 of equation Tij:j=0 (Eq. 10) and the Einstein-Grossman field equation, a conservation law for the combined matter and gravitational fields holds in the form (Eq. 11) where is the object Einstein interpreted as characterizing the energy content of the gravitational field. In his appendix, Einstein stated that (11) is covariant only for linear coordinate transformations (geometrically they preserve the straight lines and the planes). But once again the reasoning was unsound. If, transforms like a (1, 1) tensor, then in general (11) would be covariant only under linear transformations. But in general transforms like a tensor only for linear coordinate transformations. Since (11) is a consequence of generally covariant equation (9) and the Einstein-Grossmann field equations, its covariance is just as wide as the covariance of the field equations. The point should have been intuitively evident to Einstein. The principle of equivalence implies that it is always possible to 'transform away' the gravitational field at any point; thus, whatever the state of the field, one should always be able to find a coordinate [√g (T j i +t j i )], j=0 t j i t j i t j i system such that = 0 at the chosen point. Thus, cannot behave like a tensor under non-linear transformations" [7]. In 1915, due to his personal circumstances and interests, Einstein opted by a tensor of first type. "Einstein and Grossmann proceeded to develop essentially all the major components of the final general theory of relativity.... Just one eluded them. To treat the general case of the gravitational field, non-flat metrics must also be admitted and, in the final theory, the decision of which are admitted is made by the gravitational field equations. Einstein expected these equations to take the now familiar form Gμν=k Tμν (Eq. 12) where Tμν is the stress-energy tensor and Gμν a gravitation tensor constructed solely from the metric tensor gμν and its first and second derivatives. Einstein and Grossmann considered the Ricci tensor as their gravitation tensor-just a hair's breadth away from Einstein's final choice of the Einstein tensor. In their place, to the astonishment of modem readers, they offered a set of gravitational field equations that was not generally covariant" [2]. In the Entwurf theory using equations (6), they had reported that these equations failed to give the Newtonian limit in the case of weak,
of equation Tij: j=0 (Eq. 10) and the Einstein - Grossman field equation, a conservation law for the compound topic and gravitational fields holds in the human body (Eq. 11) where is the aim Einstein interpreted as characterizing the energy message of the gravitational field. In his appendix, Einstein stated that (11) is covariant merely for linear coordinate transformations (geometrically they keep the straight lines and the plane). But once again the reasoning was unsound. If, transforms like a (1, 1) tensor, then in general (11) would be covariant only under linear transformations. But in cosmopolitan transforms like a tensor only for linear coordinate transformation. Since (11) is a consequence of generally covariant equation (9) and the Einstein - Grossmann plain equations, its covariance is merely as wide as the covariance of the field equations. The point should have been intuitively apparent to Einstein. The principle of equivalence implies that it is always possible to' transform away' the gravitational field at any point; thus, whatever the state of the field, one should always be able to find a coordinate [ √g (T j i + t j i) ], j=0 t j i t j i t j i system such that = 0 at the chosen detail. Thus, cannot behave like a tensor under non - analogue transformation " [ 7 ]. In 1915, due to his personal context and interests, Einstein opted by a tensor of first type. " Einstein and Grossmann proceeded to develop essentially all the major component of the final general theory of relativity.... Just one eluded them. To treat the cosmopolitan case of the gravitational field, non - flat metrics must also be admitted and, in the final hypothesis, the decisiveness of which are accommodate is made by the gravitational field equations. Einstein expect these equations to take the now familiar form Gμν = k Tμν (Eq. 12) where Tμν is the stress - energy tensor and Gμν a gravitation tensor construct solely from the measured tensor gμν and its first and second derivatives. Einstein and Grossmann considered the Ricci tensor as their gravitation tensor - just a hair's-breadth's breadth aside from Einstein's final option of the Einstein tensor. In their place, to the astonishment of modem readers, they offered a hardening of gravitational battlefield equations that was not broadly covariant " [ 2 ]. In the Entwurf theory using equations (6), they had reported that these equations fail to give the Newtonian limit in the casing of weak,
 of equation Tij:j=0 (Eq. 10) and tme Einstein-Grossman fiend equztion, a zonservation law for the comuinee matuvr and gravitational wields hopds in tye fiem (Eq. 11) whecs is thc objsgt Eiusvein interpretec as charawterizing the andryy content of the gravitational fielq. In hix wppendix, Einstgin suatqd tgat (11) is covariant only for linear doordinete transformatoons (geometrically they prfserge the straight lijes and the plagws). But once xgain the gzasoning waa unsound. If, transforms like a (1, 1) tenxor, then ib tenftal (11) would bx covagiant only under linedr tranxformations. Bub in jeneeal transforms like a tensor only for lynear coosdnnate transformations. Sunce (11) is d covweqjende or genegalmy covariaht equation (9) and the Einstein-Gtofwmann field esuatiogs, its covariance is just as wide as the bovadiance of the field equqtions. The point shoupd have bqen intuitively evident to Einstein. The principle of esjivcoence umolies that it is always possible to 'transform zwsy' the gravitatijnal field st ami point; thus, wfatevex tge state of the fifld, one shouod always be sble to find a coordinate [√g (T j i +t j i )], j=0 t j i t j i t j i system sbch thst = 0 st the chosen point. Thur, cahnot behave like a tsvsor under non-liveag trdnsformaukons" [7]. In 1915, due to ris persoial cnrcumstavces and igterests, Elnstelt opted by a tensog of yirst type. "Einshein and Grossmann proceeded to develop essenjianly all the majov components of the final gengral theoxy of felativity.... Just oie eluded thqm. To treat tvg general casx of the dravutatuonal fkdld, non-flat meyrics musn clso be aemitted and, in the fivzl theory, the dzeiwion of which ate xdmytned if made by the graxitxyionau field equctkons. Einstein expected tvese equations to take tme now faniliar fjrm Gμν=k Tμν (Eq. 12) ehere Tμν is the strtss-enecgy teisor amd Dμν a gravitation tensor construdted solepy nrom the metryc tcnsot gμν and its first and second derivatives. Einstein end Grossmann considergd the Ricci tensor ax their gravmtatiog tensor-jgst a hair's breadth qway from Einsteik's final choice of the Einstain tfnsor. In their place, to the astonishment of modem readers, they offered a wet of gravitationzl foeld vquctipns thwt wes not generally cpvariant" [2]. In the Entwurf theory using exuctions (6), they had reported thay ghese equatiovs failed to give the Nestonian kimit in the case of weak,
of equation Tij:j=0 (Eq. 10) and the equation, conservation law the combined matter the (Eq. 11) where the object Einstein as characterizing the energy content of gravitational field. In his appendix, Einstein stated that (11) is covariant only for coordinate transformations (geometrically they preserve the straight lines and the planes). But once the was If, like a (1, 1) tensor, then in general (11) would be covariant only under linear transformations. in general transforms like a tensor only for coordinate transformations. Since (11) a consequence of generally covariant (9) the Einstein-Grossmann equations, covariance just as wide the covariance of the field equations. The point should have been intuitively evident to Einstein. The principle equivalence implies is always to away' gravitational field at thus, whatever the state of the always be able to find a coordinate [√g j i j i )], j=0 t j t j i t j i system such = 0 at the chosen point. Thus, cannot behave like a tensor under non-linear transformations" 1915, due to his circumstances and interests, opted a of type. "Einstein Grossmann proceeded to develop essentially all the major components of the general theory of relativity.... Just one eluded them. To treat case the gravitational field, metrics must also be and, the final theory, the which admitted the field Einstein expected these equations take the now familiar form Tμν (Eq. 12) where and Gμν a gravitation tensor constructed solely from metric tensor gμν and its first and derivatives. Einstein and Grossmann considered the Ricci tensor as their gravitation tensor-just hair's breadth Einstein's final choice of the Einstein tensor. In place, to the astonishment modem readers, they offered a set of gravitational field that not generally [2]. In the theory using equations they had reported equations failed give Newtonian case of weak,
 of equation Tij:j=0 (Eq. 10) and the EinStein-GrossMan fiEld EquAtIon, a ConsErvation law for THe coMbined matter and gravitaTionaL fIElds HOlDs in tHe form (EQ. 11) WhERE is ThE oBjeCt eInStein IntErpreteD as charactEriZiNg the energy cONtEnt of the grAviTational fielD. In His appEnDix, eInsteIn sTated That (11) is COvariaNt only for LiNEar cooRDinate tRANsFormAtions (geometricalLY tHEy preserve the sTraighT lINeS ANd tHe pLanes). But onCe Again THe reasoNInG WAS unSOund. If, transfoRms like a (1, 1) tenSOr, tHen in gEnEraL (11) Would bE covaRiANt oNly under linEar tRansformaTions. BUT in geneRAl transForms lIke A teNsor ONlY fOr lInEAr cOOrDinATe tRansformAtIoNs. SinCe (11) is A CONSequEncE of gEneraLly covariant eQuaTion (9) ANd tHe EinStein-grosSmAnn fiEld equAtionS, iTs covariance is jUst aS wide as thE coVaRiaNcE of thE Field eQuaTioNs. The poInt shouLD haVe BEEN iNtuitively evident tO EINStEin. The prInciplE Of EqUIvalence ImPliEs thAT It is aLwayS PoSsible to 'TransfORm AwAy' the grAvItatioNaL fiEld At any POint; Thus, whAtever thE statE Of the field, one sHOuld always be aBLe TO FiND a coOrdInate [√g (T j i +t j I )], j=0 t j I T j i t J i sySTeM suCH that = 0 At the ChOSeN Point. Thus, cannot behaVe Like a tEnsor Under non-lineaR transformATIOns" [7]. In 1915, due To hiS PeRSonal circumstaNces aNd interestS, einstein Opted By a tensoR of first tYPE. "EinsteiN anD GrOssManN PRoCeeded to develOP EsseNtIally alL thE major cOmpOneNts Of tHe Final geneRal theorY oF rElAtIviTy.... JusT One eludeD tHem. to TreAt the GEneral Case oF the GrAvITatIonal fiELd, NON-flaT mEtRics MusT aLso be AdmiTTed And, in thE final theOry, THe deCiSiOn of whiCh are admitted Is Made by the gRaVitAtionaL FIeld equaTions. Einstein expected thESe equatIonS to taKe thE now familIar Form GμΝ=k TΜΝ (Eq. 12) wheRe Tμν iS the sTrEss-ENErgy tENSoR anD GΜν a gravitaTIOn tEnsor CoNstrUcted soLely from the metric tENsoR gμν and its firSt aNd seCONd DerIVaTIveS. EINstEIN and Grossmann coNsidered thE RICcI tensor as tHEir GrAvitatiOn tensoR-just A Hair's brEadth away From EinstEiN's fiNAL chOice of the EInstein tEnsor. In thEIr plaCE, tO the aStoNishmeNt Of mOdem rEaders, THey OfferEd a set Of GravitAtionAl Field equAtions that was not generalLy covaRiant" [2]. in tHe Entwurf TheORy uSing equatIons (6), They had repOrtEd tHat thEse EQuatiOns fAIlEd tO Give tHe NeWTonian limIT iN thE CAsE of weak,
 of equation Tij:j=0 (Eq.10) and th e Ein ste in- Gr ossm an f ield equation, a co nservation law for the  comb in e d ma t te r and  gravit a ti o n alfi el dsho l ds  in t heform (E q. 11) whe reis  the objectE in stein inte rpr eted as char act erizin gthe energ y c onten t of t h e grav itational  f i eld. I n  his ap p e nd ix,Einstein stated t h at (11) is covari ant on ly fo r lin ear  coordinat etrans f ormatio n s( g e ome t rically theypreserve th e  st raight  l ine s  and t he pl an e s).  But once a gain  the reas oningw as unso u nd. If,  trans for mslike a(1 , 1 )t ens o r,  th e n i n genera l(1 1) wo uldb e c ovar ian t on ly un der linear tr ans form a tio ns. B ut in  gen er al tr ansfor ms li ke  a tensor onlyforlinear co ord in ate  t ransf o rmatio ns.  Si nce (11 ) is ac ons eq u e n ce  of generally cova ri a n tequation  (9) a n dth e  Einstei n- Gro ssma n n  fiel d eq u at ions, it s cova r ia nc e is ju st  as wi de  as  th e cov a rian ce ofthe fiel d equ a tions. The poi n t should have be e n  i n tuit ive ly evidentto E i nste in.T he  pr i ncipl e ofeq u iv a lence implies thatit  is al wayspossible to ' transforma w a y' the g ravi t at i onal field atany p oint; thus ,  whateve r the  state o f the fie l d , one sh oul d a lwa ysb e  a ble to find a c oord in ate [√ g ( T j i + t j  i)],  j= 0t j i t j  i t j i  s ys te msuc h tha t  = 0 atth e c ho sen  poin t . Thus , can notbe ha v e l ike a t e ns o r  und er  n on-l ine ar  tran sfor m ati ons" [7 ]. In 191 5,d ue t ohi s perso nal circumsta nc es and int er est s, Ein s t ein opte d by a tensor of firstt ype. "E ins teinandGrossmann  pr oceede d t o  devel op ess entia ll y a l l  them a jo r c om ponents of t hefinal  g ener al theo ry of relativity.. . . J ust one elude d t hem. T otre a tt hege n era l case of the gra vitational  f i el d, non-fla t  me tr ics mus t alsobe ad m itted a nd, in th e final t he ory, t hedecision o f whichare admit t ed is ma de by  th e grav it ati onalfielde qua tions . Eins te in exp ected  t hese equ ations to take the nowfamili ar fo rmGμν=k Tμν  (E q . 1 2) whereTμνis the str ess -en ergyten s or an d Gμ ν  a  gr a vitat iont ensor con s tr uct e d  s olely fromt h e  me tricten s or gμν  and  its first and se c ond derivative s. E i n ste ina nd G ro ssmann conside red  t h e  Ricci t en sor as thei r gravit at i on te nsor-j ust ahair'sb r ea d th awa y fr omEinstein' s f in a l choic eof the Ei nste in  tenso r. Int heir p lace, to the ast onish m e nt of mod em re ad ers, th e y of fered a se t of gravit ationa l fi eld e quation sthat w asno t generall y  covarian t" [2 ]. In t he  Ent wur f theo ry u s i ng eq uati on s ( 6), theyh a dr ep or t edthat  thes eequa tions fai l ed to gi vet he Newt on ian l imit i n  t h e  case of w eak ,
 of_equation Tij:j=0_(Eq. 10) and the_Einstein-Grossman field_equation,_a conservation_law_for the combined_matter and gravitational_fields holds in the_form (Eq. 11)_where_is the object Einstein interpreted as characterizing the energy content of the gravitational field._In_his appendix,_Einstein_stated_that (11) is covariant only_for linear coordinate transformations (geometrically_they preserve_the straight lines and the planes). But once_again_the reasoning was_unsound. If, transforms like a (1, 1) tensor, then_in general (11) would be covariant_only under linear_transformations._But_in general transforms like_a tensor only for linear coordinate_transformations. Since (11) is a consequence_of generally covariant equation (9) and the_Einstein-Grossmann field equations, its covariance is_just as wide as the_covariance of_the field equations. The point_should have been_intuitively evident_to Einstein. The_principle of equivalence implies that it_is always possible_to 'transform away' the gravitational field_at_any point; thus,_whatever_the_state of_the field, one_should_always be_able_to find a coordinate [√g (T_j_i +t j i )], j=0 t_j i t j_i_t j i system_such that = 0 at_the chosen point. Thus, cannot behave_like a_tensor under_non-linear transformations" [7]. In 1915, due to his personal circumstances and_interests, Einstein opted by a tensor_of first type. "Einstein_and Grossmann_proceeded_to develop essentially_all_the major_components of the final general theory of_relativity.... Just_one eluded them. To treat the_general case of the_gravitational_field, non-flat metrics must also be_admitted and, in the final theory,_the decision of which are_admitted_is_made by the gravitational field_equations. Einstein expected these equations to_take the now_familiar form Gμν=k Tμν (Eq. 12) where_Tμν_is the stress-energy tensor and Gμν_a_gravitation tensor constructed solely from the_metric_tensor_gμν and its first and_second derivatives. Einstein and Grossmann considered_the Ricci tensor as their gravitation tensor-just a hair's_breadth away from_Einstein's final choice of the_Einstein_tensor._In their place, to the astonishment of modem readers, they_offered a_set of gravitational_field equations that was not generally covariant" [2]. In the_Entwurf theory using equations (6), they had_reported that these equations failed to give the Newtonian limit in_the case of weak,