Electrovac Robinson-Trautman spacetime without gravitational radiation is stationary
Phys. Rev. D 112, 064060 – Published 19 September, 2025
DOI: https://doi.org/10.1103/pzzj-vcnf
Abstract
It is apparent that a stationary spacetime does not admit gravitational radiation. But whether a spacetime without gravitational radiation is stationary is not clear. Especially when a spacetime holds matter such as electromagnetic field, gravitational radiation in general cannot determine the matter radiation and the matter behavior. In this paper we show that, remarkably, electrovac Robinson-Trautman spacetimes without gravitational radiation are necessarily stationary. More precisely, if the gravitational news function of a Robinson-Trautman spacetime containing a Maxwell field vanishes, the electromagnetic radiation must vanish as well. Furthermore, we prove that any Robinson-Trautman spacetime endowed with a Maxwell field and zero gravitational news is exactly the Reissner-Nordström solution. Our results provide a new perspective on the uniqueness of the Reissner-Nordström spacetime.
