Physics 523, Problem Sets
The TA for this class is Hans Bantilan ([email protected]). Problem sets should be dropped off in Hans'
mail box by midnight of the due date. Late assignments will not be accepted. Solutions will be posted soon afterwards
on
Physics 523, Introduction to Relativity
Homework 4
Due Friday, 28th October 2011
Hans Bantilan
Geodesics on S 2
Consider the 2-sphere, with metric expressed in spherical polars xi = (, ) as
g = d2 + sin2 d2 .
Given a tangent vector eld () of some curve :[
Physics 523, Introduction to Relativity
Homework 8
Due Tuesday, 10th January 2012
Hans Bantilan
Angular Size in an FRW Spacetime
Consider a matter-dominated, at FRW spacetime so that the metric in comoving coordinates can be
written as
gij dxi dxj = dt2 +
Physics 523, Introduction to Relativity
Homework 7
Due Tuesday, 13th December 2011
Hans Bantilan
Gravitational Plane Wave
Consider an exact gravitational plane wave solution to the Einstein equations, expressed in double-null
coordinates (u, v, x, y ) as
Physics 523, Introduction to Relativity
Homework 6
Due Tuesday, 6th December 2011
Hans Bantilan
Massless Particle near a Kerr Black Hole
Consider the Kerr spacetime with mass M and angular momentum per unit mass a such that 0 a M ,
so that the metric can
Physics 523, Introduction to Relativity
Homework 5
Due Thursday, 17th November 2011
Hans Bantilan
TOV Star in 2+1 Dimensions
Consider a static circularly symmetric spacetime in 2+1 dimensions, so that the metric takes the form
gij dxi dxj = exp (2)dt2 + e
Physics 523, Introduction to Relativity
Homework 3
Due Tuesday, 18th October 2011
Hans Bantilan
Gradient, Divergence, and Curl
Let xi be the coordinate basis of Tp M associated with coordinate chart x : U , where U M is
a neighborhood containing p M , and
Physics 523, Introduction to Relativity
Homework 2
Due Thursday, 6th October 2011
Hans Bantilan
Electromagnetic Field Strength
Consider the electromagnetic eld strength in local coordinates
0 E1 E2 E3
E1
0
B3 B2
F =
E2 B3
0
B1
E3 B2 B1
0
for electric e
Physics 523, Introduction to Relativity
Homework 1
Due Tuesday, 27th September 2011
Hans Bantilan
Twin Paradox in Compact Spaces
Consider two inertial observers traveling on dierent geodesics in a at spacetime, with observer A at
rest in a coordinate syst
Physics 523, Fall 2011: Introduction to Relativity
Instructor : Frans Pretorius
Lectures : Tuesday & Thursday, 3:00-4:20pm, Jadwin A08.
Office hours : by appointment, [email protected]
TA : Hans Bantilan ([email protected])
Description
This cour
Physics 523 Midterm Exam, Fall 2011
Thursday, October 27, 3:00-4:20pm
This exam consists of 3 problems (with multiple parts) on 2 pages, worth a total of 100 pts. Do
all problems, answered in the exam booklet provided, and clearly show all your work. This
Physics 523 Midterm Exam, Fall 2010
Wednesday, May 27, 9:30-10:50am
This exam consists of 3 problems (with multiple parts) on 1 page, worth a total of 100 pts. Do
all problems, answered in the exam booklet provided, and clearly show all your work. This is
Physics 523 Midterm Exam, Fall 2009
Monday, May 26, 9:30-10:50am
This exam consists of 3 problems (with multiple parts) on 2 pages, with a total of 100 pts. Do
all problems, answered in the exam booklet provided, and clearly show all your work. This is a
Physics 523 Final Exam, Fall 2010
Wednesday, January 12, 1:30-4:30pm
This exam consists of 4 problems (with multiple parts) on 2 pages, with a total of 100 pts. Do
all problems, answered in the exam booklet provided, and clearly show all your work. This i
Physics 523 Final Exam, Fall 2009
Monday, January 18, 1:30-4:30pm
This exam consists of 5 problems (with multiple parts) on 2 pages, with a total of 100 pts. Do
all problems, answered in the exam booklet provided, and clearly show all your work. This is a