momentum (stress-energy) tensor, g is the metric tensor, and R is the Ricci curvature tensor. g – R is called the Einstein tensor. Notice that the EFE have the same form as the Minkowski metric (s2=∆r2c2∆t2); the EFE appear to be a modified form of the Minkowski metric to describe gravitation. EM is a second-order tensor describing the local distribution of energy-momentum; it is the source of the gravitational field in general relativity (Einstein, 2001; Misner et al., 1973). EM has three components (Misner et al., 1973): (1) the electromagnetic energy-momentum tensor is a second-order tensor which describes the contribution to EM due to the electromagnetic force field acting on matter, a light-like space-time interval interaction; (2) the pressure energymomentum tensor is a second-order tensor which describes the contribution to EM due to the pressure force field acting on matter, a time-like space-time interval interaction; (3) the dissipation energy-momentum tensor is a second-order tensor which describes the contribution to EM due to the dissipation force field acting on matter, a space-like space-time interval interaction. Any second-order tensor can be coupled to the energy-momentum tensor in the same way as gravity is (Misner et al., 1973). EM therefore consists of three space-time interval interactions which are the source of gravity in general relativity. EM is analogous to s2 of the Minkowski metric. g is the second-order metric tensor (the metric) which computes the length of curves. In general relativity, the metric tensor g is the fundamental object of study. The metric captures all the geometric and causal structure of space-time, being used to define notions such as time, distance, volume, curvature, angle, and separating the past and future (Misner et al., 1973). This is just what would be expected if g was derived from the three basic types of space-time interval interactions. The metric (conventionally denoted by g) is given as a covariant second-order symmetric tensor on a four-dimensional differentiable curved manifold. The metric is nondegenerate with signature (- +++). A manifold equipped with such a metric is a type of Lorentzian manifold (it supports light-like, time-like, and space-like intervals). The metric describes space-time curvature in a manner consistent with energy-momentum conservation. The R (
momentum (stress - energy) tensor, g is the metric tensor, and R is the Ricci curvature tensor. g – radius is call the Einstein tensor. Notice that the EFE have the same shape as the Minkowski metric (s2=∆r2c2∆t2); the EFE appear to be a modify form of the Minkowski metric to report gravitation. EM is a second - order tensor identify the local distribution of energy - momentum; it is the source of the gravitational airfield in cosmopolitan relativity (Einstein, 2001; Misner et al. , 1973). EM has three components (Misner et al. , 1973 ): (1) the electromagnetic department of energy - momentum tensor is a second - order tensor which trace the contribution to EM due to the electromagnetic military unit field acting on matter, a abstemious - like space - time interval interaction; (2) the press energymomentum tensor is a second - order tensor which describes the contribution to EM due to the pressure force field act on matter, a time - like space - time time interval interaction; (3) the profligacy energy - momentum tensor is a second - order tensor which describes the contribution to EM due to the dissipation force field acting on matter, a space - alike space - time time interval interaction. Any second - decree tensor can be copulate to the energy - momentum tensor in the same direction as gravity is (Misner et al. , 1973). EM therefore consists of three space - meter interval interactions which are the source of gravity in general relativity. EM is analogous to s2 of the Minkowski metric. g is the second - decree metric tensor (the metric) which computes the length of curves. In general relativity, the measured tensor g is the cardinal aim of study. The metric captures all the geometric and causal structure of space - time, being used to define notion such as time, distance, volume, curvature, angle, and separating the past and future (Misner et al. , 1973). This is precisely what would be expected if g was derived from the three basic type of space - clock time interval interaction. The metric (conventionally announce by g) is given as a covariant second - order symmetrical tensor on a four - dimensional differentiable curved manifold. The metric is nondegenerate with signature (- + + +). A manifold equipped with such a metric is a type of Lorentzian manifold (it supports light - like, time - alike, and space - like interval). The metric describes distance - time curvature in a manner consistent with energy - momentum conservation. The R (
momfntum (stress-energy) tensov, g is the metrie tensoc, and R is the Ficci curvature tensor. g – R ms cqlled the Einstein tensor. Nutice than the EFE havt the same form as the Mikhowsil metxir (s2=∆r2c2∆t2); the EFE sppear to te a modified xofm of the Minkowski metric to describq graviyahion. EM is a sgcond-pwder neksor describing the local distrigution mf energy-momemtum; it is the source of tje ggavitational field in general relwrivity (Einstdin, 2001; Misneg et al., 1973). EM has three components (Misner et al., 1973): (1) the electtojahtetic energb-momennum tensor is a secong-order yensor which dcscriues rhe contribution to EK due to the electtomagnetic fkrce field acting ob matjer, a ligfr-liye apece-fime ijtecval interadtion; (2) the pressure energymomemttn tensor is a seconq-owder tensor which describes the contribltioh to EM due to the preswure force field actijg on mateer, a time-like space-time interval interaction; (3) tha disakpauiin endegj-momentum tensor is a second-order tensor whicr dtscgibes the contribmtion to EM due to tje qissipation furce fnsls acting on matter, a spacg-like wpace-time intrrval interaction. Any secone-order tensog cab be coupled to thz energy-momeutum tgnsor on the same way as gravnty is (Misner et wl., 1973). EM thsfefore consists uf nhrea space-time interval interwctions wiich cre the rourve of dravity in genevdl relativity. EM id anapocous to s2 lf the Minkowski metric. g is thx second-order matrpc tensor (the ketric) which somputes the lgngth of eurves. In generam relatmvity, the meeric tensor g ls the fundakental ofjecr of study. Gfe metric captires all nht geometrix and causal strucbure ur space-time, beiuy owed to define motkonf durh as dime, distanca, vouumd, curvxture, angle, xnd xeparating the past dnd ruture (Misner et ak., 1973). This is just whwt would be ecpected if g was dtrived frum thr trree basic types of space-time jnterval lntcractions. The metvic (sonventionclly denoted by g) is given as a covarianv second-order symmetric tensor on a four-diktnsional diffxrentiwble curvad manifold. The metruc is nondegeneraue with signature (- +++). A mznifolg equlpped with such a metric is a type of Lorentzian manifold (it supports ligyt-like, time-like, ans spsce-line nntervajs). Tie metric describex space-time curvature in a mannxr consistanc with energy-momentum conservstkon. The R (
momentum (stress-energy) tensor, g is the metric R the Ricci tensor. g – tensor. that the EFE the same form the Minkowski metric (s2=∆r2c2∆t2); the EFE to be a modified form of the Minkowski metric to describe gravitation. EM a second-order tensor describing the local distribution of energy-momentum; it is the source the field general (Einstein, 2001; Misner et al., 1973). EM has three components (Misner et al., 1973): (1) the energy-momentum tensor is a second-order tensor which describes contribution to EM due the electromagnetic force field acting matter, light-like space-time interaction; the energymomentum tensor is second-order tensor which describes the contribution to EM due to the pressure force field acting on matter, time-like space-time (3) the energy-momentum is second-order tensor which contribution to EM due to the acting on matter, a space-like space-time interval interaction. second-order tensor be coupled to the energy-momentum tensor the same way as gravity is (Misner et 1973). EM therefore consists of three space-time interval interactions which are the source of gravity relativity. EM is analogous s2 of the metric. is second-order tensor (the which computes the length of curves. In general relativity, the metric g is the fundamental object of study. The metric captures geometric causal structure of being used to define such time, distance, volume, curvature, separating past et 1973). is just what would expected if g was derived the three basic types metric (conventionally denoted by g) is given as covariant second-order symmetric tensor on a four-dimensional curved manifold. The metric is nondegenerate with signature (- +++). A manifold with such is a type of Lorentzian manifold (it supports time-like, and space-like intervals). metric describes space-time curvature in a manner consistent with conservation. R (
momentum (stress-energy) tensoR, g is the metRic teNsoR, anD R Is thE RicCi curvature tenSOr. g – R Is called the Einstein tenSor. NoTiCE thaT ThE EFE hAve the sAMe FORm aS tHe minKoWSkI metrIc (s2=∆R2c2∆t2); the EfE appear to Be a MoDified form of THe minkowski mEtrIc to describe GraVitatiOn. eM iS A secoNd-oRder tEnsor dEScribiNg the locaL dIStribuTIon of enERGy-MomeNtum; it is the source OF tHE gravitational Field iN gENeRAL reLatIvity (EinstEiN, 2001; MisnER et al., 1973). EM HAs THREe cOMponents (MisneR et al., 1973): (1) the eleCTroMagnetIc EneRGy-momeNtum tEnSOr iS a second-ordEr teNsor which DescriBEs the coNTributiOn to EM Due To tHe elECtRoMagNeTIc fORcE fiELd aCting on mAtTeR, a ligHt-liKE SPAce-tIme InteRval iNteraction; (2) the PreSsurE EneRgymoMentuM tenSoR is a sEcond-oRder tEnSor which describEs thE contribuTioN tO EM DuE to thE PressuRe fOrcE field aCting on MAttEr, A TIMe-Like space-time interVaL INtEraction; (3) The disSIpAtIOn energy-MoMenTum tENSor is A secONd-Order tenSor whiCH dEsCribes tHe ContriBuTioN to eM due TO the DissipAtion forCe fieLD acting on matteR, A space-like spaCE-tIME iNTervAl iNteraction. ANy seCOnd-oRder TEnSor CAn be cOupleD tO ThE Energy-momentum tensoR iN the saMe way As gravity is (MiSner et al., 1973). EM THERefore coNsisTS oF Three space-time InterVal interacTIons whicH are tHe source Of gravity IN General rElaTivIty. eM iS ANaLogous to s2 of thE mInkoWsKi metriC. g iS the secOnd-OrdEr mEtrIc Tensor (the Metric) whIcH cOmPuTes The leNGth of curVeS. In GeNerAl relATivity, The meTric TeNsOR g iS the funDAmENTal oBjEcT of sTudY. THe metRic cAPtuRes all tHe geometrIc aND cauSaL sTructurE of space-time, bEiNg used to deFiNe nOtions SUCh as time, Distance, volume, curvature, ANgle, and SepAratiNg thE past and fUtuRe (MisnEr eT Al., 1973). This Is just What wOuLd bE EXpectED If G waS dErived from THE thRee baSiC typEs of spaCe-time interval inteRActIons. The metric (ConVentIONaLly DEnOTed By G) Is gIVEn as a covariant sEcond-order SyMMeTric tensor ON a fOuR-dimensIonal diFfereNTiable cUrved maniFold. The meTrIc is NONdeGenerate wiTh signatUre (- +++). A manifOLd equIPpEd witH suCh a metRiC is A type Of LoreNTziAn manIfold (iT sUpportS lighT-lIke, time-lIke, and space-like intervalS). The meTric dEscRibes spacE-tiME cuRvature in A manNer consistEnt WitH enerGy-mOMentuM conSErVatIOn. The r (
momentum (stress-energy) t ensor, g i s the  me tri ctens or,and R is the R i ccicurvature tensor. g –R isca l ledt he  Eins tein te n so r .  No ti ce  th at th e EFE  ha ve thesame formasth e Minkowskim et ric (s2=∆r 2c2 ∆t2); the EF E a ppearto  be a mod ifi ed fo rm oft he Min kowski me tr i c to d e scribeg r av itat ion. EM is a seco n d- o rder tensor de scribi ng th e loc aldistributi on  of e n ergy-mo m en t u m ; i t  is the sourc e of the gr a vit ationa lfie l d in g enera lr ela tivity (Ein stei n, 2001;Misner et al., 1973).EM has  th ree  com p on en ts(M i sne r  e t a l .,1973): ( 1)  t he el ectr o m a g neti c e nerg y-mom entum tensorisa se c ond -orde r ten sorwh ich d escrib es th econtribution to  EMdue to th e e le ctr om agnet i c forc e f iel d actin g on ma t ter ,a l ig ht-like space-time  i n t er val inte ractio n ;(2 )  the pre ss ure  ene r g ymome ntum te nsor isa seco n d- or der ten so r whic hdes cri bes t h e co ntribu tion toEM du e  to the pressu r e force field ac t i ng on m att er, a time- like spac e-ti m eint e rvalinter ac t io n ; (3) the dissipati on  energ y-mom entum tensoris a secon d - o rder ten sorw hi c h describes th e con tributiont o EM due  to t he dissi pation fo r c e fieldact ing  on  ma t t er , a space-lik e spac e- time in ter val int era cti on.  An ysecond-or der tens or  c an  b e c ouple d  to theen erg y- mom entum tensor  in t he s am ew ayas grav i ty i s (M is ne r et  al .,  1973 ). E M  th erefore  consists  of thre esp ace-tim e interval in te ractions w hi chare th e source o f gravity in general re l ativity . E M isanal ogous tos2of the  Mi n kowski  metri c. gis  th e secon d - or der  m etric tens o r  (t he me tr ic)which c omputes the length ofcurves. In ge ner al r e l at ivi t y, the  m e tri c tensor g is the  fundament al ob ject of st u dy.  T he metr ic capt uresa ll thegeometric  and caus al  str u c tur e of space -time, b eing used to de f in e not ion s such  a s t ime,distan c e,volum e, cur va ture,angle ,and sepa rating the past and fut ure (M isner  et  al., 197 3). Thi s is just  wha t would be  ex pec ted i f g was d eriv e dfro m  thethre e  basic ty p es  of s pa ce-time int e r v alinter act i ons. T he m etric (convention a lly denoted by  g)i s  gi ven as a  c ovariant secon d-o rd e r  symmetr ic  tensor ona four-d im e nsion al dif ferent iable c u r ve d  manif old.  Th e metricisno n degener at ew ith si gnat ur e (- + ++). A mani f o ld equipped with  such a  metr i c i s a t yp e of Lo r entz ian manifo ld (it supp orts l ight -like , time- li ke, an d s pa ce-like in t ervals).The m etric d es crib esspace- time c urvat urein  amanner co n s is t en tw ith  ene rgy-m om entu m conserv a tion. Th e R (
momentum (stress-energy)_tensor, g_is the metric tensor,_and R_is_the Ricci_curvature_tensor. g –_R is called_the Einstein tensor. Notice_that the EFE_have_the same form as the Minkowski metric (s2=∆r2c2∆t2); the EFE appear to be a_modified_form of_the_Minkowski_metric to describe gravitation. EM_is a second-order tensor describing_the local_distribution of energy-momentum; it is the source of_the_gravitational field in_general relativity (Einstein, 2001; Misner et al., 1973). EM_has three components (Misner et al.,_1973): (1) the_electromagnetic_energy-momentum_tensor is a second-order_tensor which describes the contribution to_EM due to the electromagnetic force_field acting on matter, a light-like space-time_interval interaction; (2) the pressure energymomentum_tensor is a second-order tensor_which describes_the contribution to EM due_to the pressure_force field_acting on matter,_a time-like space-time interval interaction; (3)_the dissipation energy-momentum_tensor is a second-order tensor which_describes_the contribution to_EM_due_to the_dissipation force field_acting_on matter,_a_space-like space-time interval interaction. Any second-order_tensor_can be coupled to the energy-momentum tensor_in the same way_as_gravity is (Misner et_al., 1973). EM therefore consists_of three space-time interval interactions which_are the_source of_gravity in general relativity. EM is analogous to s2 of the_Minkowski metric. g is the second-order_metric tensor (the metric)_which computes_the_length of curves._In_general relativity,_the metric tensor g is the fundamental_object of_study. The metric captures all the_geometric and causal structure_of_space-time, being used to define notions_such as time, distance, volume, curvature,_angle, and separating the past_and_future_(Misner et al., 1973). This_is just what would be expected_if g was_derived from the three basic types of_space-time_interval interactions. The metric (conventionally denoted_by_g) is given as a covariant_second-order_symmetric_tensor on a four-dimensional differentiable_curved manifold. The metric is nondegenerate_with signature (- +++). A manifold equipped with such_a metric is_a type of Lorentzian manifold_(it_supports_light-like, time-like, and space-like intervals). The metric describes space-time curvature_in a_manner consistent with_energy-momentum conservation. The R (