Radiation behavior for scalar wave sources versus point-like charges across gravitational, accelerating, and cosmological settings

Determine, for scalar wave sources in scalar field theory, the corresponding answers to the radiation questions posed for point-like charges in the following settings: (i) a source fixed in a gravitational field and its detectability by a distant observer fixed in the field and by a distant free-falling observer; (ii) a source in free fall within a homogeneous gravitational field and its detectability by a co-falling distant observer and by a distant observer fixed in the field; (iii) a source in inertial motion within Minkowski spacetime as observed from an accelerating reference frame; and (iv) a source in free fall within an expanding Universe as observed from another free-falling reference frame within the same Universe. If scalar wave sources radiate while point-like charges do not in any of these scenarios, explain the mechanism that resolves the apparent paradox between these outcomes.

Background

The paper analyzes radiation from a uniformly accelerating charge, showing that radiation is present in the wave zone seen by inertial observers (Minkowski frame) but absent within the static zone of the co-accelerating Rindler frame. In the Introduction, the authors list several related questions concerning radiation from charges in gravitational fields, accelerating frames, and expanding cosmologies.

Beyond point-like sources, the authors explicitly raise a fourth question about replacing point-like sources with wave-like sources (e.g., scalar waves) and the potential paradox if waves radiate while point-like charges do not. In the Conclusions, they state that this question remains to be considered, indicating it as an unresolved issue left for future analysis.

References

  1. What are the answers to the above questions if, instead of point-like sources of radiation, one considers, for example, scalar waves as the sources3? If radiation is produced by a wave as a source, while no radiation arises from a point-like source, what is the explanation for this apparent paradox? The question that remains to be considered is the number 4 among the questions formulated in the Introduction section.
— Once more about radiation from uniformly accelerating charge (2503.00064 - Akhmedov et al., 27 Feb 2025) in Section 6 (Conclusions and acknowledgments); referring to Question 4 in Section 1 (Introduction)