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Course Content:
Required Texts:
Relativity, Gravitation, and Cosmology,
Ta-Pei Cheng, Oxford University Press, 2010.
An Introducton to Modern Cosmology, Andrew Liddle, Wiley, 2015.
Optional Text:
A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction
to the Mathematics of Relativity,
P. Collier, 2017.
One of the greatest
achievements in theoretical physics, only later to lead to exciting
frontiers in experimental and computational physics, was Einstein’s
development of the General Theory of Relativity from 1907 to 1915.
General Relativity is a theory of gravity and is necessary to understand
recent advances at the forefront physics research, including black hole
physics, the early universe, string theory, high energy physics and
astrophysics.
The 2015 discovery of gravitational waves was recently recognized by the
awarding of the 2017 Nobel prize in physics. Einstein predicted
gravitational waves in his 1916-1918 papers based on General Relativity.
Over the last century we have learned that the universe is expanding;
our galaxy is one of billions and billions of other galaxies; the age of
the universe is 13.80±0.04 billion years; gravitational waves exist;
and, neutron stars were seen to collide.
This course is an introduction to special and general relativity as
applied to the structure and evolution of the Universe. We will use
space-time models to see general relativity as a metric theory of
gravity and will explore examples of specific solutions (black holes,
wormholes) and ‘tests’ of general relativity (bending of light). We will
probe the nature and implications of cosmological models assuming
large-scale homogeneity and isotropy. Topics may also include black
holes, neutron stars, dark matter and energy, cosmic microwave
background radiation, inflation, binary pulsars, gravitational waves,
and the standard big bang model.
Prerequisites:
Junior/Senior Standing. Preferably, students should have had a course in
classical dynamics or modern physics and should have completed Calculus III. Additional
mathematics and physics training is a
plus. Interested students should contact Dr. Herman for additional
information.
Student Learning
Outcomes
Upon completion of
this course, students will be able to
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Apply special
relativity to problems involving time dilation, length contraction, and
velocity addition.
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Work with four
vectors and Lorentz transformations;
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State and apply
the principle of equivalence;
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Define the metric
tensor (& inverse), & interpret it;
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Calculate the
special relativistic & Newtonian limits of general relativity;
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Discuss the tests
of general relativity such as the precession of Mercury's perihelion, light
bending, gravitational time dilation and redshift, and gravitational
waves;
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Derive the
Euler-Lagrange equations obtaining the geodesic equations and the
Christoffel symbols;
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Write down the
Schwarzschild and Robertson-Walker metrics; describe the meaning of all
terms;
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Discuss metric
singularities, event horizons and other properties of black holes;
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Discuss the
meaning of Einstein's equation;
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Identify the key
steps that lead to the recognition of the expanding Universe;
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Work with the
Friedman equation to understand relativistic cosmology and basic
cosmological models;
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Understand the
physical implications of the cosmological expansion;
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Describe the
physics and observational evidence for the Big Bang model;
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Explain why
Einstein introduced the cosmological constant and the current evidence its
value;
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Discuss the
physics of the observed cosmic microwave background radiation;
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Understand the
physics of the early universe, Big Bang Nucleosynthesis, and the universe's
timeline;
Course Requirements:
Homework: Homework assignments will
be collected on a regular basis and you will be told when the work is due. As
doing homework is very important for learning the material in this course, it
will count as 30% of your grade.
Papers/Projects: There are many interesting areas
that might best be explored by individuals, or groups, outside the classroom.
Such topics may arise in the course of the semester. You will be required to do
at least two in-depth papers in this class. This will count 10% of your grade.
Exams and Grades: Exams and Grades:
There will be a two 50 minute exams and a final exam. The exams will cover the basic
material up to the date of the exam. The tentative dates for the exams are
below.
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Exam I |
Feb 12 |
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Exam II |
Apr 9 |
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Final |
May 2, 11:30 AM |
Your final grade will be based on the following:
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Homework |
25% |
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Papers/Projects |
15% |
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Exams |
40% |
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Final |
20% |
This syllabus is subject to change!
Homework Assignments
You should do as many problems as you can to become
proficient in this class. However, you are required to turn in all of the
assigned problems for grading on the due date. All work is expected to be neat,
in order and with all work provided. The homework
assignments are listed at the course website. [See below.]
Materials on the Web
More information will be posted on the web related to the
topics we are studying. Links can be found with summaries to the material, study
suggestions, homework assignments, etc. These will be accessible through the
instructor's homepage at
http://people.uncw.edu/hermanr/GRcosmo/.
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Academic Honor Code: |
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All members of UNCW’s community are expected to follow the
academic Honor Code. Please read the UNCW Honor Code carefully (as covered in the
UNCW Student Handbook). Academic dishonesty in any form will not be tolerated in
this class. Please be especially familiar with UNCW’s position on plagiarism as
outlined in the UNCW Student Handbook. Plagiarism is a form of academic
dishonesty in which you take someone else’s ideas and represent them as your
own.
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Student Disabilities:
UNCW Disability
Services supplies information about disability law, documentation procedures and
accommodations that can be found at
http://uncw.edu/disability/. To obtain
accommodations the student should first contact Disability Services and present
their documentation to the coordinator for review and verification.
Campus Respect Compact.
UNCW has recently instituted a Respect Compact
to affirm our commitment to a civil community, characterized by mutual respect.
That Compact will soon be affixed to the wall of each classroom and can be
accessed at:
http://uncw.edu/diversity/documents/ApprovedSeahawkRespectCompact8x10.08.09.pdf
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