Opšta teorija relativnosti

Simulisana crna rupa sa 10 solarnih masa unutar Mlečnog puta, gledana sa rastojanja od 600 kilometera.

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. Teorija predstavlja relativističko poopštenje specijalne relativnosti i Newtonove 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, gravitationa 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 svetlosit 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

Dvodimenzionalna analogija zakrivljenosti prostorvremena

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

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

gdje je $R_{\mu \nu }$ Riccijev tenzor, $R$ Riccijev skalar, a $T_{\mu \nu }$ tenzor energije-impulsa. Konstante u jednadžbi su $c$, brzina svijetlosti i $G$, gravitacijska konstanta. Utjecaj gravitacije na čestice definiran je zakrivljenošću prostor-vremena (tj. njegovom geometrijom) koju definiraju mase i sva fizikalna polja (osim gravitacijskog).

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Vanjske veze

Opšta teorija relativnosti na Wikimedijinoj ostavi

• Relativity: The special and general theory (PDF)
• Einstein Online – Articles on a variety of aspects of relativistic physics for a general audience; hosted by the Max Planck Institute for Gravitational Physics
• 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 YouTubeu (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. http://www.mathpages.com/rr/rrtoc.htm. pristupljeno May 29, 2005. 
• Carroll, Sean M.. "Lecture Notes on General Relativity". http://arxiv.org/abs/gr-qc/9712019. pristupljeno January 5, 2014. 
• Moor, Rafi. "Understanding General Relativity". http://www.rafimoor.com/english/GRE.htm. pristupljeno July 11, 2006. 
• Waner, Stefan. "Introduction to Differential Geometry and General Relativity" (PDF). http://www.zweigmedia.com/diff_geom/tc.html. pristupljeno 2015-04-05.