"Nobel Prize Biography". Nobel Prize Biography. Nobel Prize. สืบค้นเมื่อ 25 February 2011.
"Gravitational Waves Detected 100 Years After Einstein's Prediction". 11 เมษายน 2016. สืบค้นเมื่อ 5 มีนาคม 2019.
Ehlers 1973, pp. 19–22 for similar derivations, see sections 1 and 2 of ch. 7 in Weinberg 1972. The Einstein tensor is the only divergence-free tensor that is a function of the metric coefficients, their first and second derivatives at most, and allows the spacetime of special relativity as a solution in the absence of sources of gravity, cf. Lovelock 1972. The tensors on both side are of second rank, that is, they can each be thought of as 4×4 matrices, each of which contains ten independent terms; hence, the above represents ten coupled equations. The fact that, as a consequence of geometric relations known as Bianchi identities, the Einstein tensor satisfies a further four identities reduces these to six independent equations, e.g. Schutz 1985, sec. 8.3
For the (conceptual and historical) difficulties in defining a general principle of relativity and separating it from the notion of general covariance, see Giulini 2006b
ทฤษฎ, มพ, ทธภาพท, วไป, สำหร, บบทนำท, เข, าใจง, ายกว, าและใช, พท, เทคน, คน, อยกว, าของห, วข, อน, บทนำ, บทความน, อาจต, องการตรวจสอบต, นฉบ, ในด, านไวยากรณ, ปแบบการเข, ยน, การเร, ยบเร, ยง, ณภาพ, หร, อการสะกด, ณสามารถช, วยพ, ฒนาบทความได, มพ, ทธภาพท, วไปหร, งกฤษ, ge. sahrbbthnathiekhaicngaykwaaelaichsphthethkhnikhnxykwakhxnghwkhxni du bthnathvsdismphththphaphthwip bthkhwamnixactxngkartrwcsxbtnchbb indaniwyakrn rupaebbkarekhiyn kareriyberiyng khunphaph hruxkarsakd khunsamarthchwyphthnabthkhwamidsmphththphaphthwiphruxthvsdismphththphaphthwip xngkvs general relativity hrux general theory of relativity epnthvsdikhwamonmthwngaebberkhakhnitsungxlebirt ixnsitncdphimphin kh s 1916 1 aelaepnkarphrrnnakhwamonmthwngpccubninwichafisikssmyihm smphththphaphthwipwangnythwipkwasmphththphaphphiessaelakdkhwamonmthwngsaklkhxngniwtn odyxthibaykhwamonmthwngodyrwmwaepnkhunsmbtierkhakhnitkhxngpriphumiaelaewla hruxpriphumi ewla odyechphaaxyangyingwa khwamokhngkhxngpriphumi ewlasmphnthodytrngkbphlngnganaelaomemntmkhxngssaraelarngsithimixyuthnghmd khwamsmphnthniecaacngodysmkarsnamixnsitn sungepnrabbsmkarechingxnuphnthyxykarthdsxbsmphththphaphthwipkhwamethiyngsungodyyanxwkasaekhssini syyanwithyuthisngrahwangolkaelayan khlunsiekhiyw thukhnwngodykarbidkhxngpriphumi ewla esnsinaengin enuxngcakmwlkhxngdwngxathity karthanaykhxngsmphththphaphthwipbangxyangaetktangmakcakkarthanaykhxngfisiksdngedim odyechphaathiekiywkbkarphankhxngewla erkhakhnitkhxngpriphumi karekhluxnthikhxngethhwtthu inkartkxisra aelakaraephrkracaykhxngaesng twxyangkhwamtangehlaniechn karepliynkhnadkhxngewlaechingonmthwng elnskhwamonmthwng karekhluxnipthangaedngechingonmthwngkhxngaesng aelakarepliynkhnadkhxngewlaechingonmthwng karthanaykhxngsmphththphaphthwipcnpccubnidrbkaryunyncakkarsngektaelathdlxngthnghmd aemsmphththphaphthwipmiichephiyngthvsdikhwamonmthwngsmphththniymthvsdiediywethann aetkepnthvsdingaythisudsungsxdkhlxngkbkhxmulechingthdlxng xyangirktamyngehluxkhathamsungimmikhatxb odykhxthiepnhlkmulthisudkhux thvsdismphththphaphthwipcasamarthekhakbkdfisikskhwxntmephuxsrangthvsdikhwamonmthwngkhwxntmthismburnaelaimkhdaeyngintwexngidxyangirthvsdikhxngixnsitnmikhwamhmaysakhythangfisiksdarasastr echn aesdngihehnthungkarmihlumda briewnkhxngpriphumisungpriphumiaelaewlabidebiywcnimmisingidaemkrathngaesngsamarthhnixxkmaid odyepncudcbkhxngdawvkskhnadyks mihlkthanmakphxwa rngsiekhmsungaephcakwtthuthangdarasastrbangchnidenuxngmacakhlumda echn imokhrkhwasar microquasar aelaniwekhliysdarackrkmmnt sungekidcakkarmihlumdadawvksaelahlumdamwlywdyingtamladb karokhngkhxngaesngodykhwamonmthwngsamarthnaipsupraktkarnelnskhwamonmthwng sungthaihsamarthehnphaphhlayphaphkhxngwtthudarasastrthirayathangethaknhlayphaphbnfa smphththphaphthwipyngthanaykarmikhlunkhwamonmthwng sungkarsngektkhlunehlaniodytrngepnepahmaykhxngokhrngkarxyang hxsngektkarnkhlunkhwamonmthwngodyichxinetxrefxormietxrchnidelesxr Laser Interferometer Gravitational Wave Observatory LIGO khxngnasa sayxakasxwkasxinetxrefxoremthrielesxr Laser Interferometer Space Antenna LISA khxngxiexsex aelaaethwladbtngcnghwaphlsar pulsar timing array canwnmaksunginpccubn LIGO idsngektphbkhlunkhwamonmthwngaelw 2 nxkcakni smphththphaphthwipyngepnphunthankhxngaebbcalxngckrwalwithyaexkphaphkhyaytxenuxngpccubn enuxha 1 cakklsastraebbchbbsusmphththphaphthwip 1 1 smkarkhxngixnsitn 2 bthniyamaelakarprayuktphunthan 3 duephim 4 xangxingcakklsastraebbchbbsusmphththphaphthwip aekikhsmkarkhxngixnsitn aekikh hlngkhididphlkhxngkhwamonmthwngindansmphththniymaelaerkhakhnitaelw yngkhngmikhathamwadwythimakhxngkhwamonmthwngxyu inkhwamonmthwngaebbniwtn thimannkhuxmwl insmphththphaphphiess klayepnwamwlepnswnhnungkhxngprimanthwipkwa eriyk ethnesxrphlngngan omemntm energy momentum tensor sungmithngkhwamhnaaennkhxngphlngnganaelaomemntm tlxdcnkhwamekhriyd khux khwamdnaelakhwamechuxn odyichhlkkarsmmul ethnesxrnicasamarthwangnythwipinpriphumi ewlaokhngid cakkarethiybekhiyngkbkhwamonmthwngaebbniwtnechingerkhakhnit cungepnthrrmchatithicasnnisthanwasmkarfildsahrbkhwamonmthwngechuxmethnesxrnikbethnesxrritchi Ricci tensor sungxthibayphlkhunlngchnechphaahnung khux karepliynaeplngprimatrkhxngklumhmxk cloud khxngxnuphakhthdsxbkhnadelksungerimcaksphawaningaelwtkxisra insmphththphaphphiess karxnurksphlngngan omemntmsmnykbkhxkhwamwaethnesxrphlngngan omemntmplxdidewxrecns echnediywkn sutrnisamarthwangnythwipinpriphumi ewlaokhngodykaraethnxnuphnthyxydwyxnuphnthaemniofld manifold okhngsungepnxnuphnthaeprprwnrwmekiywthisuksainerkhakhnitechingxnuphnth dwyenguxnikhthiephimkhunmani idewxrecnsaeprprwnrwmekiywkhxngethnesxrphlngngan omemntm aelaxairktamthixyuxikkhanghnungkhxngsmkaryxmepnsuny chudkhxngsmkarthingaythisudniepnsingthieriykwasmkarsnamkhxngixnsitn smkarsnamkhxngixnsitn G m n R m n 1 2 R g m n 8 p G c 4 T m n displaystyle G mu nu equiv R mu nu textstyle 1 over 2 R g mu nu 8 pi G over c 4 T mu nu khangsaymuxepnethnesxrixnsitn sungepnkarrwmethnesxrritchiaebbplxdidewxrecnsechphaa R m n displaystyle R mu nu kbethnesxremtrik odythi G m n displaystyle G mu nu smmatr odyechphaa R g m n R m n displaystyle R g mu nu R mu nu epnseklarkhwamokhng ethnesxrritchiexngsmphnthkbethnesxrkhwamokhngrimnn Riemann curvature tensor sungminythwipkwa odythi R m n R a m a n displaystyle R mu nu R alpha mu alpha nu khangkhwamux T m n displaystyle T mu nu epnethnesxrphlngngan omemntm ethnesxrthnghmdekhiyndwysykrndchninamthrrm abstract index notation 3 inkarethiybekhiyngkarthanaykhxngthvsdidngklawkbphlkarsngektsahrbwngokhcrdawekhraah hruxethiybethaenguxnikhwainkrnikhwamonmthwngxxn khwamerwtacatxngtrngkbklsastraebbniwtn caidkhakhngtwkhwamidsdswn proportionality constant epn k 8pG c4 odythi G epnkhakhngtwkhwamonmthwng aela c epnkhwamerwaesng 4 emuximmimwl ethnesxrphlngngan omemntmcahmdip phlkhux smkarixnsitnsuyyakas vacuum Einstein equation R m n 0 displaystyle R mu nu 0 nxkehnuxcaksmphththphaphthwip yngkhngmithvsditweluxkxun sungsrangbnphunthanediywkn sungmikdaela hruxkhakhngtwephimetim naipsusmkarfildtang twxyangechn Brans Dicke theory teleparallelism aela Einstein Cartan theory 5 bthniyamaelakarprayuktphunthan aekikhsmphththphaphthwipepnthvsdikhwamonmthwngemtrik odymihwicepnsmkarkhxngixnsitn sungxthibaykhwamsmphnthrahwangerkhakhnitkhxngaemniofldsimitiaebbrimnnethiym pseudo Riemannian sungepntwaethnkhxngpriphumi ewlaaelaphlngngan omemntmsungxyuinpriphumi ewlann 6 praktkarnsunginklsastraebbchbbihehtuphlwaepnkiriya action khxngaerngonmthwng echn kartkxisra karekhluxnthiaebbokhcr aelaaenwwithixwkasyan sxdkhlxngkbkarekhluxnthiechuxyphayinerkhakhnitokhngkhxngpriphumi ewlainsmphththphaphthwip odyimmiaerngonmthwngipebnwtthucakwithithrrmchatixnepnesntrngkhxngmn hakaetkhwamonmthwngsxdkhlxngkbkarepliynaeplngkhunsmbtikhxngpriphumiaelaewla sungepliynwithiesntrngthisudthiepnipidsungwtthucadaeninodythrrmchatiepnladb 7 swnkhwamokhngnnekidcakphlngngan omemntmkhxngssarxikthxdhnung thxdkhwamcaknksmphththniym cxhn xarchibld wielxr John Archibald Wheeler priphumi ewlabxkssarwacaekhluxnthixyangir ssarbxkpriphumi ewlawacaokhngxyangir 8 khnathismphththphaphthwipaethnskyakhwamonmthwngseklarkhxngklsastraebbchbbdwyethnesxrkhaladbkhnsxng rank two smmatr aetethnesxrkhaladbkhnsxngsmmatrldehluxskyakhwamonmthwngseklarinbangkrni sahrbsnamkhwamonmthwngxxnaelakhwamerwtasmphththkbkhwamerwaesng karthanaykhxngthvsdinibrrcbkbkarthanaykhxngkdkhwamonmthwngsaklkhxngniwtn 9 ephraasmphththphaphthwipsrangodyichethnesxr cungaesdngkhwamaeprprwnrwmekiywthwip odykdkhxngmn aelakdxunthikhidphayinkrxbsmphththniymthwip yudrupaebbediywkninthukrabbphikd 10 yingipkwann thvsdiniimmiokhrngsrangphunhlngerkhakhnitimaeprepliynid khux imkhunkbphunhlng channmnsxdkhlxngkbhlkkarthwipsmphththniymthiekhmngwdkwa klawkhux kdfisiksepnehmuxnkbsahrbphusngektthukkhn 11 echphaathidngaesdnginhlkkarsmmul priphumi ewlaepnaebbminkhxfski aelakdfisiksaesdngkhwamyunynglxerntsechphaathi local Lorentz invariance 12 duephim aekikhbthnathvsdismphththphaphthwipxangxing aekikh Nobel Prize Biography Nobel Prize Biography Nobel Prize subkhnemux 25 February 2011 Gravitational Waves Detected 100 Years After Einstein s Prediction 11 emsayn 2016 subkhnemux 5 minakhm 2019 Ehlers 1973 pp 19 22 for similar derivations see sections 1 and 2 of ch 7 in Weinberg 1972 The Einstein tensor is the only divergence free tensor that is a function of the metric coefficients their first and second derivatives at most and allows the spacetime of special relativity as a solution in the absence of sources of gravity cf Lovelock 1972 The tensors on both side are of second rank that is they can each be thought of as 4 4 matrices each of which contains ten independent terms hence the above represents ten coupled equations The fact that as a consequence of geometric relations known as Bianchi identities the Einstein tensor satisfies a further four identities reduces these to six independent equations e g Schutz 1985 sec 8 3 Kenyon 1990 sec 7 4 Brans amp Dicke 1961 Weinberg 1972 sec 3 in ch 7 Goenner 2004 sec 7 2 and Trautman 2006 respectively Wald 1984 ch 4 Weinberg 1972 ch 7 or in fact any other textbook on general relativity At least approximately cf Poisson 2004 Wheeler 1990 p xi Wald 1984 sec 4 4 Wald 1984 sec 4 1 For the conceptual and historical difficulties in defining a general principle of relativity and separating it from the notion of general covariance see Giulini 2006b section 5 in ch 12 of Weinberg 1972 bthkhwamekiywkbdarasastrhruxckrwalwithyaniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy darasastr bthkhwamekiywkbfisiksniyngepnokhrng khunsamarthchwywikiphiediyidodyephimkhxmul duephimthi sthaniyxy fisiksekhathungcak https th wikipedia org w index php title thvsdismphththphaphthwip amp oldid 9055926, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,