

ARTICLE ABSTRACTS
TEACHING GENERAL
RELATIVITY TO UNDERGRADUATES
AAPT TOPICAL WORKSHOP, SYRACUSE
UNIVERSITY  JULY 20, 21, 2006 
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title to see complete article
Presenting Author:
Thomas W. Baumgarte
Institution: Bowdoin
College
Department of
Physics
Brunswick, ME
04011
Abstract
Title:
Some thoughts on involving undergrads in GRrelated research
(pdf)
Body
Involving
undergraduate students in GRrelated research can be
difficult, and at the same time very rewarding. The
difficulties, I would argue, come in more or less three
closely related categories, none of which should come as a
great surprise: the limited background of typical
undergraduate students, the difficulty of finding an
appropriate project, and the limited time available for
research. By writing about these issues, based on my
experience at Bowdoin College, I risk stating the obvious,
but perhaps my observations are nevertheless a useful
startingpoint for discussions. I will also mention another
issue that I have sometimes struggled with, namely the fact
that students may carry out the research as part of a credit
course. The rewards of working with undergraduate students,
on the other hand, may be less selfevident, and should
definitely be a part of these discussions.

Presenting Author:
Jeff Bowen
Institution: Bucknell
University
Physics
Department
Lewisburg, PA
17837
Abstract Title:
Light Cones in the Schwarzschild Geometry
Body
Undergraduates
studying General Relativity need guidance to develop useful
skills. A stepbystep worksheet for plotting the
Schwarzschild light cones is presented and described.
First, the students seek to characterize the null rays by
setting the metric ds^2 to zero. For Schwarzschild in
EddingtonFinkelstein coordinates, there are then three
different types of solutions. These are expressed in terms
of TTILDA = v  r, and conditions for the slope d TTILDA/dr
are found. Finally, a table of r and light cone slope
values makes it easy to draw typical light cones on a TTILDA
vs. r plot.

Presenting Author:
Thomas J.
Brueckner
Institution: Department
of Physics
University of Central
Florida,
Orlando, Florida 32816
Abstract Title:
Stirring Up
Undergraduate Interest in Relativity Research in a
Nonrelativistic
Department (pdf)
Body
Simply offering an
advanced relativity course is sufficient to stir up interest
in relativity research at University of Central Florida.
This paper describes my experience teaching special and
general relativity at UCF in spring semester, 2003. I
conclude with a few ideas and questions about GR curriculum
innovation, especially in support of further LIGO research.

Presenting Author:
Gregory L. Comer
Institution:
Saint
Louis University
Department of Physics
St Louis, MO
631560907
Abstract
Title:
Using Mathcad to Model Neutron Star Radial Oscillations and
Rotation
Body
Neutron stars
are compact in size (typical radii being about 10
kilometers), massive (on the order of one or two solar
masses), and can be rapidly rotating (upwards of 500
rotations per second). Consequently they are firmly in a
regime where general relativity is important and are target
objects for current gravitational wave searches (eg. LIGO).
Remarkably, the equations that are used to model neutron
star oscillations and rotation in full general relativity
are solvable numerically using modern day, multipurpose
software packages such as Mathcad running on ordinary,
desktop computers. We describe two such Mathcad routines
that have been developed by undergraduates in collaboration
with the author.

Presenting Author:
Joel S. Franklin
Institution:
Reed
College
3203 SE
Woodstock Blvd.
Portland, OR
97202
Abstract Title:
Spinning Charged Bodies and the Linearized Kerr Metric
(pdf)
Body
The physics of
the Kerr metric of general relativity (GR) can be understood
qualitatively by analogy with the potentials of spinning
charged spheres in electrodynamics (E&M). We make this
correspondence explicit by comparing the Lagrangian for test
particle motion in E&M with a spinning spherical source to
the Lagrangian for a test particle in GR under the influence
of a linearized limit of the Kerr metric. The
interpretation of Kerr as the metric appropriate to spinning
massive bodies then emerges as a simple replacement of mass
for charge in the E&M case.

Presenting Author:
Seth
A. Major
Institution:
Hamilton
College
Department of
Physics
Clinton,
NY
13323
Abstract Title:
Quantum Gravity with Undergraduates
(pdf)
Body
This essay
presents a personal perspective on working on quantum
gravity research with undergraduates. One project,
``Astrophysical constraints on Modified Dispersion
Relations", is described. There are observations on the
nature of successful projects and on the role of research
with undergraduates.

Presenting Author:
Richard Mould
Institution:
SUNY
Stony Brook
Department of
Physics and Astronomy
Stony Brook,
NY
117943800
Abstract Title:
Acceleration of Light at Earth’s Surface
(pdf)
Body
General
relativity requires that light traveling upward or downward
at the earth’s surface has an acceleration equal to +2g.

Presenting Author:
Thomas A.
Moore
Institution:
Pomona
College
Department of
Physics and Astronomy, 610 N College Ave
Claremont, CA
91711
Abstract
Title:
Tips on Teaching GR (with Tensors) to Undergraduates
(pdf)
Body
This article
will present some guiding principles for successfully
teaching a tensorbased course in general relativity to
undergraduates (principles I have learned by painful
experience over many years). These principles include (1)
simultaneously developing the physics and mathematics to
maintain student interest and to provide an appropriate
context for the math, (2) liberally using twodimensional
analogies, (3) building on a student’s understanding of
vectors and vector spaces, (4) designing drills to help
students overcome common misconceptions about tensor
notation, (5) helping students “own” the derivations, (6)
designing a homework grading scheme that allows students to
try hard problems and learn from corrections. I will also
describe some tricks and worksheets that I have developed
that help students easily evaluate Christoffel symbols and
Ricci tensor components for diagonal metrics.

Presenting Author:
George
W. Rainey
Institution:
California State Polytechnic Univ., Pomona
3801 W. Temple
Ave.
Pomona, CA
91768
Abstract Title:
A OneTerm Undergraduate Course on General Relativity with
Applications
Body
A onequarter
undergraduate course on General Relativity with applications
is outlined and described. The course employs tensor
mathematics, but in a somewhat nonrigorous manner due to
time constraints. The first half of the course is devoted
to theoretical development, while the latter half involves
applications.

Presenting Author:
Ian Redmount
Institution: Saint
Louis University
3450 Lindell
Boulevard
St. Louis, MO
631031110
Abstract Title:
Teaching General RelativityA SevenLayer Cake
(pdf)
Body
General Relativity is now recognized as
central to some of the most dynamic fields in science,
including cosmology, particle physics, and
gravitationalwave astronomy. Its key ideas can be taught at
all levels. This can be divided into seven ``layers'':
noncalculus introductory courses; calculusbased
introductory courses; Modern Physics courses; specialized
undergraduate courses; undergraduate research; graduate
courses; and graduate research. In a highschool course the
principle of relativity, spacetime geometry, and connections
between gravitation and geometry can be introduced via
suitable illustrations. In a calculusbased course these can
be supplemented by calculations in specialrelativistic
mechanics. In Modern Physics calculations involving
gravitation and spacetime metrics can be introduced. A
specialized undergraduate course can include geodesics and
mechanics in curved spacetime, tensors, and the Einstein
field equations. Undergraduates' research can involve quite
sophisticated theory, provided they are given suitably
limited problems. 

