**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)

**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 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.

- Note: This homework has been updated. The original version had 2 significant typos -- [i] some missing *'s (r where there should have been r
- 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

- 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___.

There is no final exam third term, in its place there will be a final project. Details are here.