- #1

center o bass

- 560

- 2

$$T^{\mu \nu} = (\rho + p) U^\mu U^\nu + p\eta^{\mu \nu} $$

where ##U^\mu## is the four-velocity field of the fluid. ##\partial_\mu T^{\mu \nu} = 0## then

implies the relativistic continuity equation

$$\partial_\mu(\rho U^\mu) + p \partial_\mu U^\mu = 0$$

which reduces to the ordinary continuity equation for matter

$$\partial_t \rho + \nabla \cdot (\rho \vec v) = 0$$

in the non-relativistic limit ##v << c## and ##p << \rho##. Charge obeys an identical equation in the same limit, but does it has a relativistic analogue? If not, why?