Opšta teorija relativnosti

Opšta relativnost ili opšta teorija relativnosti (OTR) je geometrijska teorija gravitacije koju je Albert Ajnštajn objavio u članku Osnove opšte teorije relativnosti (nem. Die Grundlage der allgemeinen Relativitätstheorie), 1915. godine u Annalen der Physik.^[1]^[2] Teorija predstavlja relativističko poopštenje specijalne relativnosti i Njutnove teorije gravitacije. Ona pruža ujedinjeni opis gravitacije kao geometrijskog svojstva prostora i vremena, ili prostor-vremena. Specifično, zakrivljenost prostor-vremena je direktno povezana sa energijom i momentom nezavisno od toga koja materija i radijacija su prisutne. Odnos je specificiran u Ajnštajnovim jednačinama polja, sistemu parcijalnih diferencijalnih jednačina.

Neka od predviđanja opšte relativnosti se znatno razlikuju od klasično fizičkih stavova, posebno u pogledu protoka vremena, geometrije prostora, kretanja tela pri slobodnom padu, i prostiranja svetlosti. Primeri tih razlika obuhvataju gravitacionu dilaciju vremena, gravitaciona sočiva, Gravitacioni crveni pomak svetlosti, i gravitaciono vremensko kašnjenje. Predviđanja teorije opšte relativnosti su do sad bila potvrđena u svim opažanjima i eksperimentima. Mada opšta relativnost nije jedina relativistička teorija gravitacije, ona je najjednostavnija teorija koja je konzistentna sa eksperimentalnim podacima. Međutim, pitanja bez odgovora ostaju, najfundamentalnije od kojih je usaglašavanje opšte relativnosti sa zakonima kvantne fizike kojim bi se proizvela kompletna i usaglašena teorija kvantne gravitacije.

Ajnštajnova teorija ima važne astrofizičke implikacije. Na primer, iz nje proističe mogućnost postojanja crnih rupa — prostornih regiona u kojima su prostor i vreme zakrivljeni na takav način da ništa, čak ni svetlost, ne može da pobegne — kao krajnjeg stadijuma masivnih zvezda. Postoji obilje dokaza da je intenzivna radijacija koju emituju pojedine vrste astronomskih objekata uzrokovana crnim rupama; na primer, mikrokvazari i aktivna galaktika jezgra su rezultat prisustva zvezdanih crnih rupa i crnih rupa daleko masivnijeg tipa, respektivno. Savijanje svetlosti dejstvom gravitacije može da dovede do fenomena gravitacionog sočiva, usled kojeg su višestruke slike istog udaljenog astronomskog objekta vidljive na nebu. Opšta relativnost takođe predviđa postojanje gravitacionih talasa, koji su indirektno uočeni; direktna merenja su cilj projekata kao što su LIGO (engl. Laser Interferometer Gravitational-Wave Observatory) i NASA/ESA (engl. Laser Interferometer Space Antenna) i raznih nizova za pulsarske vremenske proračune. Pored toga, opšta relativnost je osnova današnjih kosmoloških modela konzistentno ekspandirajućeg svemira.

Postulati i struktura teorije uredi

Dvodimenzionalna analogija zakrivljenosti prostorvremena

Za razliku od klasičnog, njutnovog opisa gravitacije kao sile koja se javlja među masivnim telima na pozadini apsolutnog prostor-vremena, u OTR ulogu gravitacije uzima samo prostor-vreme. Njega sada opisujemo pomoću metričkog tenzora ( $g_{\mu \nu }$ ) koji je rešenje Ajnštajnovih jednačina:

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

gde je $R_{\mu \nu }$ Ričijev tenzor, $R$ Ričijev skalar, a $T_{\mu \nu }$ tenzor energije-impulsa. Konstante u jednačnii su $c$ , brzina svetlosti i $G$ , gravitacijska konstanta. Uticaj gravitacije na čestice definisan je zakrivljenošću prostor-vremena (tj. njegovom geometrijom) koju definišu mase i sva fizička polja (osim gravitacionog).

Reference uredi

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

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Szabados, László B. (2004), „Quasi-Local Energy-Momentum and Angular Momentum in GR”, Living Reviews in Relativity, 7, doi:10.12942/lrr-2004-4, Pristupljeno 23. 08. 2007
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
Thiemann, Thomas (2006), „Approaches to Fundamental Physics: Loop Quantum Gravity: An Inside View”, Lecture Notes in Physics, 721: 185—263, Bibcode:2007LNP...721..185T, ISBN 978-3-540-71115-5, arXiv:hep-th/0608210  , doi:10.1007/978-3-540-71117-9_10
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
't Hooft, Gerard; Veltman, Martinus (1974), „One Loop Divergencies in the Theory of Gravitation”, Ann. Inst. Poincare, 20: 69
Thorne, Kip S. (1972), „Nonspherical Gravitational Collapse—A Short Review”, Ur.: Klauder, J., Magic without Magic, W. H. Freeman, str. 231—258
Thorne, Kip S. (1994), Black Holes and Time Warps: Einstein's Outrageous Legacy, W W Norton & Company, ISBN 978-0-393-31276-8
Thorne, Kip S. (1995), „Gravitational radiation”, Particle and Nuclear Astrophysics and Cosmology in the Next Millenium: 160, Bibcode:1995pnac.conf..160T, ISBN 978-0-521-36853-7, arXiv:gr-qc/9506086 
Townsend, Paul K. (1997). „Black Holes (Lecture notes)”. arXiv:gr-qc/9707012  [gr-qc].
Townsend, Paul K. (1996). „Four Lectures on M-Theory”. arXiv:hep-th/9612121  [hep-th].
Traschen, Jenny (2000), Bytsenko, A.; Williams, F., ur., „An Introduction to Black Hole Evaporation”, Mathematical Methods of Physics (Proceedings of the 1999 Londrina Winter School), World Scientific: 180, Bibcode:2000mmp..conf..180T, arXiv:gr-qc/0010055 
Trautman, Andrzej (2006), „Einstein–Cartan theory”, Ur.: Françoise, J.-P.; Naber, G. L.; Tsou, S. T., Encyclopedia of Mathematical Physics, Vol. 2, Elsevier, str. 189—195, Bibcode:2006gr.qc.....6062T, arXiv:gr-qc/0606062 
Unruh, W. G. (1976), „Notes on Black Hole Evaporation”, Phys. Rev. D, 14 (4): 870—892, Bibcode:1976PhRvD..14..870U, doi:10.1103/PhysRevD.14.870
Valtonen, M. J.; Lehto, H. J.; Nilsson, K.; Heidt, J.; Takalo, L. O.; Sillanpää, A.; Villforth, C.; Kidger, M.; et al. (2008), „A massive binary black-hole system in OJ 287 and a test of general relativity”, Nature, 452 (7189): 851—853, Bibcode:2008Natur.452..851V, PMID 18421348, arXiv:0809.1280  , doi:10.1038/nature06896
Veltman, Martinus (1975), „Quantum Theory of Gravitation”, Ur.: Balian, Roger; Zinn-Justin, Jean, Methods in Field Theory - Les Houches Summer School in Theoretical Physics., 77, North Holland
Wald, Robert M. (1975), „On Particle Creation by Black Holes”, Commun. Math. Phys., 45 (3): 9—34, Bibcode:1975CMaPh..45....9W, doi:10.1007/BF01609863
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, Pristupljeno 08. 08. 2007
Walsh, D.; Carswell, R. F.; Weymann, R. J. (1979), „0957 + 561 A, B: twin quasistellar objects or gravitational lens?”, Nature, 279 (5712): 381—4, Bibcode:1979Natur.279..381W, PMID 16068158, doi:10.1038/279381a0
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, Pristupljeno 20. 07. 2007
Weinberg, Steven (1972), Gravitation and Cosmology, John Wiley, ISBN 978-0-471-92567-5
Weinberg, Steven (1995), The Quantum Theory of Fields I: Foundations, Cambridge University Press, ISBN 978-0-521-55001-7
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"”, Ur.: 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, Arhivirano iz originala 08. 02. 2007. g., Pristupljeno 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, Pristupljeno 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 izd.). 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 izd.). 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.

Spoljašnje veze uredi

Relativnost: specijalna i opšta teorija Arhivirano na sajtu Wayback Machine (9. maj 2008) (PDF)
Ajnštajn onlajn – Članci o raznim aspektima relativističke fizike za opšte čitalaštvo; hostuje Maks Plank institut za gravitacionu fiziku
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 na sajtu 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. Arhivirano iz originala 18. 12. 2015. g. Pristupljeno 29. 5. 2005.
Carroll, Sean M. „Lecture Notes on General Relativity”. Pristupljeno 5. 1. 2014.
Moor, Rafi. „Understanding General Relativity”. Arhivirano iz originala 28. 12. 2015. g. Pristupljeno 11. 7. 2006.
Waner, Stefan. „Introduction to Differential Geometry and General Relativity”. Arhivirano iz originala (PDF) 19. 04. 2015. g. Pristupljeno 05. 04. 2015.

[1] Albert Einstein: Die Grundlage der allgemeinen Relativitätstheorie. U: Annalen der Physik. 49, 1916, S. 769–822 (Faksimil Arhivirano na sajtu Wayback Machine (23. avgust 2006), PDF)

[2] O'Connor, J.J. and E.F. Robertson (1996), "General relativity". Mathematical Physics index, School of Mathematics and Statistics Arhivirano na sajtu Wayback Machine (5. decembar 2015), University of St. Andrews, Scotland, May, 1996. Pristupljeno 2015-02-04.

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