Introduction to General Relativity

(Physics/Astronomy 469)

INSTRUCTOR: Professor Fulvio Melia LECTURES: MWF, 9:00 am - 9:50 am, Bio Sciences West Rm 212 OFFICE HOURS: MWF, 10:00 am - 11:00 am (most other times ok too, but please call first) HOMEWORK & SOLUTIONS: Homework # 1 (Due Friday, Feb 24): Solutions Homework # 2 (Due Wed, Mar 29): Solutions Homework # 3 (Due Friday, Apr 7): Solutions Homework # 4 (Due Friday, Apr 21): Solutions Homework # 5 (Due Wed, May 3): Solutions COURSE OBJECTIVE: Although this is an introductory course in General Relativity, we will develop this classical theory from its most basic elements, including the mathematical language of tensor algebra, to the point where you should all understand where Einstein's equations come from and what they mean physically. In addition, you should be able to use them to solve for the spacetime metric given any set of symmetries and boundary conditions. ABSENCE and CLASS PARTICIPATION: You will not be forced to attend every lecture, but past experience has shown that engaging with the material in class will significantly improve your understanding of it. In addition, we intend to have extensive discussion, along with the lectures themselves, so invariably new questions and ideas are introduced that you may not find in the book or the notes. GENERAL POLICIES: [1] You are all taking this class because you have a passion for this subject. I am not concerned about the possibility that we will encounter any disruption, but we are required by the UA to emphasize our commitment to providing a positive learning experience for everyone. So please do not use any electronic devices (computer or phone) while in class, and let us all be supportive of our fellow students. [2] Please be aware of the UA Threatening Behavior by Students policy, which prohibits threats of physical harm to any member of the University community: policy.arizona.edu/education-and-student-affairs/threatening-behavior-students [3] You must also be aware of the Student Code of Academic Integrity that prohibits plagiarism: deanofstudents.arizona.edu/policies-and-codes/code-academic-integrity [4] You are expected to abide by UA Policy 200E on prohibited behaviors: policy.arizona.edu/human-resources/nondiscrimination-and-anti-harassment-policy [5] If you have a disability, please be aware of the reasonable accommodations provided by the Disability Resources Center: drc.arizona.edu/instructors/syllabus-statement [6] We will try to adhere to the schedule of topics listed below. However, please note that the information contained in this course syllabus, other than the grade and absence policies, may be subject to change with reasonable advance notice, as deemed appropriate by the instructor. TEXTBOOK: Weinberg, Steven, Gravitation and Cosmology TOPICS COVERED DURING THIS CLASS: 1. INTRODUCTION 1.1 Special Relativity (SR) 1.2 Lorentz Transformations 1.3 Physical Laws in 4-D Spacetime 2. MAXWELL'S EQUATIONS 2.1 Lorentz Transformation of Electrodynamics 2.2 Stress-Energy Tensor for the Electrodmagnetic Field 3. ACTION PRINCIPLES IN 4-D SPACETIME 3.1 Motion of Point Particles 3.2 Relativistic Lagrangians 3.3 Field Lagrangians 3.4 Invariances and Conservations Laws 3.5 Noether's Theorem 4. GENERAL RELATIVITY (GR) 4.1 Generalized Coordinate Systems 4.2 Tensor Algebra 4.3 Particle Mechanics in Generalized Coordinates 4.4 Accelerated Systems 5. CONTINUUM MECHANICS IN GR 5.1 Stress-Energy Tensor in Generalized Coordinates 5.2 Equations of Motion 6. GRAVITATION 6.1 Classical View 6.2 Mach's Principle 6.3 Principle of Equivalence (PoE) 6.4 Geodesics 6.5 Experimental Test of PoE 6.6 Gravitational Redshift 7. CURVATURE OF SPACETIME 7.1 Riemann Curvature Tensor 7.2 Bianchi Identities 8. FIELD EQUATIONS OF GR 8.1 Einstein's equations 8.2 Action Principle in GR 9. SOME SOLUTIONS AND APPLICATIONS 9.1 Schwarzschild and Kerr Metrics 9.2 Black Holes 9.3 Gravitational Waves 9.4 Standard Model of Cosmology METHOD OF EVALUATION Problems (50%) Written Final: Thursday, May 11 (50%)