Behaviour of asymptotically electro-$\Lambda$ spacetimes

TL;DR

This paper derives asymptotic solutions for Einstein-Maxwell equations with a positive cosmological constant, analyzing electromagnetic radiation and mass-loss in asymptotically de Sitter spacetimes using Newman-Penrose formalism.

Contribution

It extends previous vacuum solutions to include electromagnetic fields and a positive cosmological constant, providing new insights into asymptotic behavior and mass-loss in such spacetimes.

Findings

Outgoing EM radiation decreases the Bondi mass.

Incoming EM radiation from beyond the horizon increases the Bondi mass.

Electromagnetic radiation does not couple with $ abla$ in the mass-loss formula, unlike gravitational radiation.

Abstract

We present the asymptotic solutions for spacetimes with non-zero cosmological constant $\Lambda$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $\Lambda\neq0$. The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $\Lambda>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with $\Lambda$ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces non-conformal flatness of $\mathcal{I}$. These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where $\Lambda=0$, to now incorporate the cosmological constant $\Lambda$.