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

TL;DR

This work generalizes the Hayward regular black hole by incorporating a cosmological constant, quintessence, a cloud of strings, and electric charge, yielding an exact static, spherically symmetric solution with metric function $f(r)=1-a-\frac{2 m r^2}{r^3+2 l^2 m}-\frac{\alpha}{r^{3\omega_q+1}}+\frac{Q^2}{r^2}-\frac{\Lambda r^2}{3}$. It analyzes curvature via the Kretschmann scalar $K$ across multiple subcases, showing that the original Hayward spacetime is regular at the origin while the addition of strings, charge, or certain quintessence configurations can introduce singular behavior depending on $\omega_q$, $\Lambda$, and other parameters. The paper also derives the geodesic structure and an effective potential $V_{eff}=f(r)\left(\frac{J^2}{r^2}+L\right)$, examining radial and nonradial motion and the conditions for stable circular orbits, highlighting how each source alters particle dynamics. Overall, the study clarifies how multi-source generalizations modify regularity and orbital properties, with implications for observables such as shadows and thermodynamics in extended Hayward spacetimes.

Abstract

A family of exact solutions extending the Hayward black hole by incorporating multiple sources is obtained. The most comprehensive scenario describes a charged Hayward black hole with a cosmological constant, immersed in quintessence and accompanied by a cloud of strings. The study examines how the Kretschmann scalar varies with the parameters linked to the various sources and concludes with an analysis of the geodesics and the corresponding effective potential.

Figures (10)

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