- #1
Rasalhague
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Rindler (1977): Essential Relativity, 2nd ed., p. 249, deriving Maxwell's equations for orthonormal/inertial coordinate systems on Minkowski space:
And [itex]A^{\mu\nu}_{\enspace,\nu}[/itex] is the electromagnetic field tensor.
Just checking if I've understood this right. Is the "4-velocity of the source distribution" that of the worldlines of particles at rest in the centre-of-momentum coordinate system of the sources? And is comoving volume the spatial (3-dimensional) volume (rather than a 4d volume of spacetime), as measured in these coordinates?
Hence we are led to posit the following field equations
[tex]A^{\mu\nu}_{\enspace,\nu} = k \rho_0U^\mu = k J^\mu,[/tex]
where [itex]k[/itex] is some constant, [itex]U^\mu[/itex] the 4-velocity of the source distribution, [itex]\rho_0[/itex] its proper charge density (i.e. the charge per unit comoving volume--a scalar), and where the 4-current density is defined by this equation.
And [itex]A^{\mu\nu}_{\enspace,\nu}[/itex] is the electromagnetic field tensor.
Just checking if I've understood this right. Is the "4-velocity of the source distribution" that of the worldlines of particles at rest in the centre-of-momentum coordinate system of the sources? And is comoving volume the spatial (3-dimensional) volume (rather than a 4d volume of spacetime), as measured in these coordinates?