Општа теорија релативности

Општа релативност или општа теорија релативности (ОТР) је геометријска теорија гравитације коју је Алберт Ајнштајн објавио у чланку Основе опште теорије релативности (нем. Die Grundlage der allgemeinen Relativitätstheorie), 1915. године у Annalen der Physik.^[1]^[2] Теорија представља релативистичко поопштење специјалне релативности и Њутнове теорије гравитације. Она пружа уједињени опис гравитације као геометријског својства простора и времена, или простор-времена. Специфично, закривљеност простор-времена је директно повезана са енергијом и моментом независно од тога која материја и радијација су присутне. Однос је специфициран у Ајнштајновим једначинама поља, систему парцијалних диференцијалних једначина.

Нека од предвиђања опште релативности се знатно разликују од класично физичких ставова, посебно у погледу протока времена, геометрије простора, кретања тела при слободном паду, и простирања светлости. Примери тих разлика обухватају гравитациону дилатацију времена, гравитациона сочива, Гравитациони црвени помак светлости, и гравитационо временско кашњење. Предвиђања теорије опште релативности су до сад била потврђена у свим опажањима и експериментима. Мада општа релативност није једина релативистичка теорија гравитације, она је најједноставнија теорија која је конзистентна са експерименталним подацима. Међутим, питања без одговора остају, најфундаменталније од којих је усаглашавање опште релативности са законима квантне физике којим би се произвела комплетна и усаглашена теорија квантне гравитације.

Ајнштајнова теорија има важне астрофизичке импликације. На пример, из ње проистиче могућност постојања црних рупа — просторних региона у којима су простор и време закривљени на такав начин да ништа, чак ни светлост, не може да побегне — као крајњег стадијума масивних звезда. Постоји обиље доказа да је интензивна радијација коју емитују поједине врсте астрономских објеката узрокована црним рупама; на пример, микроквазари и активна галактика језгра су резултат присуства звезданих црних рупа и црних рупа далеко масивнијег типа. Савијање светлости дејством гравитације може да доведе до феномена гравитационог сочива, услед којег су вишеструке слике истог удаљеног астрономског објекта видљиве на небу. Општа релативност такође предвиђа постојање гравитационих таласа, који су индиректно уочени; директна мерења су циљ пројеката као што су ЛИГО (енгл. Laser Interferometer Gravitational-Wave Observatory) и НАСА/ЕСА (енгл. Laser Interferometer Space Antenna) и разних низова за пулсарске временске прорачуне. Поред тога, општа релативност је основа данашњих космолошких модела конзистентно експандирајућег свемира.

Постулати и структура теорије

За разлику од класичног, Њутновог описа гравитације као силе која се јавља међу масивним телима на позадини апсолутног простор-времена, у ОТР улогу гравитације узима само простор-време. Њега сада описујемо помоћу метричког тензора ( $g_{\mu \nu }$ ) који је решење Ајнштајнових једначина:

$R_{\mu \nu }-{\frac {1}{2}}\,R\,g_{\mu \nu }={\frac {8\pi G}{c^{2}}}\,T_{\mu \nu }$

где је $R_{\mu \nu }$ Ричијев тензор, $R$ Ричијев скалар, а $T_{\mu \nu }$ тензор енергије-импулса. Константе у једначини су $c$ , брзина светлости и $G$ , гравитацијска константа. Утицај гравитације на честице дефинисан је закривљеношћу простор-времена (тј. његовом геометријом) коју дефинишу масе и сва физичка поља (осим гравитационог).

Референце

^ Albert Einstein: Die Grundlage der allgemeinen Relativitätstheorie. U: Annalen der Physik. 49, 1916, S. 769–822 (Faksimil Архивирано на сајту Wayback Machine (23. август 2006), PDF)
^ O'Connor, J.J. and E.F. Robertson (1996), "General relativity". Mathematical Physics index, School of Mathematics and Statistics Архивирано на сајту Wayback Machine (5. децембар 2015), University of St. Andrews, Scotland, May, 1996. Приступљено 2015-02-04.

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Stairs, Ingrid H. (2003), „Testing General Relativity with Pulsar Timing”, Living Reviews in Relativity, 6, Bibcode:2003LRR.....6....5S, arXiv:astro-ph/0307536 , doi:10.12942/lrr-2003-5, Приступљено 21. 07. 2007
Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; Herlt, E. (2003), Exact Solutions of Einstein's Field Equations (2 изд.), Cambridge University Press, ISBN 978-0-521-46136-8
Synge, J. L. (1972), Relativity: The Special Theory, North-Holland Publishing Company, ISBN 978-0-7204-0064-9
Szabados, László B. (2004), „Quasi-Local Energy-Momentum and Angular Momentum in GR”, Living Reviews in Relativity, 7, doi:10.12942/lrr-2004-4, Приступљено 23. 08. 2007
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Thiemann, Thomas (2003), „Lectures on Loop Quantum Gravity”, Lecture Notes in Physics, 631: 41—135, Bibcode:2003LNP...631...41T, ISBN 978-3-540-40810-9, arXiv:gr-qc/0210094 , doi:10.1007/978-3-540-45230-0_3
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Veltman, Martinus (1975), „Quantum Theory of Gravitation”, Ур.: Balian, Roger; Zinn-Justin, Jean, Methods in Field Theory - Les Houches Summer School in Theoretical Physics., 77, North Holland
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Wald, Robert M. (1984), General Relativity, University of Chicago Press, ISBN 978-0-226-87033-5
Wald, Robert M. (1994), Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, ISBN 978-0-226-87027-4
Wald, Robert M. (2001), „The Thermodynamics of Black Holes”, Living Reviews in Relativity, 4, Bibcode:2001LRR.....4....6W, doi:10.12942/lrr-2001-6, Приступљено 08. 08. 2007
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Wambsganss, Joachim (1998), „Gravitational Lensing in Astronomy”, Living Reviews in Relativity, 1, Bibcode:1998LRR.....1...12W, arXiv:astro-ph/9812021 , doi:10.12942/lrr-1998-12, Приступљено 20. 07. 2007
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Weinberg, Steven (1996), The Quantum Theory of Fields II: Modern Applications, Cambridge University Press, ISBN 978-0-521-55002-4
Weinberg, Steven (2000), The Quantum Theory of Fields III: Supersymmetry, Cambridge University Press, ISBN 978-0-521-66000-6
Weisberg, Joel M.; Taylor, Joseph H. (2003), „The Relativistic Binary Pulsar B1913+16"”, Ур.: Bailes, M.; Nice, D. J.; Thorsett, S. E., Proceedings of "Radio Pulsars," Chania, Crete, August, 2002, ASP Conference Series
Weiss, Achim (2006), „Elements of the past: Big Bang Nucleosynthesis and observation”, Einstein Online, Max Planck Institute for Gravitational Physics, Архивирано из оригинала 08. 02. 2007. г., Приступљено 24. 02. 2007
Wheeler, John A. (1990), A Journey Into Gravity and Spacetime, Scientific American Library, San Francisco: W. H. Freeman, ISBN 978-0-7167-6034-4
Will, Clifford M. (1993), Theory and experiment in gravitational physics, Cambridge University Press, ISBN 978-0-521-43973-2
Will, Clifford M. (2006), „The Confrontation between General Relativity and Experiment”, Living Reviews in Relativity, 9, Bibcode:2006LRR.....9....3W, arXiv:gr-qc/0510072 , doi:10.12942/lrr-2006-3, Приступљено 12. 06. 2007
Zwiebach, Barton (2004), A First Course in String Theory, Cambridge University Press, ISBN 978-0-521-83143-7
Geroch, R (1981). General Relativity from A to B. Chicago: University of Chicago Press. ISBN 978-0-226-28864-2.
Lieber, Lillian (2008). The Einstein Theory of Relativity: A Trip to the Fourth Dimension. Philadelphia: Paul Dry Books, Inc. ISBN 978-1-58988-044-3.
Wald, Robert M. (1992). Space, Time, and Gravity: the Theory of the Big Bang and Black Holes. Chicago: University of Chicago Press. ISBN 978-0-226-87029-8.
Wheeler, John; Ford, Kenneth (1998). Geons, Black Holes, & Quantum Foam: a life in physics. New York: W. W. Norton. ISBN 978-0-393-31991-0.

Beginning undergraduate textbooks

Callahan, James J. (2000). The Geometry of Spacetime: an Introduction to Special and General Relativity. New York: Springer. ISBN 978-0-387-98641-8.
Taylor, Edwin F.; Wheeler, John Archibald (2000). Exploring Black Holes: Introduction to General Relativity. Addison Wesley. ISBN 978-0-201-38423-9.
B. F. Schutz (2009). A First Course in General Relativity (Second Edition). Cambridge University Press. ISBN 978-0-521-88705-2.
Cheng, Ta-Pei (2005). Relativity, Gravitation and Cosmology: a Basic Introduction. Oxford and New York: Oxford University Press. ISBN 978-0-19-852957-6.
Gron, O.; Hervik, S. (2007). Einstein's General theory of Relativity. Springer. ISBN 978-0-387-69199-2.
Hartle, James B. (2003). Gravity: an Introduction to Einstein's General Relativity. San Francisco: Addison-Wesley. ISBN 978-0-8053-8662-2.
Hughston, L. P.; Tod, K. P. (1991). Introduction to General Relativity. Cambridge: Cambridge University Press. ISBN 978-0-521-33943-8.
d'Inverno, Ray (1992). Introducing Einstein's Relativity. Oxford: Oxford University Press. ISBN 978-0-19-859686-8.
Ludyk, Günter (2013). Einstein in Matrix Form (1st изд.). Berlin: Springer. ISBN 978-3-642-35797-8.
Carroll, Sean M. (2004). Spacetime and Geometry: An Introduction to General Relativity. San Francisco: Addison-Wesley. ISBN 978-0-8053-8732-2.
Grøn, Øyvind; Hervik, Sigbjørn (2007). Einstein's General Theory of Relativity. New York: Springer. ISBN 978-0-387-69199-2.
Landau, Lev D.; Lifshitz, Evgeny F. (1980). The Classical Theory of Fields (4th изд.). London: Butterworth-Heinemann. ISBN 978-0-7506-2768-9.
Misner, Charles W.; Thorne, Kip. S.; Wheeler, John A. (1973). Gravitation. W. H. Freeman. ISBN 978-0-7167-0344-0.
Stephani, Hans (1990). General Relativity: An Introduction to the Theory of the Gravitational Field. Cambridge: Cambridge University Press. ISBN 978-0-521-37941-0.
Wald, Robert M. (1984). General Relativity. University of Chicago Press. ISBN 978-0-226-87033-5.

Спољашње везе

Релативност: специјална и општа теорија Архивирано на сајту Wayback Machine (9. мај 2008) (ПДФ)
Ајнштајн онлајн – Чланци о разним аспектима релативистичке физике за опште читалаштво; хостује Макс Планк институт за гравитациону физику
NCSA Spacetime Wrinkles – produced by the numerical relativity group at the National Center for Supercomputing Applications, with an elementary introduction to general relativity
Einstein's General Theory of Relativity на сајту YouTube (lecture by Leonard Susskind recorded September 22, 2008 at Stanford University).
Series of lectures on General Relativity given in 2006 at the Institut Henri Poincaré (introductory/advanced).
General Relativity Tutorials by John Baez.
Brown, Kevin. „Reflections on relativity”. Mathpages.com. Архивирано из оригинала 18. 12. 2015. г. Приступљено 29. 5. 2005.
Carroll, Sean M. „Lecture Notes on General Relativity”. Приступљено 5. 1. 2014.
Moor, Rafi. „Understanding General Relativity”. Архивирано из оригинала 28. 12. 2015. г. Приступљено 11. 7. 2006.
Waner, Stefan. „Introduction to Differential Geometry and General Relativity”. Архивирано из оригинала (PDF) 19. 04. 2015. г. Приступљено 05. 04. 2015.

[1] Albert Einstein: Die Grundlage der allgemeinen Relativitätstheorie. U: Annalen der Physik. 49, 1916, S. 769–822 (Faksimil Архивирано на сајту Wayback Machine (23. август 2006), PDF)

[2] O'Connor, J.J. and E.F. Robertson (1996), "General relativity". Mathematical Physics index, School of Mathematics and Statistics Архивирано на сајту Wayback Machine (5. децембар 2015), University of St. Andrews, Scotland, May, 1996. Приступљено 2015-02-04.

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