A New Cloud of Strings

Abstract: In this manuscript, we generalize the cloud of strings model originally introduced by Letelier~\cite{Letelier:1979ej} by incorporating a \textit{magnetic-like component}, $\Sigma_{23}$, alongside the \textit{electric-like component}, $\Sigma_{01}$, considered in the original model. This extension yields a uniquely determined stress-energy tensor of the form $\mathrm{diag}(\rho, -\rho, p, p)$, governed by a specific equation of state and parameterized by two constants. The resulting black hole solution exhibits significant modifications, including the presence of \textit{two independent hairs}, distinguishing it from classical no-hair solutions. We analyze the thermodynamic properties of this black hole and demonstrate the existence of a \textit{remnant mass} and finite entropy at the end of the Hawking evaporation process, suggesting a stable end-state. Furthermore, the presence of \textit{two hairs} introduces new features that could influence black hole shadows and gravitational wave signals, offering valuable observational signatures for testing these exotic configurations.