Four-tensor

In physics, specifically for special relativity and general relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. In physics, specifically for special relativity and general relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. General four-tensors are usually written in tensor index notation as with the indices taking integer values from 0 to 3, with 0 for the timelike components and 1, 2, 3 for spacelike components. There are n contravariant indices and m covariant indices. In special and general relativity, many four-tensors of interest are first order (four-vectors) or second order, but higher order tensors occur. Examples are listed next. In special relativity, the vector basis can be restricted to being orthonormal, in which case all four-tensors transform under Lorentz transformations. In general relativity, more general coordinate transformations are necessary since such a restriction is not in general possible.