Ph 236: General Relativity

Course Description

FIRST TERM: The mathematical foundations and formulation of GR.

• Special relativity in the language of tensors
  • Vectors, tensors, and forms in flat spacetime (2011 Sep 28)
  • Coordinate bases, tensor algebra in flat spacetime, and special relativity (2011 Sep 30)
  • Tensor calculus and electrodynamics in flat spacetime (2011 Oct 05)
  • Stress-energy tensor and conservation of energy and momentum (2011 Oct 07)
• Calculus in curved spacetime
  • Vectors and vector calculus in curved spacetime (2011 Oct 12)
  • Tensor calculus (2011 Oct 14)
  • Geodesics and curvature (2011 Oct 19)
  • More curvature tensors (2011 Oct 21)
• General relativity
  • Field equations, cosmological constant, and tides (2011 Oct 28)
• Linearized gravity and its applications
  • Linearized gravity (2011 Nov 09)
  • Weak field tests of GR: the gravitational redshift, deflection of light, and Shapiro delay (2011 Nov 11)
  • External field of an isolated system (2011 Nov 16)
• Weakly nonlinear gravity and gravitational radiation
  • Weakly nonlinear GR in asymptotically flat spacetime -- Concepts (2011 Nov 23)
  • The "energy" of gravitational waves (2011 Nov 30)
  • Gravitational energy and orbital decay by gravitational radiation (2011 Dec 02)

SECOND TERM: Symmetrical solutions to the Einstein equations.

• Spherical stars
  • Symmetrical spacetimes (2012 Jan 04)
  • Spherical stars -- I. The metric structure (2012 Jan 11)
  • Spherical stars -- II. Equations for radial structure (2012 Jan 13)
  • Particle motion exterior to spherical stars (2012 Jan 18)
  • The equation of state of dense matter (2012 Jan 20)
  • White dwarfs and neutron stars -- mass-radius relations
  • Radial pulsations and stability (2012 Jan 25)
  • Radial pulsations and stability -- implications (2012 Feb 08)
• Black holes
  • The Schwarzschild black hole (2012 Feb 10)
  • External appearance of a black hole (2012 Feb 15)
  • Reissner-Nordstrom black holes (2012 Feb 17)
  • Kerr black holes: I. Metric structure and regularity of particle orbits (2012 Feb 22)
  • Kerr black holes: II. Precession, circular orbits, and stability (2012 Mar 02)
  • Horizons and the area theorem (2012 Mar 07)

THIRD TERM: Cosmology, initial conditions, and advanced topics.

• Cosmology, Part I
  • The FRW metric (2012 Apr 04)
  • Dynamics of cosmic expansion (2012 Apr 11)
  • The classical tests and density parameters (2012 Apr 17)
  • Thermal history of the Universe - I. Radiation (2012 Apr 20)
• Initial value problems and degrees of freedom
  • Lagrangian formulation of GR (2012 Apr 27)
  • Hypersurfaces and the 3+1 formulation of geometry (2012 May 4)
  • Hamiltonian formulation of GR (2012 May 4)
• Cosmology, Part II
  • Introduction to cosmological perturbations (2012 May 9)
  • Inflation (2012 Jun 1)
  • Primordial perturbations: tensor sector (2012 Jun 6)

Logistics

• Instructor: Chris Hirata (Cahill #272; chirata@tapir.caltech.edu)
• TA: Jing Luan (Cahill #357; jingluan@caltech.edu)
• Location: Lauritsen #269, Wednesday & Friday 2:30-4:00 PM
• Prerequisites: Standard undergraduate coursework on classical mechanics, electrodynamics, and special relativity.
• Textbook: Misner, Thorne, and Wheeler, Gravitation (1973). This will be supplemented with more recent material as appropriate.
• Homework: Due Fridays.
• Office Hours: Thursday 10-11 AM (Cahill #272) and Thursday 5-6 PM (Cahill #357).
• Grading: 80% weekly homeworks, 20% final exam. A "passing" grade is ≥50%. In spring term, a final project will substitute for the exam.

Homework

• Homework 1: due 10/07/11
• Homework 2: due 10/14/11
• Homework 3: due 10/21/11
• Homework 4: due 10/28/11
• No homework due 11/04/11
• Homework 5: due 11/11/11
• Homework 6: due 11/18/11
• No homework due 11/25/11
• Homework 7: due 12/02/11

• Homework 8: due 01/13/12
• Homework 9: due 01/23/12
  • The originally posted version had a missing factor of i in Eq (2).
  • As a result of this (and the late posting) no penalty will be applied for homeworks turned in by Monday 1/23.
• Homework 10: due 01/27/12
• Homework 11: due 02/03/12
• No homework due 02/10/12
• Homework 12: due 02/17/12
• Homework 13: due 02/24/12
  • Note: This homework has been updated. The original version had 2 significant typos -- [i] some missing *'s (r where there should have been r_*) in Eqs. (7) and (8), and [ii] a spurious factor of 2 in the denominator of Eq. (8). If you've already printed the homework please see the new version.
• Homework 14: due 03/02/12
• Homework 15: due 03/09/12

• Homework 16: due 04/20/12
• Homework 17: due 04/27/12
• Homework 18: due 05/04/12
• Homework 19: due 05/11/12

Final Exam

• The exam is to be completed in 3 hours. It is due Friday 12/9 to Jing Luan's mailbox on the 3rd floor of Cahill.
• You may consult the main text (Misner/Thorne/Wheeler), the course lecture notes, and your returned homeworks and solution sets. You may not consult other references (papers, other books, Internet sites other than the notes posted here, your classmates).
• When you are ready to start the exam, download the PDF ___here___.

• The exam is to be completed in 3 hours. It is due Wednesday 3/21 to Jing Luan's mailbox on the 3rd floor of Cahill.
• You may consult the main text (Misner/Thorne/Wheeler), the course lecture notes, and your returned homeworks and solution sets. [You will want the notes -- yes, you may use the Internet to read them off this site.] You may not consult other references (papers, other books, Internet sites other than the notes posted here, your classmates).
• When you are ready to start the exam, download the PDF ___here___.