Course: PHZ 7608, Special and General Relativity 2, Class Hours: M Period 10, W Period 9, Room 1200
Lecturer: J. N. Fry, Office NPB 2172, phone 392-6692, e-mail fry#phys.ufl.edu, Office Hours: MWF Period 6   [Schedule]

Course Description:

This is the second semester of relativity, following PHZ 6607, wherein we apply the machinery of the general theory of relativity to a variety of special topics.

Topics:

• Black holes
  • nonrotating — Schwarzschild
  • charged — Reissner-Nordstrom
  • rotating — Kerr, Kerr-Newman
  • methods: curvature two-forms
  • Killing horizons, surface gravity
  • Hawking radiation
  • singularity theorems
• cosmology — global
  • Robertson-Walker metric, Friedmann equations
  • cosmological redshift
  • contents of the universe
  • thermal history in the standard model, nucleosynthesis, recombination, the microwave background
  • the early universe, inflation
• cosmology — local
  • microwave background anisotropies
  • large scale structure, clustering statistics, baryon acoustic oscillations
• scalar tensor (Brans Dicke) gravity

Grading:

Grades will be based entirely on periodic homework sets.

Books: (Relativity , Global Cosmology / Local Cosmology, Relativistic Astrophysics)

• Sean Carroll, Spacetime and Geometry: An Introduction to General Relativity (Addison-Wesley, 2003).
    Online Lecture Notes on General Relativity.   Preposterous Universe   @seanmcarroll
• S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time (Cambridge University Press, 1973).
• Charles W. Misner, Kip S. Thorne, and John A. Wheeler, Gravitation (W. H. Freeman, 1973).
• Michael P. Ryan and Lawrence C. Shepley, Homogeneous Relativistic Cosmologies (Princeton, 1975)
• Steven Weinberg, Gravitation and Cosmology (Wiley, 1972; 2008).   ——, Cosmology (Oxford, 2008).
• Jeremy Bernstein, Kinetic theory in the expanding universe (Cambridge, 1988)

• Edward W. Kolb and Michael S. Turner, The Early Universe (Addison Wesley, 1990)
• John A. Peacock, Cosmological Physics (Cambridge University Press, 1999)
• P. J. E. Peebles, Principles of Physical Cosmology (Princeton, 1993)   NPR 28 Dec 16
  ——, Physical Cosmology (Princeton, 1972)

• David Arnett, Supernovae and Nucleosynthesis: An Investigation of the History of Matter, from the Big Bang to the Present (Princeton, 1996)
• Scott Dodelson, Modern Cosmology (Academic Press, 2003).   [Errata]
• P. J. E. Peebles, The Large Scale Structure of the Universe (Princeton, 1980)
• Ya. B. Zel'dovich and I. D. Novikov, Relativistic Astrophysics, Volume 1: Stars and Relativity (Chicago, 1978)
  ——, Relativistic Astrophysics, Volume 2: The Structure and Evolution of the Universe (Chicago, 1978)

Links: (a growing list)

Orbits in Strongly Curved Spacetime
Black Holes in Java
Andrew Hamilton's Relativity and Black Hole Links
Andrew Hamilton's Cosmology Links
Ned Wright's Cosmology Tutorial
Infall in proper time τ(r), coordinate time t(r)
Families of photon trajectories: Schwarzschild, Eddington-Finkelstein HE74 Figure 23
Kruskal coordinates, INSPIRE plots
Penrose diagram for Reissner Nordström, more INSPIRE plots
Black Holes
Karl Schwarzschild, Sir Arthur Stanley Eddington, George Szekeres
Reissner-Nordstrom Black Holes in two-dimensional string theory [arXiv]
Riemann tensor calculation for Kerr geometry
The Adventures of Archibald Higgins [download]
Geodesics of the Kerr metric  
visualization of orbits in the Kerr metric   Wolfram Demonstration Project   Kerr Orbit Visualizer
AJSH Penrose diagrams   Penrose diagram of a Kerr black hole   Penrose diagram of a RN black hole
SW galaxies counting sheet Coma Cluster again 2dF SDSS cmass (4.5GY × 6GY) .
NVSS radio sky.   COBE DMR 53GHz   WMAP/Planck   Planck Chromoscope   EUVE sky   Swift/BAT X-ray sky   Fermi GRB sky
Published values of H₀ up tp 2010 [plot]   HST Key Project Final Results
Curved surfaces with k=+1, k=−1
Photons Brake the Sun
Albert Einstein and the origins of modern cosmology
H₀t₀, Δθ–z, m–z, Δm–z  
galaxy luminosity function
synthesized Hubble diagram m vs. cz for galaxies, supernovae
observations: Sandage 1972 (21), Riess, Press, & Kirshner 1995 (3) Riess et al. 1998 (14) Perlmutter et al. 1999 (4)
(nearby) Hubble flow (39), ESSENCE Survey (56-57), z > 1 (64)
Fig. 8.4
Boesgaard and Steigman 1985 (7), Olive, Steigman, and Walker 1999 (15),
kibble mechanism
baryon number evolution
WIMP production (Gelmini and Gondolo)
Rocky Kolb Taking Sides (34)
thermal effective potential
Scalar field dynamics: small field, coherent oscillations, large field,
Gaussian random noise, n = −2, −1, 0, +1, two parts in 1/f
Andrew Liddle An introduction to cosmological inflation (https://arxiv.org/abs/astro-ph/9901124)
random vector field, longitudinal vector field, transverse vector field
f(Ω), D(x), Virgo cluster
X_e   Ω = 0.025, 0.15, 1
CAMB, baseline parameters, C_l, P(k) LAMBDA web interface
Wayne Hu Animations
Planck 2015 XIII: Cosmological parameters. (TT 8), (EE 13), BAO in SDSS-III BOSS DR9. (Fig8, 14),
Dark Matter History
nongaussian distribution
voids in the galaxy distribution
APM S_n
correlation functions from generating function voids SDSS red/blue
perturbation theory bispectrum
Max Tegmark parameter animations
Rotation curves of spiral galaxies [13]
Tully Fisher relation [5]
Lensing cluster density profile [30]
NFW profile
Bullet cluster
SPT-SZ Cluster Survey [11,14]
Parameters (ESO) Parameters (PanStarrs) Parameters (SPT)
Ly-α forest SDSS redshift z > 6 quasars [35-36]
precession in the orbit of the star S2 [fig]
Binary-Black-Hole Coalescence with Asymmetric Masses

Evolution of the interior of a charged black hole, W. A. Hiscock, Phys. Lett. 93A, 110 (1981).
The Kerr spacetime: A brief introduction, M. Visser, arXiv:0706.0622.
Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics, R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
A new class of vacuum solutions of the Einstein field equations, R. P. Kerr, A. Schild, Gen. Relat. Gravit. 41, 2485 (2009). (reprinted)
On the discovery of the Kerr metric, R. P. Kerr, in Proceedings of The Eleventh Marcel Grossmann Meeting On Recent Developments
  in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (World Scientific, 2008), pp 9–38.
The Kerr Metric, S. A. Teukolsky, Class. Quantum Grav. 32, 2485 (2015).
Rotating cylinders and the possibility of global causality violation, F. J. Tipler, Phys. Rev. D 8, 2203 (1974).
A note on Komar's anomalous factor, J. Katz, Class. Quantum Grav. 2, 423 (2015).
Particle creation by black holes, S. W. Hawking, Commun. math. Phys 43, 199 (1975).
A measurement of the mass density of the universe, E. D. Loh and E. J. Spillar, Ap. J. Lett. 307, 1L (1986).
Constraining Dark Energy with the DEEP2 Redshift Survey, M. Davis, B. F. Gerke, J. A. Newman; DEEP2 Team, ASPC 339, 128 (2005).
The 2dF QSO Redshift Survey – XII. The spectroscopic catalogue and luminosity function, S. M. Croom et al., M.N.R.A.S. 349, 1397 (2004).
The Sloan Digital Sky Survey Quasar Catalog. II. First Data Release, D. P. Schneider et al., A.J. 126, 2579 (2003).
Cosmological evolution of radio sources, J. J. Condon, Ap. J. 287, 461 (1984).
Extragalactic Background Light at 5100 Å, R. Dube, W. C. Wickes, and D. T. Wilkinson, Ap.J.Lett. 215, L51 (1977).
Upper limit on the extragalactic background light, R. Dube, W. C. Wickes, and D. T. Wilkinson, Ap.J. 232, 333 (1979).
First Detections of the Extragalactic Background Light at 3000, 5500, and 8000 Å. I. Results, R. A. Bernstein, W. L. Freedman, and B. F. Madore, Ap.J. 571, 56 (2002).
Magnetic monopoles in unified gauge theories, G. 't Hooft, Nucl. Phys. B 79, 276 (1974).
Particle spectrum in quantum field theory, A. M. Polyakov, JETP Lett. 20, 194 (1974).
Cosmological Production of Superheavy Magnetic Monopoles, J. P. Preskill, Phys. Rev. Lett. 43, 1365 (1979).
First Results from a Superconductive Detector for Moving Magnetic Monopoles, B. Cabrera, Phys. Rev. Lett. 48, 1378 (1982).
Inflationary universe: A possible solution to the horizon and flatness problems, A. H. Guth, Phys. Rev. D 23, 347 (1981). (5755)
A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, A. Linde, Phys. Lett. B 108, 389 (1982). (3375)
Cosmology for grand unified theories with radiatively induced symmetry breaking, A. Albrecht and P. J. Steinhardt, Phys. Rev. Lett. 48, 1220 (1982). (2936)
Cosmological consequences of a rolling homogeneous scalar field, B. Ratra and P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988).
The observed infall of galaxies towards the Virgo cluster, I, D. Karachentsev and O. G. Nasonova, M.N.R.A.S. 405, 1075 (2010).
Recombination of the Primeval Plasma, P. J. E. Peebles, Ap. J. 153, 1 (1968).
Gauge-invariant cosmological perturbations, J. M. Bardeen, Phys. Rev. D 8, 1882 (1980).
Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges, C.-P. Ma and E. Bertschinger, Ap. J. 455, 7 (1995).
A Numerical Study of the Stability of Flattened Galaxies: Or, can Cold Galaxies Survive?, J. P. Ostriker and P. J. E. Peebles, Ap. J. 186, 467 (1973).
Rotational properties of 21 SC galaxies with a large range of luminosities and radii ... , V. C. Rubin, K. W. Ford, and N. Thonnard, Ap. J. 238, 471 (1980).
Clustering in a neutrino-dominated universe, C. Frenk, S. D. M. White, and M. Davis, Ap. J. 274, 1 (1983).
Formation of galaxies and large-scale structure with cold dark matter, G. R. Blumenthal, S. M. Faber, J. R. Primack, and M. J. Rees, Nature, 311, 517 (1984).
On the spatial correlations of Abell clusters, N. Kaiser, Ap. J. 284, 9 (1984).
A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, M. Milgrom, Ap. J. 270, 365 (1983).
Testing modifications of gravity, G. Lake, Ap. J. Lett. 345L, 17 (1989).
Dwarf spheroidal galaxies and non-Newtonian gravity, E. G. Ortwin and D. N. Spergel Ap. J. 397, 38 (1992).
Origin of the large-scale galaxy peculiar velocity field: A minimal isocurvature model, P. J. E. Peebles, Nature 327, 210 (1987).
Quintessential Cosmology Novel Models of Cosmological Structure Formation, R. R. Caldwell, R. Dave, and P. J. Steinhardt, Astrophys. Space Sci., 261, 303 (1998).
No evidence for extensions to the standard cosmological model, A. Heavens, Y. Fantaye, E. Sellentin, H. Eggers, Z. Hosenie, S. Kroon, and A. Mootoovaloo arXiv:1704.03467
Cosmological parameters from SDSS and WMAP, M. Tegmark et al, (the SDSS collaboration) Phys. Rev. D 69, 103501 (2004).

The Arrow of Time   Entropic Time  
Active supernovae
Star Trek the musical

Class Diary

Homework:

1. Homework 1. Due February 1. Solution.
2. Homework 2. Due February 15. Solution.
3. Homework 3. Due April 5. Solution.
4. Homework 4 (takehome final). Due April 26.