General Relativity

Glenn Elert

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Resources

General
- General Relativity, MacTutor History of Mathematics archive
- Usenet Relativity FAQ
Black holes
- Early papers
  - On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars…. John Michell. Philosophical Transactions. Vol. 74 (1784).
- Schwarzschild radius
- Chandrasekhar limit
  - The Limiting Density in White Dwarf Stars. E.C. Stoner. Philosophical Magazine Series 7. Vol. 7 No. 41 (1929): 63–70.
  - The Equilibrium of Dense Stars. E.C. Stoner. Philosophical Magazine Series 7. Vol. 9 No. 60 (1930): 944–963.
  - The Density of White Dwarf Stars. S. Chandrasekhar. Philosophical Magazine Series 7. Vol. 11 No. 70 (1931): 592–596. Reprinted in the Journal of Astrophysics and Astronomy. Vol. 15 No. 2 (1994): 105–109.
  - The Maximum Mass of Ideal White Dwarfs. S. Chandrasekhar. Astrophysical Journal. Vol. 74 (1931): 81–82.
  - The Highly Collapsed Configurations of a Stellar Mass. S. Chandrasekhar. Monthly Notices of the Royal Astronomical Society. Vol. 91 (1931): 456–466.
  - Stellar Configurations with Degenerate Cores. S. Chandrasekhar. The Observatory. Vol. 57 (1934): 373–377.
  - The Highly Collapsed Configurations of a Stellar Mass (Second Paper). S. Chandrasekhar. Monthly Notices of the Royal Astronomical Society. Vol. 95 (1935): 207–225.
- Tolman-Oppenheimer-Volkoff limit
  - Static Solutions of Einstein's Field Equations for Spheres of Fluid. R.C. Tolman. Physical Review. Vol. 55 No. 4 (1939): 364–373.
  - On Massive Neutron Cores. J.R. Oppenheimer and G.M. Volkoff. Physical Review. Vol. 55 No. 4 (1939): 374–381.
  - On Continued Gravitational Contraction. J.R. Oppenheimer and H. Snyder. Physical Review. Vol. 56 No. 5 (1939): 455–459.
- Word origin
  - Black Hole. Michael Quinion. World Wide Words. Short article on the probable origin of the term "black hole".
  - Black Holes in Space. Science News Letter. Vol. 85 No. 3 (1964). Oldest known written use of the term "black hole".
- Singularity theorem
  - The Singularities of Gravitational Collapse and Cosmology. S.W. Hawking and R. Penrose. Proceedings of the Royal Society. Vol. 314 No. 1519 (1970): 529–548.
- Evaporation and explosion
  - Black Hole Explosions? S.W. Hawking. Nature. Vol. 248 (1974): 30–31.
  - Particle creation by black holes. S.W. Hawking. Communications in Mathematical Physics. Vol. 43 No. 3 (1975), 199–220.
- Formation in particle accelerators
  - Ultra Relativistic Particle Collisions. Matthew W. Choptuik, Frans Pretorius. Physical Review Letters. Vol. 104 No. 11 (2010).
  - Will the LHC destroy the world? Sixty Symbols. YouTube (2012). CERN's Large Hadron Collider will NOT destroy our planet. But many of you asked about it — and the "scenarios" are a good excuse to discuss some cool physics.
einstein
- Die Grundlage der allgemeinen Relativitätstheorie (The basis of the general theory of relativity). Albert Einstein. Annalen der Physik. Vol. 354 No. 7 (1916): 769–822 [open access copy].
- Prinzipielles zur allgemeinen Relativitätstheorie (Principles of general relativity). Annalen der Physik. Vol. 360 No. 4 (1918): 241–244 [open access copy].
- Relativity: the Special and General Theory. Albert Einstein. London: Methuen (1916). Translated by Robert W. Lawson (1920).
  - Einstein Reference Archive
  - Project Guttenberg
- A Brief Outline of the Development of the Theory of Relativity. Albert Einstein. Nature. Vol. 106 No. 2677 (1921): 782–784.
expanding universe
- Origins
  - Die Feldgleichungen der Gravitation. Albert Einstein. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse. (1915): 844–847 [open access copies]. Translated into English as The Field Equations of Gravitation.
  - Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie. Albert Einsterin. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-Mathematische Klasse. Vol. 7 No. 14 (1917): 142–152.
  - Über die Krümmung des Raumes. Alexander Friedmann. Zeitschrift für Physik. Vol. 10 No. 1 (1922): 377–386. Translated into English as On the curvature of space. Alexander Friedmann. General Relativity and Gravitation. Vol. 31 No. 12 (1999): 1991–2000.
  - Über die Möglichkeiten einer Welt mit konstanter negativer Krümmung des Raumes (On the possibilitiy of a universe with constant negative curvature of space). Alexander Friedmann. Zeitschrift für Physik. Vol. 21 No. 1 (1924): 326–332.
  - Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Georges Lemaître. Annales de la Société Scientifique de Bruxelles, Sèrie A. Vol. 47 (1927): 49–59. Translated into English as A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae. Georges Lemaître. Monthly Notices of the Royal Astronomical Society. Vol. 91 (1931): 483–490.
  - A relation between distance and radial velocity among extra-galactic nebulae. Edwin Hubble. Proceedings of the National Academy of Sciences. Vol. 15 No. 3 (1929): 168–173.
  - Evolution of the Expanding Universe. Georges Lemaître. Proceedings of the National Academy of Sciences. Vol. 20 No. 1 (1934): 12–17.
  - H₀: The Incredible Shrinking Constant 1925–1975. Virginia Trimble. Publications of the Astronomical Society of the Pacific. Vol. 108 No. 730 (1996): 1073–1082.
- inflation
  - Inflationary universe: A possible solution to the horizon and flatness problems. Alan Guth. Physical Review D. Vol. 23 No. 2 (1981): 347–356.
  - (paid link)
    The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (paid link). Alan Guth. Reading, MA: Perseus (1997).
  - Chaotic inflation. Andrei Linde. Physics Letters B. Vol. 129 No. 3 (1983): 171–181.
    - open access version at kit.edu
    - paywall version at sciencedirect.com
  - BICEP and Keck Array. BICEP stands for "Background Imaging of Cosmic Extragalactic Polarization". This experiment was thought to offer the first evidence for primordial gravitational waves. The signal turned out to be dust in the Milky Way.
- Acceleration
  - Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. Adam G. Riess et al. Astronomical Journal. Vol. 116 No. 3 (1998): 1009–1038.
  - Measurements of Ω and Λ from 42 High-Redshift Supernovae. Saul Perlmutter et al. Astrophysical Journal. Vol. 517 No. 2 (1999): 565–586.
  - Phantom Energy and Cosmic Doomsday. Robert R. Caldwell, Marc Kamionkowski, and Nevin N. Weinberg. Physical Review Letters. Vol. 91 (2003): 071301. Open access copy at arXiv.org.
  - Supernovae, Dark Energy and the Accelerating Universe. Saul Perlmutter. Physics Today. Vol. 56 No. 4 (2003).
  - Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution. Adam G. Riess, et al. Astrophysical Journal. Vol. 607 No. 1 (2004): 665–687.
  - Nobel Prize in Physics 2011to Saul Perlmutter, Brian P. Schmidt and Adam G. Riess for the discovery of the accelerating expansion of the Universe through observations of distant supernovae.
gravitational doppler effect and time dilation
- Gravitational Red-Shift in Nuclear Resonance. Robert V. Pound and Glen A. Rebka Jr. Physical Review Letters. 3 (1959): 439–441.
- Apparent Weight of Photons. Robert V. Pound and Glen A. Rebka Jr. Physical Review Letters. 4 (1960): 337.
- Effect of Gravity on Nuclear Resonance. R. V. Pound and J. L. Snider. Physical Review Letters. 13 (1964): 539.
- Performance and Results of Portable Clocks in Aircraft. J.C. Hafele. Proceedings of the Third Annual Department of Defense (DoD) Precise Time and Time Interval (PTTI) Strategic Planning Meeting. (1971): 261-288. DTIC Accession Number: ADA489971.
- Around-the-World Atomic Clocks: Predicted Relativistic Time Gains. J.C. Hafele and Richard E. Keating. Science. Vol. 177 No. 4044 (1972): 166–168.
- Around-the-World Atomic Clocks: Observed Relativistic Time Gains. J.C. Hafele and Richard E. Keating. Science. Vol. 177 No. 4044 (1972): 168–170.
- Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser [Gravity Probe A]. R.F. Vessot et al. Physical Review Letters. 45 (1980): 2081.
- Weighing Photons I, Robert V. Pound, Physics in Perspective. 2 (2000): 224.
- Weighing Photons II, Robert V. Pound, Physics in Perspective. 3 (2001): 4.
- Relativity in the global positioning system. Neil Ashby. Living Reviews. Relativity. (2003).
- The Weight of Light. David Lindley. Physical Review Focus. Vol. 16 No. 1 (12 July 2005). A good general overview of the Pound-Rebka experiment that verified Einstein's gravitational doppler efect.

A precision measurement of the gravitational redshift by the interference of matter waves. Holger Müller, Achim Peters, Steven Chu. Nature. Vol. 463 (18 February 2010): 926–29.
Atomic Clock Ensemble in Space (ACES), European Space Agency

gravitational waves
- detectors
  - LIGO (Laser Interferometer Gravitational Wave Observatory) is a pair of gravitational wave detectors located in Livingston, Louisiana and Hanford, Washington in the United States. It is operated by Caltech and MIT.
  - Virgo is a laser interferometer located near Pisa, Italy. It is operated by an international collaboration of scientists from France, Italy, the Netherlands, Poland, and Hungary.
  - GEO600 is a laser interferometer located near Hannover, Germany. It is operated by the Max Planck Institute for Gravitational Physics, Leibniz Universität Hannover, and partners in the United Kingdom.
  - KAGRA (Kamioka Gravitational Wave Detector) is a laser interferometer being built in the tunnels of the Kamioka mine in Japan.
  - IndIGO (Indian Initiative in Gravitational-wave Observations) is an initiative to set up a laser intereferometer in India.
  - eLISA (Evolved Laser Interferometer Space Antenna) will be the first gravitational observatory in space. eLISA is a joint effort of eight European countries – Denmark, France, Germany, Italy, the Netherlands, Spain, Switzerland and the United Kingdom. The original LISA was to be a joint project of NASA and ESA.
- Historical
  - Näherungsweise Integration der Feldgleichungen der Gravitation. Albert Einstein. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin). Sitzungsberichte (1916): 688–696. Approximate integration of the gravitational field equations. Albert Einstein. Meeting reports of the Royal Prussian Academy of Sciences (Berlin). Session reports (1916): 688–696.
  - Über Gravitationswellen. Albert Einstein. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin). (1918): 154–167. Einstein admits that his equations derived a few years ealier permit the existance of gravitational waves.
  - Discovery of a pulsar in a binary system. R.A. Hulse and J.H. Taylor. Astrophysical Journal. Vol. 195 (1975): L51–L53. Why is this pulsar losing mechanical energy? The first evidence for gravitational waves.
  - BICEP and Keck Array. BICEP stands for "Background Imaging of Cosmic Extragalactic Polarization". This experiment was thought to offer the first evidence for primordial gravitational waves. The signal turned out to be dust in the Milky Way.
  - Observation of Gravitational Waves from a Binary Black Hole Merger. B.P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Physical Review Letters. 116, 061102 (2016). The first direct detection of gravitational waves.
- sounds
  - Sounds of Spacetime. An audio guide to understanding gravitational wave signals.
Miscellaneous
- Gravity Probe B
Video on demand
- Brady Haran
  - Mass and Weight are (sort of) the SAME. Sixty Symbols. YouTube (2014). The Equivalence Principle, starring Professor Mike Merrifield from the University of Nottingham (plus Albert Einstein and Isaac Newton).
  - Black Holes. Sixty Symbols. YouTube (2009). Crushing the Earth into a Black Hole and looking into the core of the Milky Way.
  - Cosmic Superstrings. Sixty Symbols. YouTube (2013). Professor Ed Copeland on strings and superstrings.
  - Dark Energy & The Big Rip. Sixty Symbols. YouTube (2014). Third in our "trilogy" of extended interviews with Professor Ed Copeland.
  - Inflation & the Universe in a Grapefruit. Sixty Symbols. YouTube (2013). Professor Ed Copeland discusses inflation, the Big Bang, and when the observable universe fit inside a grapefruit.
  - The Remarkable Way We Eat Pizza. Numberphile. YouTube (2016). Cliff Stoll discusses a "Remarkable Theorem", Gaussian curvature, and pizza.
- The Mechanical Universe and Beyond (1985)
  - From Kepler to Einstein. From Kepler's laws and the theory of tides, to Einstein's general theory of relativity, into black holes, and beyond.
- Physics for the 21st century (2010)
- World Science Festival
  - The Perfect Gravitational Wave. World Science Festival. YouTube (2016). LIGO's first detection seemed almost too perfect to be true. Scientists who made the discovery recount their own journey from self-doubt to confidence that the experiment had indeed made a historic breakthrough.