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$$G_{\mu\nu}=8\pi T_{\mu\nu}$$






  1. Interesting Links
    1. On Relativity,
    2. Usenet,
    3. Black Hole Visualizations,
    4. Feynman,
    5. Relativity and the Dimensionality of the World,
    6. Μαύρες Τρύπες Kerr ή κάτι άλλο;
    7. Space, Time, and Spacetime,
    8. On Cosmology
    9. On Compact Objects
    10. Conversion to geometric units
    11. On Bicycle Stability
    12. Quantum Mechanics in your face
    13. The Scenario Machine
    14. Αχιλλέας Παπαπέτρου
    15. O Δ. Χριστοδούλου στο ΕΚΠΑ.
    16. V.I. Arnold on teaching mathematics.




Interesting Links:



1. On Relativity

I. Einsteins relativity Papers
A. Einstein, ON THE ELECTRODYNAMICS OF MOVING BODIES
A. Einstein, DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?
II. What is the experimental basis of Special Relativity?
III. Special Relativity: A Centenary Perspective, Clifford M. Will (2005)
IV. The Confrontation between General Relativity and Experiment, Clifford M. Will (2006)
V. Tests of Gravity Using Lunar Laser Ranging, Stephen M. Merkowitz (2010)
VI. Modern Tests of Lorentz Invariance, David Mattingly (2005)
VII. Teaching General Relativity, Robert M. Wald (2005, "Resource Letter" to American Journal of Physics)

VIII. Reflections on Relativity, by Kevin Brown


2. Usenet Physics FAQ


3. Black Hole Visualizations

Journey into a Schwarzschild black hole from Andrew Hamilton on Vimeo.


A.J.S. Hamilton, J. P. Lisle, The river model of black holes, Am.J.Phys.76:519-532,2008
A.J.S. Hamilton, G. Polhemus, The edge of locality: visualizing a black hole from the inside, arXiv:0903.4717v1 [gr-qc]
A.J.S. Hamilton, G. Polhemus, Stereoscopic visualization in curved spacetime: seeing deep inside a black hole, New J. Phys. 12 (2010) 123027
Inside Black Holes


4. Feynman on "Why?" Questions and on understanding Science and perceiving Reality (from "Fun to Imagine")




5. Relativity and the Dimensionality of the World, Vesselin Petkov, Springer 2007

1. The Meaning of Dimensions, Paul S. Wesson
2. Some Remarks on the Spacetime on Newton and Einstein, Graham Hall
3. The adventures of Spacetime, Orfeu Bertolami
4. Physics in the Real Universe: Time and Spacetime, George F. R. Ellis (See also George Ellis at the FQXi SETTING TIME ARIGHT conference, an interdisciplinary meeting investigating the nature of time.)
5. The Real World and Spacetime, Hans C. Ohanian
6. Four-dimensional Reality and Determinism; an Answer to Stein, W Rietdijk
7. Relativity, Dimensionality, and Existence, V Petkov
8. Canonical Relativity and the Dimensionality of the World, Martin Bojowald
9. Relativity theory does not imply that the future already exists: a counterexample, Rafael D. Sorkin
10. Absolute Being vs Relative Becoming, Joy Christian
11. An Argument for 4D Blockworld from a Geometric Interpretation of Non-relativistic Quantum Mechanics, Michael Silberstein, Michael Cifone, W.M. Stuckey
12. Spacetime: Arena or Reality?, H. I. Arcos, J. G. Pereira
13. Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity, Luca Lusanna, Massimo Pauri
14. Lorentzian Space-Times from Parabolic and Elliptic Systems of PDEs, Carlos Barcelo


6. Μαύρες τρύπες Kerr ή κάτι άλλο; Εντοπίστε τη διαφορά.

Μαύρες τρύπες Kerr ή κάτι άλλο; Εντοπίστε τη διαφορά. from Vagelford on Vimeo.


Phys.Rev.Lett.103:111101,2009 How to observe a non-Kerr spacetime, Theocharis A. Apostolatos, Georgios Lukes-Gerakopoulos, George Contopoulos
Phys. Rev. D 81, 124005 (2010) An observable signature of a background deviating from Kerr, Georgios Lukes-Gerakopoulos, Theocharis A. Apostolatos, George Contopoulos


7. Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski's Unification of Space and Time, Vesselin Petkov, Springer 2010

Part 1 / Minkowskis Representation of Special Relativity -- Examples of Its Impact on the Twentieth Century Physics
The Minkowskian Background of Whitehead’s Theory of Gravitation, Ronny Desmet
The Experimental Verdict on Spacetime from Gravity Probe B, James Overduin
Rigidity and the Ruler Hypothesis, Stephen N. Lyle
Minkowski Space and Quantum Mechanics, Paul O’Hara
Relativity and Quantum Field Theory, Jonathan Bain
Ether, the Theory of Relativity and Quantum Physics, Eduardo V. Flores
Part 2 / Implications of Minkowski’s Ideas for the Philosophy of Space and Time
Minkowski’s Proper Time and the Status of the Clock Hypothesis, Richard T. W. Arthur
Why Spacetime Is Not a Hidden Cause: A Realist Story, Graham Nerlich
Structural Explanations in Minkowski Spacetime: Which Account of Models?, Mauro Dorato and Laura Felline
Relativity of Simultaneity and Eternalism: In Defense of the Block Universe, Daniel Peterson and Michael Silberstein
Minkowski Space-Time and Thermodynamics, Friedel Weinert
No Presentism in Quantum Gravity, Christian Wuthrich
Part 3 / The Impact of Minkowski’s Ideas Beyond the Philosophy of Space and Time
Space-Time, Phenomenology, and the Picture Theory of Language, Hans Herlof Grelland
The Fate of Mathematical Place: Objectivity and the Theory of Lived-Space from Husserl to Casey, Edward Slowik


8. On Cosmology

1. "Primordial Nucleosynthesis: from precision cosmology to fundamental physics", (Phys.Rept.472:1-76,2009)
2. "REVIEW OF BIG BANG NUCLEOSYNTHESIS AND PRIMORDIAL ABUNDANCES", (Physica Scripta, 85, p. 12, 2000)
3. "BIG BANG NUCLEOSYNTHESIS: PROBING THE FIRST 20 MINUTES", (In "Measuring and Modeling the Universe", from the Carnegie Observatories Centennial Symposia. Published by Cambridge University Press, as part of the Carnegie Observatories Astrophysics Series. Edited by W. L. Freedman, 2004, p. 169. )
4. "PRIMORDIAL NUCLEOSYNTHESIS", (In the proceedings of the May 2003 STScI Symposium, "The Local Group as an Astrophysical Laboratory".)
5. "PRIMORDIAL NUCLEOSYNTHESIS: SUCCESSES AND CHALLENGES", (International Journal of Modern Physics E, Volume 15, Issue 01, pp. 1-35 (2006))
6. "THE COSMOLOGICAL TESTS", (astro-ph/0102327)
7. "Foundations of Supernova Cosmology", (A chapter contributed to "Dark energy-- observational and theoretical approaches" edited by Pilar Ruiz-Lapuente (ISBN-13: 9780521518888), Cambridge University Press, arXiv:0910.0257v1 [astro-ph.CO])
8. "LARGE-SCALE SURVEYS AND COSMIC STRUCTURE", (Lectures delivered at the 2002 Tenerife Winter School, "Dark matter and dark energy in the universe")
9. "What is dust? - Physical foundations of the averaging problem in cosmology", (Invited review by Classical and Quantum Gravity for the special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology", arXiv:1106.1693v1 [gr-qc])
10. "Is backreaction really small within concordance cosmology?", (Invited contribution to Classical and Quantum Gravity special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology", arXiv:1105.1886v1 [astro-ph.CO])
11. "Toward physical cosmology: focus on inhomogeneous geometry and its non-perturbative effects", (Invited review for Classical and Quantum Gravity Focus Section "Inhomogeneous Cosmological Models and Averaging in Cosmology", arXiv:1103.2016v2 [gr-qc])
12. "Observational constraints on inhomogeneous cosmological models without dark energy", (Invited contribution to CQG special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology", arXiv:1102.1015v2 [astro-ph.CO])
13. "Backreaction: directions of progress", (Contribution to Classical and Quantum Gravity special issue "Inhomogeneous Cosmological Models and Averaging in Cosmology", arXiv:1102.0408v2 [astro-ph.CO])
14. "Detection of Pristine Gas Two Billion Years after the Big Bang", (arXiv:1111.2334v1 [astro-ph.CO] -> Science)
15. "The Lyman-alpha Forest as a Cosmological Tool", (arXiv:astro-ph/0301186v1)
16. "Lyman alpha systems and cosmology"
17. "Quasar Absorption Lines", (arXiv:astro-ph/0112521v1)
18. "Evidence for Reionization at z ~ 6: Detection of a Gunn-Peterson Trough in a z=6.28 Quasar", (arXiv:astro-ph/0108097v3, Astron.J. 122 (2001) 2850)
19. "Promising Observational Methods for Detecting the Epoch of Reionization", (arXiv:1003.1750v2 [astro-ph.CO])
20. "THE LYMAN ALPHA FOREST IN THE SPECTRA OF QSOS", (Annu. Rev. Astron. Astrophys. 1998. 36: 267-316)



9. On Compact Objects

1. "Isolated neutron stars and studies of their interiors" (arXiv:1111.1158v1 [astro-ph.HE]),
2. "The physics of neutron stars" (arXiv:1102.5735v3 [astro-ph.SR]),
3. "Measurement of neutron star parameters: a review of methods for low-mass X-ray binaries" (arXiv:1001.1642v1 [astro-ph.HE]),
4. "Neutron Star Observations: Prognosis for Equation of State Constraints" (arXiv:astro-ph/0612440v1, Phys.Rept.442:109-165,2007),
5. "What a Two Solar Mass Neutron Star Really Means" (arXiv:1012.3208v1 [astro-ph.SR]),
6. "The Equation of State from Observed Masses and Radii of Neutron Stars" (arXiv:1005.0811v2 [astro-ph.HE]),
7. "Can the maximum mass of neutron stars rule out any equation of state of dense stellar matter before gravity is well understood?" (arXiv:1101.1504v1 [astro-ph.SR]),
8. "Reconstructing the Neutron-Star Equation of State from Astrophysical Measurements" (arXiv:0905.1959v2 [astro-ph.HE], Phys.Rev.D80:103003,2009),
9. "Neutron star stiff equation of state derived from cooling phases of the X-ray burster 4U 1724-307" (arXiv:1004.4871v3 [astro-ph.HE], Astrophysical Journal, 742:122, 2011),
10. "EXO 0748-676 Rules out Soft Equations of State for Neutron Star Matter" (arXiv:astro-ph/0605106v1, NATURE),
11. "Constraints on neutron-star theories from nearby neutron star observations" (arXiv:1111.0447v1 [astro-ph.SR]),
12. "The missing compact star of SN1987A: a solid quark star?" (arXiv:1201.3101v1 [astro-ph.HE])


10. Conversion to geometric units

Constants in SI:
$$c=299792458~m/s^2$$
$$G=6.673\times 10^{-11} m^3 kg^{-1} s^{-2}$$
$$k=1.3806503 \times 10^{-23} m^2 kg s^{-2} K^{-1}$$
$$\epsilon_0=\frac{10^7~A^2/N}{4\pi c^2}$$

Physical Quantity conversion factor units
Time (sec) $$\times c$$ m
Mass (kg) $$\times \frac{G}{c^2}$$ m
Pressure (Pascal) $$\times \frac{G}{c^4}$$ $$1/m^2$$
Temperature (Kelvin) $$\times \frac{Gk}{c^4}$$ m
Electric Charge (Coulomb) $$\times \frac{G^{1/2}}{(4\pi\epsilon_0)^{1/2}c^2}$$ m
Magnetic field (Tesla) $$\times \frac{G^{1/2}}{c}(4\pi\epsilon_0)^{1/2}$$ 1/m
Electric Field (N/C) $$\times \frac{G^{1/2}}{c^2}(4\pi\epsilon_0)^{1/2}$$ 1/m
Magnetic field (Gauss) $$\times \frac{G^{1/2}}{c^2}$$ (with constants in cgs) 1/cm
Magnetic moment ($$A m^2$$) $$\times \frac{G^{1/2}}{c^3(4\pi\epsilon_0)^{1/2}}$$ $$m^2$$


11. On Bicycle Stability

"A bicycle can be self-stable without gyroscopic or caster effects", Science 15 April 2011: 332(6027), 339-342. [doi:10.1126/science.1201959]
D.E.H. Jones. "The stability of the bicycle". Physics Today, 23(4):34–40, 1970. DOI:10.10631/1.3022064
F. Klein and A. Sommerfeld. "Uber die Theorie des Kreisels." Teubner, Leipzig, 1910. Ch IX §8, "Stabilitat des Fahrrads", by F. Noether, pp. 863–884. (English translation)


12. Quantum Mechanics in your face. (Sidney Coleman)


13. The Scenario Machine
Senario Machine : Main Menu
The Scenario Machine: restrictions on key parameters of binary evolution. (A&A 310 (1996) 489L)
The scenario machine: Binary star population synthesis (Amsterdam: Harwood Academic Publishers, |c1996)
 Example:


14. Αχιλλέας Παπαπέτρου

Αχιλλέας Παπαπέτρου (1907-1997) (Achilles Papapetrou) from Vagelford on Vimeo.



Διάλεξη του Prof. Dr. Dieter Hoffmann από το Max Planck for the History of Science με θέμα τον Αχιλλέα Παπαπέτρου και συγκεκριμένα τα χρόνια από την Ελλάδα μέχρι τη Γερμανία.


16. V.I. Arnold on teaching mathematics
On teaching mathematics (An extended text of the address at the discussion on teaching of mathematics in Palais de Decouverte in Paris on 7 March 1997)
Published in: Uspekhi Mat. Nauk 53 (1998), no. 1, 229-234;
English translation: Russian Math. Surveys 53 (1998), no. 1, 229-236.

An interesting lecture by V.I. Arnold, one of his last lectures, where some of the issues mentioned in the previous text are demonstrated.
Continued Fractions of Quadratic Irrationals (May 03, 2007)
rtsp://videos.msri.org/13407/13407-13407-QuickTime.mov