RADIATIVE VS. NONRADIATIVE MOMENERGY

Consider a dipole moment, m or d, which is time-independent in its own accelerated frame. The augmented Larmor formula, Eq.(70) and (69), yields zero radiative $\tau$-momentum relative the expanding inertial frame in Rindler sector $F$:

$$\int_0^\infty \int_0^\infty \int _0^{2\pi} T^\xi_{~\tau}\,\xi d\tau \, rdr \,d\theta =0~.$$ (73)

However, for a non-zero static dipole moment the other momenergy components, also measured in $F$, are non-zero:

$$\int_0^\infty \int_0^\infty \int _0^{2\pi} T^\xi_{~\xi}\,\xi d\tau \, rdr \,d\theta \not = 0$$ (74)

$$\int_0^\infty \int_0^\infty \int _0^{2\pi} T^\xi_{~r}\,\xi d\tau \, rdr \,d\theta \not = 0$$ (75)

$$\int_0^\infty \int_0^\infty \int _0^{2\pi} T^\xi_{~\theta}\,\xi d\tau \, rdr \,d\theta = 0~~~~~~~~~~~~~~~~~~~~~~~~~~(\textrm{\lq\lq axial symmetry''})$$ (76)

Equations (73)-(76) express an observationally and hence conceptually precise distinction between the radiative and non-radiative e.m. fields of a dipole source accelerated in Rindler sector $I$: The augmented Larmor formula implies that the dipole emits radiation if and only if its $\tau$-momentum, the spatial integral of $T^\xi_{~\tau}$ in the expanding inertial frame, is non-zero. Furthermore, the existence of a dipole field, static in Rindler sector $I$, is expressed by the non-vanishing of the other momenergy components, Eqs.(74)-(75). Like the $\tau$-momentum, these components are also measurable in the expanding inertial frame. If the dipole is not static then the the emitted radiation gets tracked by the $\tau$-momentum. In that case the other momenergy components play an auxiliary role. They only track the sum of static dipole field and the radiative field, not the separate contributions.