General Relativity. Solve HW(3-2). 8.1.3 Covariant Derivative For Tensors Let us now define the covariant derivatives for

General Relativity. Solve HW(3-2).

 

Transcribed Image Text:

8.1.3 Covariant Derivative For Tensors Let us now define the covariant derivatives for other types of tensors such that they transform covariantly, and that the Leibniz rule holds V(AB) = (VA)B + A(VB). (8.6) In principle, we should use different symbols for covariant derivatives acting on different types of tensors, but in practice we use the same symbol V for all of them. For a scalar o, the usual derivative is already covariant, so Recall that for a covariant vector V₁, Vμφ = Ομφ. that V₁V₂ = 8₁μV₂ - V₁. HW: (3-2) How to define VW? HV Since the contraction of WV is a scalar, and we know the covariant derivatives of both a scalar and V₁, we deduce from the Leibniz rule V{W*V) = (VW*)V +W°V_V V₁W² = ₁W² +FW. на (8.7) (8.8) (8.9) (8.10) 8.1.3 Covariant Derivative For Tensors Let us now define the covariant derivatives for other types of tensors such that they transform covariantly, and that the Leibniz rule holds V(AB) = (VA)B + A(VB). (8.6) In principle, we should use different symbols for covariant derivatives acting on different types of tensors, but in practice we use the same symbol V for all of them. For a scalar o, the usual derivative is already covariant, so Recall that for a covariant vector V₁, Vμφ = Ομφ. that V₁V₂ = 8₁μV₂ - V₁. HW: (3-2) How to define VW? HV Since the contraction of WV is a scalar, and we know the covariant derivatives of both a scalar and V₁, we deduce from the Leibniz rule V{W*V) = (VW*)V +W°V_V V₁W² = ₁W² +FW. на (8.7) (8.8) (8.9) (8.10)

Answer rating: 100% (QA)

Sol Now Giver and Vu Vo emre wt 2w V Fow rem na Du No V Juw ... View the full answer