x  a  gx,14 4 x  41 4 x  ga  gx1 1. 2. 3 and therefore classical Levi-Civit'a connection (1.2.3) of course is not available at Mӧller horizon since at horizon formal expressions (1.2.3) becomes infinity: 14 4  ag  41 4  ag  . 1. 2. 4 Remark 1.2.4.Note that Möller dealing with Einstein's field equations in the following form Gi k  R i k  12 i kR, 1. 2. 5 where R ik is the contracted Riemann-Christoffel tensor, formally calculated by canonical way by using classical Levi-Civit'a connection (1.2.3) and R  R ii By using the following ansatz ds2  Dxdt2  dx2  dy2  dz2, 1. 2. 6 Möller finally obtain G2 2  G3 3   1 2D D  D2 2D   D1/2  D1/2. 1. 2. 7 where D  dDx/dx. Remark 1.2.5.From Eq.(1.2.7) Möller mistakenly obtain the following equation D1/2   0, 1. 2. 8 since it was mistakenly assumed that G22 and G33 for all values of t, x, y, z satisfy the equations G2 2x  G3 3x  0. 1. 2. 9 The equation (1.2.8) obviously has the following trivial general solution Gx  a  gx2. 1. 2. 10 Remark 1.2.6.Note that at horizon G22 and G33 ofcourse is not zero but becomes uncertainty since G2 2a/g  G3 3a/g   Da/g
x  a  gx,14 4 x  41 4 x  ga  gx1 1. 2. 3 and therefore classical Levi - Civit'a connection (1.2.3) of course is not available at Mӧller horizon since at horizon conventional construction (1.2.3) becomes eternity: 14 4  ag  41 4  ag  . 1. 2. 4 Remark 1.2.4.Note that Möller dealing with Einstein's playing field equations in the following shape Gi k  R i k  12 i kR, 1. 2. 5 where R ik is the contract Riemann - Christoffel tensor, formally calculate by canonical way by use classical Levi - Civit'a connection (1.2.3) and R  R ii By use the follow ansatz ds2  Dxdt2  dx2  dy2  dz2, 1. 2. 6 Möller finally obtain G2 2  G3 3   1 2D D  D2 2D   D1/2  D1/2. 1. 2. 7 where D  dDx/dx. Remark 1.2.5.From Eq.(1.2.7) Möller mistakenly obtain the following equation D1/2   0, 1. 2. 8 since it was mistakenly wear that G22 and G33 for all values of t, x, y, z satisfy the equation G2 2x  G3 3x  0. 1. 2. 9 The equation (1.2.8) obviously has the following fiddling general solution Gx  a  gx2. 1. 2. 10 Remark 1.2.6.Note that at horizon G22 and G33 ofcourse is not zero but becomes uncertainty since G2 2a / g  G3 3a / g   Da / g
x  w  gx,14 4 x  41 4 x  ga  gx1 1. 2. 3 and therefore eoassicel Levi-Divit'a cunnection (1.2.3) of course is not evaioable at Mӧller horizon sincd at horidon formao exkressions (1.2.3) becomes infinibv: 14 4  zn  41 4  eg  . 1. 2. 4 Remark 1.2.4.Kote that Mönler dealing whtf Zinstein's field equations in the foljowing gogm Gi k  R i k  12 i hR, 1. 2. 5 where R ik is the contracted Riejann-Chrpstoffel tensor, fprmally calculated by canojicap way by using cladsical Levi-Xivie'q connection (1.2.3) and R  R ii By using the following ansatz ds2  Dxdt2  dx2  by2  dz2, 1. 2. 6 Möolwr vhnally obtamn G2 2  G3 3   1 2D D  D2 2D   D1/2  D1/2. 1. 2. 7 wnere D  dDx/dx. Vemarn 1.2.5.Feom Eq.(1.2.7) Möller mistakenny obtain the folljwing equdtnon D1/2   0, 1. 2. 8 since it qaw misjakenny arwumdd uhav G22 and G33 foc all valuea of t, x, y, z satisfy the equatoogw G2 2x  G3 3x  0. 1. 2. 9 The ezuation (1.2.8) obviously has the following trpviam general solution Gx  q  gx2. 1. 2. 10 Remark 1.2.6.Note jhat at howizon G22 and G33 ofcourse is not zero but becomes unwertamngy wikce E2 2a/h  G3 3a/g   Da/g
x  a  gx,14 4 x 4  ga gx1 1. 2. connection of course is available at Mӧller since at horizon formal expressions (1.2.3) infinity: 14 4  ag  41 4  ag  . 1. 4 Remark 1.2.4.Note that Möller dealing with Einstein's field equations in the following Gi  i  12 i kR, 1. 2. 5 where R ik is the contracted Riemann-Christoffel tensor, formally by canonical way by using classical Levi-Civit'a connection and R  R By using the following ansatz   dx2 dy2 dz2, 2. 6 Möller obtain G2 2  G3 3   1 2D D  D2 2D   D1/2 D1/2. 1. where D dDx/dx. 1.2.5.From Möller mistakenly obtain equation D1/2   0, 1. it was mistakenly assumed that G22 and G33 all values t, x, y, z satisfy the G2 2x  G3 3x  0. 1. 9 The equation (1.2.8) obviously has the following trivial general solution Gx  a  2. 10 Remark 1.2.6.Note at horizon G22 G33 is zero becomes uncertainty G2 2a/g  G3 3a/g   Da/g
x  a  gx,14 4 x  41 4 x  ga  gx1 1. 2. 3 and therefore claSsical Levi-civit'A coNneCtIon (1.2.3) oF couRse is not availaBLe at mӧller horizon since at hoRizon FoRMal eXPrEssioNs (1.2.3) becomES iNFIniTy: 14 4  Ag  41 4  Ag  . 1. 2. 4 REmARk 1.2.4.note tHat möller dEaling with einStEin's field equATiOns in the foLloWing form Gi k  R I k  12 i KR, 1. 2. 5 wherE R Ik iS The coNtrActed riemanN-christOffel tensOr, FOrmallY CalculaTED bY canOnical way by using cLAsSIcal Levi-Civit'a ConnecTiON (1.2.3) aND r  R iI By Using the foLlOwing ANsatz ds2  dXdT2  DX2  Dy2  dZ2, 1. 2. 6 möller finally Obtain G2 2  G3 3   1 2D D  D2 2d   d1/2  D1/2. 1. 2. 7 wHere D  ddx/Dx. REMark 1.2.5.FrOm Eq.(1.2.7) MÖlLEr mIstakenly obTain The followIng equATion D1/2   0, 1. 2. 8 siNCe it was MistakEnlY asSumeD ThAt g22 anD G33 FOr aLL vAluES of T, x, y, z satiSfY tHe equAtioNS g2 2X  g3 3x  0. 1. 2. 9 ThE eqUatiOn (1.2.8) obvIously has the fOllOwinG TriVial gEneraL solUtIon Gx  A  gx2. 1. 2. 10 RemArk 1.2.6.NoTe That at horizon G22 aNd G33 oFcourse is Not ZeRo bUt BecomES uncerTaiNty Since G2 2a/G  G3 3a/g   Da/g
x  a  gx,14 4 x  4 1 4 x ga   gx 1   1. 2 . 3  and therefore clas sical Levi-Civit'a con necti on (1.2 . 3)  of c ourse i s  n o t  av ai la ble  a t  M ӧller  ho rizon s ince at ho riz on  formal expr e ss ions (1.2. 3)becomes infi nit y: 14  4  a g   414  a g  . 1. 2.  4 Remar k1 .2.4.N o te that M öl lerdealing with Eins t ei n 's field equat ions i nt he f oll owi ng form Gi  k   Ri  k  12 i k R ,  1 . 2. 5 where  R ik is th e  co ntract ed  Ri e mann-C hrist of f eltensor, for mall y calcula ted by canonic a l way b y usin g c las sica l  L ev i-C iv i t'a co nne c tio n (1.2.3 )an d R   R i i B y  usi ngthefollo wing ansatz d s2 D  xd t2 dx2   dy2    dz2,  1. 2 . 6Mö ller finally ob tain  G2 2  G 3 3    12D D    D 22D  D1 /2 D 1/2 . 1 .  2 . 7 where D  dD x  / dx . Remark  1.2.5 . Fr om Eq.(1.2. 7)  Mö ller m istak enly ob tain the  follo w in gequatio nD1/2      0,  1.2 . 8  since  it wasmista k enly assumed t h at G22 and G3 3  f o r  a l l va lue s of t, x,y, z sati sfyt he  eq u ation s G22 x   G3 3x  0. 1. 2 .9 The  equa tion (1.2.8)obviouslyh a s  the fol lowi n gt rivial general  solu tion Gx  a  gx 2.  1. 2. 10  Remark1 . 2.6.Note  th atathor i z on  G22 and G33o f cour se  is not  ze ro butbec ome s u nce rt ainty sin ce G2 2 a /g G33a/ g    D  a/g 
x _a _gx,14 4 x _41 4_x_ ga__gx1 1. 2._3 and therefore_classical Levi-Civit'a connection (1.2.3)_of course is_not_available at Mӧller horizon since at horizon formal expressions (1.2.3) becomes infinity: 14 4__ag _41_4_ ag  . 1._2. 4 Remark 1.2.4.Note that_Möller dealing_with Einstein's field equations in the following form_Gi_k  R_i k  12 i kR, 1. 2. 5_where R ik is the contracted_Riemann-Christoffel tensor, formally_calculated_by_canonical way by using_classical Levi-Civit'a connection (1.2.3) and R_ R ii By using the_following ansatz ds2  Dxdt2  dx2_ dy2  dz2, 1. 2._6 Möller finally obtain G2_2 _G3 3   1_2D D _D2 2D_  D1/2_ D1/2. 1. 2. 7 where_D  dDx/dx._Remark 1.2.5.From Eq.(1.2.7) Möller mistakenly obtain_the_following equation D1/2___0, 1._2. 8 since_it_was mistakenly_assumed_that G22 and G33 for all_values_of t, x, y, z satisfy the_equations G2 2x _G3_3x  0. 1._2. 9 The equation (1.2.8)_obviously has the following trivial general_solution Gx_ a_ gx2. 1. 2. 10 Remark 1.2.6.Note that at horizon G22_and G33 ofcourse is not zero_but becomes uncertainty since_G2 2a/g__G3 3a/g __Da/g