::::: It's mentioned [[Einsteinian_gravitation#Step_8._Flatness_of_spacetime|here]] that the the "Hubble tensor" is anti-symmetric. If so, this equation doesn't make sense since the stress-energy tensor, <math>T_{\mu\nu}</math>, is symmetric. The only way for the above equation to hold is if the "Hubble Tensor" and the stress-energy tensor are both zero ( <math>H_{\mu\nu}=-8\pi T_{\mu\nu} = -8\pi T_{\nu\mu}= H_{\nu\mu} = - H_{\mu\nu}</math> and <math>H_{\mu\nu} = - H_{\mu\nu} \Rightarrow H_{\mu\nu} = 0</math>). Actually, since in the linked article the "Hubble Tensor" is defined as the antisymmetric part of Ricci tensor it is exactly zero. --[[User:MatthewQ|MatthewQ]] 19:44, 20 August 2011 (EDT) | ::::: It's mentioned [[Einsteinian_gravitation#Step_8._Flatness_of_spacetime|here]] that the the "Hubble tensor" is anti-symmetric. If so, this equation doesn't make sense since the stress-energy tensor, <math>T_{\mu\nu}</math>, is symmetric. The only way for the above equation to hold is if the "Hubble Tensor" and the stress-energy tensor are both zero ( <math>H_{\mu\nu}=-8\pi T_{\mu\nu} = -8\pi T_{\nu\mu}= H_{\nu\mu} = - H_{\mu\nu}</math> and <math>H_{\mu\nu} = - H_{\mu\nu} \Rightarrow H_{\mu\nu} = 0</math>). Actually, since in the linked article the "Hubble Tensor" is defined as the antisymmetric part of Ricci tensor it is exactly zero. --[[User:MatthewQ|MatthewQ]] 19:44, 20 August 2011 (EDT) |