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ARTICLE ABSTRACTS
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Presenting Author: Thomas W. Baumgarte
Institution: Bowdoin
College Abstract Title: Some thoughts on involving undergrads in GR-related research (pdf) Body Involving undergraduate students in GR-related 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 starting-point 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 self-evident, and should definitely be a part of these discussions.
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Presenting Author: Jeff Bowen
Institution: Bucknell
University Abstract Title: Light Cones in the Schwarzschild Geometry Body Undergraduates studying General Relativity need guidance to develop useful skills. A step-by-step 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 Eddington-Finkelstein coordinates, there are then three different types of solutions. These are expressed in terms of T-TILDA = v - r, and conditions for the slope d T-TILDA/dr are found. Finally, a table of r and light cone slope values makes it easy to draw typical light cones on a T-TILDA vs. r plot.
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Presenting Author: Thomas J. Brueckner
Institution: Department
of Physics
Abstract Title:
Stirring Up
Undergraduate Interest in Relativity Research in a
Non-relativistic 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.
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Presenting Author: Gregory L. Comer
Institution:
Saint
Louis University 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, multi-purpose 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.
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Presenting Author: Joel S. Franklin
Institution:
Reed
College 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.
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Presenting Author: Seth A. Major
Institution:
Hamilton
College 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.
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Presenting Author: Richard Mould
Institution:
SUNY
Stony Brook 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. |
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Presenting Author: Thomas A. Moore
Institution:
Pomona
College Abstract Title: Tips on Teaching GR (with Tensors) to Undergraduates (pdf) Body This article will present some guiding principles for successfully teaching a tensor-based 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 two-dimensional 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.
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Presenting Author: George W. Rainey
Institution:
California State Polytechnic Univ., Pomona Abstract Title: A One-Term Undergraduate Course on General Relativity with Applications Body A one-quarter undergraduate course on General Relativity with applications is outlined and described. The course employs tensor mathematics, but in a somewhat non-rigorous manner due to time constraints. The first half of the course is devoted to theoretical development, while the latter half involves applications.
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Presenting Author: Ian Redmount
Institution: Saint
Louis University Abstract Title: Teaching General Relativity--A Seven-Layer Cake (pdf) Body General Relativity is now recognized as central to some of the most dynamic fields in science, including cosmology, particle physics, and gravitational-wave astronomy. Its key ideas can be taught at all levels. This can be divided into seven ``layers'': non-calculus introductory courses; calculus-based introductory courses; Modern Physics courses; specialized undergraduate courses; undergraduate research; graduate courses; and graduate research. In a high-school course the principle of relativity, spacetime geometry, and connections between gravitation and geometry can be introduced via suitable illustrations. In a calculus-based course these can be supplemented by calculations in special-relativistic 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. |