Here are some important equations for General Relativity.

Image from Wikipedia Babylonian equations.

So far these are the basic maths that I have learnt in Carroll. I have done and not listed the Lorentz transformation. I hope I will add to the list as time goes on and include Lorentz and others.

Carroll's (1.68) where the Levi-Civita symbol is defined says "the Levi-Civita symbol is a ##(0,4)## tensor. It is NOT a tensor as he reminds us elsewhere.

- Definition of ##{\partial }_{\mu }## (Carroll 1.54)
- (Anti)symmetrisation operator (Carroll 1.79)
- Vector as derivative (Carroll 2.16)
- Commutator (Carroll 2.20)
- Tensor transformation equation (Carroll 2.30)
- Basis vectors (Physics Forums)
- Differential equation rules (Wikipedia)
- Multi dimensional Chain Rule
- Pullback / Pushforward operators (Carroll A.9, A.10)
- Levi-Civita symbol and tensor (Carroll section 2.8)
- p-forms (Carroll section 2.9)
- Exterior derivative (Carroll 2.76)
- Wedge product (Carroll 2.73)
- Hodge star operator (Carroll 2.82)
- Covariant derivative / Christoffel symbol (Carroll 3.2)
- The most important formula (C Eq 3.27)
- Stokes's theorem (C Eq 3.35)
- The geodesic equation (C Eq 3.44)

Image from Wikipedia Babylonian equations.

So far these are the basic maths that I have learnt in Carroll. I have done and not listed the Lorentz transformation. I hope I will add to the list as time goes on and include Lorentz and others.

Carroll's (1.68) where the Levi-Civita symbol is defined says "the Levi-Civita symbol is a ##(0,4)## tensor. It is NOT a tensor as he reminds us elsewhere.

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