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- Meaning of "radiative terms" in the connection of Kinnersley's "photon rocket" solution and their relation with usual gravitational radiation?

In this paper by Carlip, a comparison is made between electromagnetic and gravitational aberration.

For the latter case, he takes as a study subject the Kinnersley’s “photon rocket”, an exact solution which is known to have the strange property of not producing any gravitational waves, even though it models a point-particle accelerating due to the anisotropic emission of a photon flux.

The metric has the following linearized form (eq. 2.1):$$g_{\mu\nu} = \eta_{\mu\nu} - \frac{2Gm(s_R)}{r^3}\sigma_\mu\sigma_\nu$$

Where ##m## is the time-varying mass and ##\sigma_\mu\sigma_\nu## is proportional to the stress-energy tensor and represents radiation/null dust streaming out from the world line.

Carlip then writes the connection coefficients, and in particular ##-\Gamma^i_{00}##, since in the Newtonian limit this corresponds to the "acceleration" that a test particle undergoes in the metric 2.1

Schematically:$$\Gamma^i_{00} =nonradiative\;terms + radiative\;terms $$

In the previous chapter on electromagnetic aberration he decomposed the electric field in a similar way, and he specified that the radiative terms "depend explicitly on acceleration and fall off as ##\frac{1}{R}##"

If the notation is consistent, then, it would seem that the radiative terms in the gravitational case must depend on the same quantities.

The equation for gravitational radiation amplitude also depends on acceleration and falls of as ##\frac{1}{R}## (I'm not talking about the radiated power formula, I mean the equation 4 at page 8 https://www.ego-gw.it/public/events/vesf/2010/Presentations/Quadrupole-Ferrari.pdf)What is the relation between these radiative terms in the connection and the usual gravitational radiation (which should be null in this case)?

For the latter case, he takes as a study subject the Kinnersley’s “photon rocket”, an exact solution which is known to have the strange property of not producing any gravitational waves, even though it models a point-particle accelerating due to the anisotropic emission of a photon flux.

The metric has the following linearized form (eq. 2.1):$$g_{\mu\nu} = \eta_{\mu\nu} - \frac{2Gm(s_R)}{r^3}\sigma_\mu\sigma_\nu$$

Where ##m## is the time-varying mass and ##\sigma_\mu\sigma_\nu## is proportional to the stress-energy tensor and represents radiation/null dust streaming out from the world line.

Carlip then writes the connection coefficients, and in particular ##-\Gamma^i_{00}##, since in the Newtonian limit this corresponds to the "acceleration" that a test particle undergoes in the metric 2.1

Schematically:$$\Gamma^i_{00} =nonradiative\;terms + radiative\;terms $$

In the previous chapter on electromagnetic aberration he decomposed the electric field in a similar way, and he specified that the radiative terms "depend explicitly on acceleration and fall off as ##\frac{1}{R}##"

If the notation is consistent, then, it would seem that the radiative terms in the gravitational case must depend on the same quantities.

The equation for gravitational radiation amplitude also depends on acceleration and falls of as ##\frac{1}{R}## (I'm not talking about the radiated power formula, I mean the equation 4 at page 8 https://www.ego-gw.it/public/events/vesf/2010/Presentations/Quadrupole-Ferrari.pdf)What is the relation between these radiative terms in the connection and the usual gravitational radiation (which should be null in this case)?

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