next up previous
Next: UNIFYING PERSPECTIVE Up: RADIATION FROM VIOLENTLY ACCELERATED Previous: VIOLENT ACCELERATION

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 $F$:

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

However, for a non-zero static dipole moment the other momenergy[*] components, also measured in $F$, are non-zero:
$\displaystyle \int_0^\infty \int_0^\infty \int _0^{2\pi}
T^\xi_{~\xi}\,\xi d\tau \, rdr \,d\theta$ $\textstyle \not =$ $\displaystyle 0$ (74)
$\displaystyle \int_0^\infty \int_0^\infty \int _0^{2\pi}
T^\xi_{~r}\,\xi d\tau \, rdr \,d\theta$ $\textstyle \not =$ $\displaystyle 0$ (75)
$\displaystyle \int_0^\infty \int_0^\infty \int _0^{2\pi}
T^\xi_{~\theta}\,\xi d\tau \, rdr \,d\theta$ $\textstyle =$ $\displaystyle 0~~~~~~~~~~~~~~~~~~~~~~~~~~(\textrm{\lq\lq axial symmetry''})$ (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.


next up previous
Next: UNIFYING PERSPECTIVE Up: RADIATION FROM VIOLENTLY ACCELERATED Previous: VIOLENT ACCELERATION
Ulrich Gerlach 2001-10-09