Opća teorija relativnosti

Opća teorija relativnosti, također poznata i kao opća relativnost ili Einsteinova teorija gravitacije, geometrijska je teorija gravitacije koju je 1915. objavio Albert Einstein i predstavlja trenutni opis gravitacije u modernoj fizici. Opća relativnost generalizuje posebnu relativnost i usavršava Newtonov zakon gravitacije, pružajući jedinstven opis gravitacije kao geometrijske osobine prostora i vremena ili četvorodimenzionalnog prostorvremena. Konkretno, zakrivljenost prostorvremena je direktnoj povezana s energijom i količinom kretanja bilo koje prisutne materije i zračenja. Odnos je određen Einsteinovim jednačinama polja, sistemom parcijalnih diferencijalnih jednačina drugog reda.

Usporena računarska simulacija binarnog sistema crne rupe GW150914 kako ga vidi obližnji posmatrač, tijekom 0.33 s njegovog posljednjeg opadanja, stapanja i ringdowna. Zvjezdano polje iza crnih rupa je veoma izobličeno i čini se da se rotira i kreće, zbog efekta ekstremne gravitacijske leće, jer je i samo prostorvrijeme izobličeno i povučeno rotirajućim crnim rupama.^[1]

Newtonov zakon gravitacije, koji opisuje klasičnu gravitaciju, može se posmatrati kao predviđanje opće relativnosti za skoro ravnu geometriju prostorvremena oko stacionarne raspodjele mase. Međutim, neka predviđanja opće relativnosti su izvan Newtonov zakon gravitacije u klasičnoj fizici. Ova predviđanja se tiču protoka vremena, geometrije prostora, kretanja tijela u slobodnom padu i širenja svjetlosti, a uključuju gravitacijsku vremensku dilataciju, gravitacijsku leću, gravitacijski crveni pomak svjetlosti, Shapirovo vremensko kašnjenje i singularnosti/crne rupe. Do sada se pokazalo da su svi testovi opće relativnosti u skladu s teorijom. Vremenski zavisna rješenja opće relativnosti omogućavaju nam da govorimo o historiji svemira i dala su moderni okvir za kosmologiju, što je dovelo do otkrića Velikog praska i kosmičkog mikrovalnog pozadinskog zračenja. Uprkos uvođenju brojnih alternativnih teorija, opća teorija relativnosti je i dalje najjednostavnija teorija koja je konzistentna s eksperimentalnim podacima.

Pomirenje opće teorije relativnosti sa zakonima kvantne fizike ostaje problem, jer postoji nedostatak samodosljedne teorije kvantne gravitacije. Još nije poznato kako se gravitacija može ujediniti s tri negravitacijske sile: jakom, slabom i elektromagnetnom.

Einsteinova teorija ima važne astrofizičke posljedice. Na primjer, ona podrazumijeva postojanje crnih rupa—regija u prostoru u kojima su prostor i vrijeme iskrivljeni na takav način da ništa, čak ni svjetlo, ne može pobjeći—kao završno stanje masivnih zvijezda. Postoji mnogo dokaza da intenzivna zračenja koje emitiraju određene vrste astronomskih objekata dešavaju zbog crnih rupa; na primjer, mikrokvazari i aktivna galaksijska jezgra su rezultat postojanja zvjezdanih crnih rupa i crnih rupa znatno veće masivne vrste. Savijanje svjetlosti gravitacijom može dovesti do fenomena gravitacione leće, u kojem je više slika istog udaljenog astronomskog objekta vidljivo na nebu. Opća relativnost također predviđa postojanje gravitacionih talasa, koji su posredno bili posmatrani; direktna mjerenja su cilj projekata kao što su LIGO i NASA/ESA Laser Interferometer Space Antenna i raznih "pulsar timing arrays". Osim toga, opća relativnost je osnova tekućih kosmoloških modela konzistentnog širenja svemira.

Historija

Ubrzo nakon što je 1905. objavio specijalnu teoriju relativnosti, Einstein je počeo da razmišlja o tome kako da ugradi gravitaciju u svoj novi relativistički okvir. Godine 1907., počevši od jednostavnog misaonog eksperimenta koji je uključivao posmatrača u slobodnom padu, krenuo je u osmogodišnju potragu za relativističkom teorijom gravitacije. Nakon brojnih zaobilaznica i lažnih startova, njegov rad je kulminirao prezentacijom Pruskoj akademiji nauka u novembru 1915. onoga što je danas poznato kao jednačine Einsteinovog polja, koje čine jezgro Einsteinove opšte teorije relativnosti.^[2] Ove jednačine određuju kako na geometriju prostora i vremena utiču bilo koja materija i radijacija. Verzija neeuklidske geometrije, nazvana Rimanova geometrija, omogućila je Einsteinu da razvije opštu relativnost obezbeđujući ključni matematički okvir na koji je uklapao svoje fizičke ideje gravitacije.^[3] Ovu ideju je ukazao matematičar Marcel Grossman, a objavili su je Grosman i Einstein 1913. godine.^[4]

Jednačine Einsteinovog polja su nelinearne i smatraju se teškim za rješavanje. Einstein je koristio metode aproksimacije u izradi početnih predviđanja teorije. Ali 1916. godine, astrofizičar Karl Schwarzschild pronašao je prvo netrivijalno egzaktno rješenje jednačina Einsteinovog polja, Schwarzschildovu metriku. Ovo rješenje je postavilo temelje za opis završnih faza gravitacionog kolapsa i objekata danas poznatih kao crne rupe. Iste godine poduzeti su prvi koraci ka generalizaciji Schwarzschildovog rješenja na električno nabijene objekte, što je na kraju rezultiralo Reissner-Nordströmovim rješenjem, koje je sada povezano s električno nabijenim crnim rupama.^[5] Godine 1917. Einstein je primjenio svoju teoriju na univerzum kao cjelinu, pokrećući polje relativističke kosmologije. U skladu sa savremenim razmišljanjem, on je pretpostavio statičan univerzum, dodajući novi parametar svojim originalnim jednačinama polja – kosmološku konstantu – kako bi odgovarao toj opservacionoj pretpostavci.^[6] Do 1929. godine, međutim, rad Hubblea i drugih pokazao je da se naš svemir širi. Ovo se lako opisuje proširenim kosmološkim rješenjima koja je pronašao Friedman 1922. godine, a koja ne zahtijevaju kosmološku konstantu. Lemaître je koristio ova rješenja kako bi formulisao najraniju verziju modela Velikog praska, u kojem je naš svemir evoluirao iz izuzetno vrućeg i gustog ranijeg stanja.^[7] Einstein je kasnije proglasio kosmološku konstantu najvećom greškom u svom životu.^[8]

Postulati i struktura teorije

Glavni postulat OTR je da je gravitacija geometrijski efekat, a ne sila. Drugim riječima, prisustvo mase i energije mijenja geometriju prostorvremena i na taj način utiče na kretanje masivnih čestica i svjetlosti.

Geometrija prostorvremena u okviru Opće teorije relativnosti je opisana pomoću Riemannovog tenzora zakrivljenosti.

Reference

1. "GW150914: LIGO Detects Gravitational Waves". Black-holes.org. Pristupljeno 18. 4. 2016.
2. O'Connor, J.J.; Robertson, E.F. (maj 1996). "General relativity]". History Topics: Mathematical Physics Index, Scotland: School of Mathematics and Statistics, University of St. Andrews, arhivirano s originala, 4. 2. 2015, pristupljeno 4. 2. 2015
3. Moshe Carmeli (2008).Relativity: Modern Large-Scale Structures of the Cosmos. str.92, 93.World Scientific Publishing
4. Grossmann for the mathematical part and Einstein for the physical part (1913). Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation (Outline of a Generalized Theory of Relativity and of a Theory of Gravitation), Zeitschrift für Mathematik und Physik, 62, 225–261. English translate
5. Schwarzschild 1916a, Schwarzschild 1916b and Reissner 1916 (later complemented in Nordström 1918)
6. Einstein 1917, cf. Pais 1982, ch. 15e
7. Hubble's original article is Hubble 1929; an accessible overview is given in Singh 2004, ch. 2–4
8. As reported in Gamow 1970. Einstein's condemnation would prove to be premature, cf. the section Cosmology, below

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Vanjski linokvi

• Einstein Online Arhivirano 1. 6. 2014. na Wayback Machine – Članci o različitim aspektima relativističke fizike za širu publiku (Institut za gravitacijsku fiziku "Max Planck")
• GEO600 početna stranica, službeni veb-sajt projekta GEO600.
• LIGO laboratorija
• NCSA Spacetime Wrinkles – proizvela grupa za numeričku relativnost pri NCSA, s elementarnim uvodom u opću relativnost

• Kursevi
• Predavanja
• Tutorijali

• Einstein's General Theory of Relativity na YouTubeu (predavanje Leonarda Susskinda snimljeno 22. septembra 2008. na Univerzitetu Stanford).
• 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 s originala, 18. 12. 2015. Pristupljeno 29. 5. 2005.
• Carroll, Sean M. (1997). "Lecture Notes on General Relativity". arXiv:gr-qc/9712019.
• Moor, Rafi. "Understanding General Relativity". Pristupljeno 11. 7. 2006.
• Waner, Stefan. "Introduction to Differential Geometry and General Relativity". Pristupljeno 5. 4. 2015.
• The Feynman Lectures on Physics Vol. II Ch. 42: Curved Space