Changes

:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as  

:Differentiating the above equation at <math>r=0</math> we get the relation between HTD in deep space <math>(d^2\tau/dtdr)^2</math> and the curvature of space of Einstein's universe <math>(1/R_E)^2</math> as  

:<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

::<math>(d^2\tau/dtdr)^2-(1/R_E)^2=0</math>

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.  

:It suggests the existence of overlooked by cosmologists the antisymmetric part of Ricci tensor in time domain, named tentatively <math>H_{\mu\nu}</math> or Hubble Tensor (HT) such that <math>H_{\mu\nu}+R_{\mu\nu}=0</math>, where <math>R_{\mu\nu}</math> is as before the (spatial) part of Ricci tensor, and <math>H_{\mu\nu}</math> is its anti symmetric (temporal) part, agreeing with the fact that conservation of energy (or 4-vectors in general, during their parallel transport) require the flatness of spacetime proposed already by Narlikar and Arp. It would explain also the flatnes of <math>T_{\mu\nu}</math> (stress-energy tensor) and the application of Noether Theorem in flat spacetime that implies conservation of all four components of stress-energy tensor as asserted by Feynman in 2nd volume of ''"Feynman lectures on physics"''.