 6239)
1. Compute t
Phys 231B Winter 2015
Assignment 2 Solutions
1. Using r as the parameter, the (t, r) components of the tangent to a radial null geodesic
are = (1/f, 1). It follows that (/t) = 1. Since this is a const
Phys 231B Winter 2015
Assignment 6 Solutions
1. An isotropic spacetime is lled by a congruence of timelike curves with tangents ua .
Isotropy implies that it is impossible to construct a geometrically
Phys 231B Winter 2015
Assignment 1 Solutions
Problem 1
(a) Lets begin with the metric
2M
ds = 1
r
2
1
2M
dt + 1
r
2
dr2 + r2 d2 .
For geodesics that are radial (d2 = 0) and null (ds2 = 0), this give
UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Physics
Physics 231B
Winter 2015
Prof. Gary Horowitz
Grader: Philip Saad
ASSIGNMENT #1
Due Wednesday, Jan. 14 at 5pm (in Broida 6239)
1. (a) Show