Dressing rotating black holes with anisotropic matter

TL;DR

This work introduces a Kerr-like rotating black hole solution sourced by anisotropic matter, constructed using a non-complexification variant of the Newman-Janis algorithm. The authors derive a rotating metric with $\Sigma(r,\theta)=r^2+a^2\cos^2\theta$, $\Delta(r)=r^2+a^2-2Mr+v(r)$, and $\Gamma(r)=r^2+a^2$, where the matter content is encoded in a function $v(r)$ that yields an exponentially decaying energy density near the horizon. They present a concrete model with $v(r)=v_2\bar{\Delta}(\sqrt{v_c}\,r)$ leading to explicit expressions for the energy density and pressures, horizons, and a pair of new hair charges $C_1$, $C_2$ that appear in the Smarr relation and first law, together with a modified temperature and entropy. The analysis shows the horizon structure and thermodynamics are sensitive to the anisotropic matter, with the Kerr limit recovered as the matter contribution vanishes, providing a framework to study hair that is not asymptotically visible and its physical implications for black hole thermodynamics.

Abstract

We present a new rotating black hole solution to the Einstein equations as an extension of the Kerr spacetime. Interestingly, the solution we find may not be uniquely characterized by asymptotic parameters such as mass, angular momentum, and charge, thereby it would be the additional hair. We also analyze in detail how this additional characteristics or this hair affects the thermodynamic properties of the black hole.

Figures (4)

• Figure 1: (color online). The characteristic form of the function $\Delta(r)$ for various values of $v_2$ and $a$, respectively.
• Figure 2: (color online). The energy density as a function of $r$.
• Figure 3: (color online). Temperature as a function of the horizon radius $r_H$.
• Figure 4: (color online). Heat capacity as a function of the horizon radius $r_H$.