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ASTR-581: Gravitation and Cosmology
Announcements:
- Meeting room and times for the lectures: 12:10 - 13:00Hrs on MWF, in Webster B12.
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- Course text:
- Primary textbook: Bernard F. Schutz, "A first course in general relativity," Cambridge University Press; 2 edition (14 May 2009), ISBN-13: 978-0521887052, ISBN-10: 0521887054.
- Additional recommended text (requested for placing in Owen Library's Reserve Section):
- 1. "Spacetime and geometry: an introduction to general relativity," Sean M. Carroll c2004; available at Owen Science and Engineering Library Stacks (QC173.6 .C377 2004 )
- 2. "General relativity," Robert M. Wald; 1984; available at Owen Science and Engineering Library Stacks (QC173.6 .W35 1984 )
Course outline:
In this course, we will study Einstein's theory of gravity, namely, General
Relativity, and its solutions. Specifically, we will obtain the spacetime
geometry of spherically symmetric distributions of matter, such as those of
non-rotating (or very slowly rotating) stars and planets. This geometry
explains the results of 3 key tests of General Relativity: (a) The precession
of the perihelion of Mercury, (b) the bending of light around massive objects,
and (c) gravitational red-shift.
We will also solve Einstein's equations to deduce the axisymmetric
geometry around rotating stars and explore the rotational frame-dragging
(or Lense-Thirring) effect. The above solutions will be applied
to the special case of rotating and non-rotating black holes.
When applied to the case of isotropic and homogeneous spacetime geometries,
the Einstein equations give us the cosmological solutions for different
types of geometries and energy components (such as radiation, matter, and the
dark energy). We will study these solutions and find the spacetime geometry
and the mix of the energy components that best fit the current observations.
In linearized gravity, the gravitational wave solution in this theory will be derived. The
Hulse and Taylor binary pulsar system, which proved the existence of gravitational waves
will be studied.
Relevance to topics not limited to General Relativity:
We will learn about tensor algebra and Lie groups and use them to explore the properties of certain solutions of Einstein's equations. These mathematical concepts, however, have important applications beyond GR as well. For example, they simplify the exploration of properties of the solutions to Maxwell's equations of electrodynamics. We will use these concepts to describe the stress-energy-momentum tensor of perfect fluids and understand its (local) laws of conservation of mass, entropy and vorticity.
Comparison with the ASTR 581 class taught in the past:
There will be very little overlap with the Astrophysical Fluids class taught in the fall of 2011. Note that a student can repeat PHYS / ASTR 581, which is a course in Advanced Topics, three times as long as the subject matter is different each time. The name of the course will appear in your transcript and will attest to this difference.
Prerequisites:
Students should have taken the graduate course on
Mathematical Methods before attending this course. Although knowledge of Special Relativity is not assumed and will be
taught in the first few days of the course, nevertheless prior
familiarity with it, such as through a course on Electrodynamics or
Classical Mechanics will be helpful. Similarly, prior knowledge of
tensor algebra and differential geometry is not required.
Topics we plan to cover:
1. A brief review of Special Relativity,
2. Tensor algebra,
3. Curvature,
4. Einstein's equations of General Relativity,
5. Predictions and tests of General Relativity,
6. Gravitational waves,
7. Cosmological and astrophysical sources of gravitational radiation,
For questions and suggestions, please
email me!
Sukanta Bose, sukanta at wsu dot edu
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