New charged dynamical particles in spatially flat FLRW space-times

TL;DR

The paper addresses charged dynamical black holes in spatially flat FLRW space-times by extending prior κ-models to $(κ,λ)$-models with a time-dependent Coulomb field, where the charge satisfies $Q(t)=λ M(t)^{1/3}$. The authors formulate the Einstein-Maxwell equations in physical Painlevé-Gullstrand frames, derive a diagonal stress-energy tensor combining a perfect-fluid background with an EM term, and obtain the metric function $h_{(κ,λ)}(t,r)$ along with a real-domain threshold $r_{min}(t)$. They show that the total fluid contains a dust component $\delta\rho$ and that horizons are determined by solving a quartic in $r$, which reduces to a cubic in certain expanding cases; a finite charge bound $|λ|\le λ_{max}$ emerges, with $λ_{max}≈0.727415$ in their illustrative example. The work reveals that charged dynamical black holes can be observed only within a physical domain bounded by horizons and a growing prohibited sphere after a critical time, motivating further study of photon spheres and shadows as potential observational probes.

Abstract

New time-dependent metric tensors with spherical symmetry satisfying the Einstein-Maxwell equations in space-times with FLRW asymptotic behaviour are derived here for the first time. These geometries describe dynamical charged non-rotating black holes hosted by the perfect fluid of the asymptotic FLRW space-times. Their gravitational sources are the stress-energy tensors formed by a contribution of the perfect fluid and an electromagnetic one due to the Coulomb field produced by the time-dependent black-hole charge in the asymptotic FLRW background. The dynamics of these models is determined by the dynamical mass, which may be an arbitrary function of time, and two arbitrary real-valued parameters. The first one simulates the effect of a cosmological constant as in our $κ$-models we proposed recently [I. I. Cotaescu, Eur. Phys. J. C (2024) 84:819]. The second parameter relates surprisingly the dynamical black hole charge to the cubic root of the mass function. The role of these parameters is investigated analyzing simple examples of dynamical charged black holes in the matter-dominated universe.

Figures (3)

• Figure 1: In the left panel we plot the function $\Delta(t, 0)$ (dotted line) and $\Delta(t, 0.35)$ (solid line) which has a second root for $t=t_{\lambda}$. In the right panel we see the function $l(t)$ and how $t_{\lambda}$ can be derived graphically.
• Figure 2: The functions $r_c(t)$ and $r_b(t)$ forming a complete C-curve for $\lambda=0$ (left panel) or an incomplete one for $\lambda=0.35$ but which is connected with the non-physical solution $r_{np}(t)$ taking real values for $0<t<t_{\lambda}$ (right panel).
• Figure 3: The functions $r_{max\,1}$ (left panel) and $r_{max\,2}$ (right panel), plotted with dashed lines, complete the borders of the physical domains of the models with $\lambda\not= 0$.