A New Cloud of Strings

In this work, we present a generalization of the cloud of strings model originally proposed by Letelier, by introducing a magnetic-like component, $\Sigma_{23}$, in addition to the electric-like component, $\Sigma_{01}$, considered in the original formulation. This extension leads to a new black hole solution of the form \begin{equation} f(r) = 1 - \frac{2M}{r} + \frac{g_s^2 \ell_s^2}{r^2} \, {}_2F_1\left(-\frac{1}{2}, -\frac{1}{4}, \frac{3}{4}, -\frac{r^4}{\ell_s^4}\right), \end{equation} where ${}_2F_1$ denotes the Gaussian hypergeometric function. The solution is characterized by the string length $\ell_s$ and the string coupling constant $g_s$ yields the condition $0 < a < 1$, which now emerges from the model itself, ensuring both energy positivity and the existence of horizons-rather than being imposed ad hoc. We also investigate the thermodynamic properties of the resulting black hole, and find that the entropy remains consistent with the Bekenstein-Hawking formula, $S = A/4$, in agreement with several string-theoretic derivations.