Charged Bardeen black hole with a cosmological constant and surrounded by quintessence and a cloud of strings

TL;DR

This work extends the Bardeen regular black hole to a charged, spherically symmetric solution including a cosmological constant, quintessence, and a cloud of strings. Using nonlinear electrodynamics and additional source terms, it derives the metric function $f(r)$ and analyzes curvature via the Kretschmann scalar, showing that regularity depends on the interplay of sources and state parameters, with several configurations yielding singular cores. The paper also develops the geodesic framework for the generalized spacetime, deriving conserved quantities and the effective potential $V_{eff}$ to study radial and nonradial motion, including the existence of possible stable circular orbits depending on the parameters. Overall, the results map how quintessence, string clouds, and charge shape horizons, asymptotics, and particle dynamics, offering a comprehensive platform for exploring non-singular BHs under realistic cosmic environments.

Abstract

Exact solutions which generalize the Bardeen black hole solution, in the sense that several sources are taken into account, are derived. The most general case corresponds to a charged Bardeen black hole with a cosmological constant and surrounded by quintessence and a cloud of strings. A discussion is presented concerning the Kretschmann scalar and its dependence with the parameters associated to the different sources. Finally, the geodesics and effective potential are analyzed.

Figures (10)

• Figure 1: Kretschmann scalar referring to the charged Bardeen black hole with a cosmological constant and surrounded by quintessence and a cloud of strings, for different values of the parameters $q$, $\Lambda$, and $\omega_q$.
• Figure 2: Kretschmann scalar referring to the Bardeen black hole for different values of $q$.
• Figure 3: Kretschmann scalar referring to the Bardeen black hole surrounded by quintessence for different values of $q$, $\omega_q$, and $\alpha$.
• Figure 4: Kretschmann scalar referring to the Bardeen black hole with a cosmological constant for different values of $q$ and $\Lambda$.
• Figure 5: Kretschmann scalar referring to the Bardeen black hole with an electromagnetic field for different values of $q$ and $Q$.