Physics — General Relativity · energy-momentum-tensor-field-theory
Problem
Consider the two field theories we explicitly discussed, Maxwell's electromagnetism (let Jμ=0) and the scalar field theory defined by (1.148).
(a) Express the components of the energy-momentum tensors of each theory in three-vector notation, using the divergence, gradient, curl, electric, and magnetic fields, and an overdot to denote time derivatives.
(b) Using the equations of motion, verify (in any notation you like) that the energy-momentum tensors are conserved.