Општа теорија релативности — разлика између измена

Садржај обрисан Садржај додат

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Верзија на датум 12. март 2017. у 18:26

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 дилацију времена, гравитатиона 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, респективно. Савијање светлосит 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 Ајнштајнове једначине

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

где је $R_{\mu \nu }$ Ричијев тензор, $R$ Ричијев скалар, а $T_{\mu \nu }$ тензор енергије-импулса. Константе у једначнии 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, PDF)
^ O'Connor, J.J. and E.F. Robertson (1996), "General relativity". Mathematical Physics index, School of Mathematics and Statistics, University of St. Andrews, Scotland, May, 1996. Retrieved 2015-02-04.

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Spergel, D. N.; Verde, L.; Peiris, H. V.; Komatsu, E.; Nolta, M. R.; Bennett, C. L.; Halpern, M.; Hinshaw, G.; et al. (2003), „First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters”, Astrophys. J. Suppl., 148 (1): 175—194, Bibcode:2003ApJS..148..175S, arXiv:astro-ph/0302209 , doi:10.1086/377226
Spergel, D. N.; Bean, R.; Doré, O.; Nolta, M. R.; Bennett, C. L.; Dunkley, J.; Hinshaw, G.; Jarosik, N.; et al. (2007), „Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology”, Astrophysical Journal Supplement, 170 (2): 377—408, Bibcode:2007ApJS..170..377S, arXiv:astro-ph/0603449 , doi:10.1086/513700
Springel, Volker; White, Simon D. M.; Jenkins, Adrian; Frenk, Carlos S.; Yoshida, Naoki; Gao, Liang; Navarro, Julio; Thacker, Robert; et al. (2005), „Simulations of the formation, evolution and clustering of galaxies and quasars”, Nature, 435 (7042): 629—636, Bibcode:2005Natur.435..629S, PMID 15931216, arXiv:astro-ph/0504097 , doi:10.1038/nature03597
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 2007-07-21
Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; Herlt, E. (2003), Exact Solutions of Einstein's Field Equations (2 изд.), Cambridge University Press, ISBN 0-521-46136-7
Synge, J. L. (1972), Relativity: The Special Theory, North-Holland Publishing Company, ISBN 0-7204-0064-3
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 2007-08-23
Taylor, Joseph H. (1994), „Binary pulsars and relativistic gravity”, Rev. Mod. Phys., 66 (3): 711—719, Bibcode:1994RvMP...66..711T, doi:10.1103/RevModPhys.66.711
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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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Thorne, Kip S. (1994), Black Holes and Time Warps: Einstein's Outrageous Legacy, W W Norton & Company, ISBN 0-393-31276-3
Thorne, Kip S. (1995), „Gravitational radiation”, Particle and Nuclear Astrophysics and Cosmology in the Next Millenium: 160, Bibcode:1995pnac.conf..160T, ISBN 0-521-36853-7, arXiv:gr-qc/9506086 
Townsend, Paul K. (1997). „Black Holes (Lecture notes)”. arXiv:gr-qc/9707012  [gr-qc].
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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 0-226-87033-2
Wald, Robert M. (1994), Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, ISBN 0-226-87027-8
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 2007-08-08
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Weinberg, Steven (1972), Gravitation and Cosmology, John Wiley, ISBN 0-471-92567-5
Weinberg, Steven (1995), The Quantum Theory of Fields I: Foundations, Cambridge University Press, ISBN 0-521-55001-7
Weinberg, Steven (1996), The Quantum Theory of Fields II: Modern Applications, Cambridge University Press, ISBN 0-521-55002-5
Weinberg, Steven (2000), The Quantum Theory of Fields III: Supersymmetry, Cambridge University Press, ISBN 0-521-66000-9
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, Приступљено 2007-02-24
Wheeler, John A. (1990), A Journey Into Gravity and Spacetime, Scientific American Library, San Francisco: W. H. Freeman, ISBN 0-7167-6034-7
Will, Clifford M. (1993), Theory and experiment in gravitational physics, Cambridge University Press, ISBN 0-521-43973-6
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 2007-06-12
Zwiebach, Barton (2004), A First Course in String Theory, Cambridge University Press, ISBN 0-521-83143-1
Geroch, R (1981), General Relativity from A to B, Chicago: University of Chicago Press, ISBN 0-226-28864-1
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 0-226-87029-4
Wheeler, John; Ford, Kenneth (1998), Geons, Black Holes, & Quantum Foam: a life in physics, New York: W. W. Norton, ISBN 0-393-31991-1

Beginning undergraduate textbooks

Callahan, James J. (2000), The Geometry of Spacetime: an Introduction to Special and General Relativity, New York: Springer, ISBN 0-387-98641-3
Taylor, Edwin F.; Wheeler, John Archibald (2000), Exploring Black Holes: Introduction to General Relativity, Addison Wesley, ISBN 0-201-38423-X
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 0-19-852957-0
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 0-8053-8662-9
Hughston, L. P.; Tod, K. P. (1991), Introduction to General Relativity, Cambridge: Cambridge University Press, ISBN 0-521-33943-X
d'Inverno, Ray (1992), Introducing Einstein's Relativity, Oxford: Oxford University Press, ISBN 0-19-859686-3
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 0-8053-8732-3
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 ed.), London: Butterworth-Heinemann, ISBN 0-7506-2768-9
Misner, Charles W.; Thorne, Kip. S.; Wheeler, John A. (1973), Gravitation, W. H. Freeman, ISBN 0-7167-0344-0
Stephani, Hans (1990), General Relativity: An Introduction to the Theory of the Gravitational Field, Cambridge: Cambridge University Press, ISBN 0-521-37941-5
Wald, Robert M. (1984), General Relativity, University of Chicago Press, ISBN 0-226-87033-2

Спољашње везе

Релативност: специјална и општа теорија (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. Приступљено 29. 5. 2005.
Carroll, Sean M. „Lecture Notes on General Relativity”. Приступљено 5. 1. 2014.
Moor, Rafi. „Understanding General Relativity”. Приступљено 11. 7. 2006.
Waner, Stefan. „Introduction to Differential Geometry and General Relativity” (PDF). Приступљено 2015-04-05.

[1] Albert Einstein: Die Grundlage der allgemeinen Relativitätstheorie. U: Annalen der Physik. 49, 1916., S. 769–822 (Faksimil, PDF)

[2] O'Connor, J.J. and E.F. Robertson (1996), "General relativity". Mathematical Physics index, School of Mathematics and Statistics, University of St. Andrews, Scotland, May, 1996. Retrieved 2015-02-04.

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[2]

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