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Kerr-Bertotti-Robinson Black Holes Surrounded by a Cloud of Strings

Faizuddin Ahmed, İzzet Sakallı, Ahmad Al-Badawi

TL;DR

The study addresses how a cloud of strings surrounding a Kerr-like black hole interacts with a uniform Bertotti-Robinson magnetic field to modify horizons, photon trajectories, and thermodynamics. It constructs an exact KBR BH solution with CoS, derives horizon locations from $Δ=0$, computes the photon sphere and ISCO, and obtains thermodynamic quantities including a modified Smarr relation and first law that include the string parameter $α$ and field $B$. The results show that the string cloud and BR field significantly shift the horizon radii, area, entropy, and temperature, and alter geodesic structures compared to the Podolsky2025 case, with limiting cases reducing to Letelier Kerr and Schwarzschild-BR with CoS. These findings highlight environmental effects in realistic black-hole models and could inform observational signatures in magnetized, string-rich astrophysical environments.

Abstract

In a recent study [1], authors introduced a new class of exact space-times in Einstein's gravity, which are Kerr black holes immersed in an external uniform magnetic field that is oriented along the rotational axis. Motivated by this work, we investigate a Kerr-like black hole solution with a cloud of strings surrounded by a uniform magnetic field. For the zero rotation case, the space-time reduces to the Schwarzschild-Bertotti-Robinson black hole with a cloud of strings. Moreover, for zero magnetic field, the metrics simplify to a Kerr-like black hole surrounded by a cloud of strings, and its static counterpart reduces to the Schwarzschild black hole with a cloud of strings.

Kerr-Bertotti-Robinson Black Holes Surrounded by a Cloud of Strings

TL;DR

The study addresses how a cloud of strings surrounding a Kerr-like black hole interacts with a uniform Bertotti-Robinson magnetic field to modify horizons, photon trajectories, and thermodynamics. It constructs an exact KBR BH solution with CoS, derives horizon locations from , computes the photon sphere and ISCO, and obtains thermodynamic quantities including a modified Smarr relation and first law that include the string parameter and field . The results show that the string cloud and BR field significantly shift the horizon radii, area, entropy, and temperature, and alter geodesic structures compared to the Podolsky2025 case, with limiting cases reducing to Letelier Kerr and Schwarzschild-BR with CoS. These findings highlight environmental effects in realistic black-hole models and could inform observational signatures in magnetized, string-rich astrophysical environments.

Abstract

In a recent study [1], authors introduced a new class of exact space-times in Einstein's gravity, which are Kerr black holes immersed in an external uniform magnetic field that is oriented along the rotational axis. Motivated by this work, we investigate a Kerr-like black hole solution with a cloud of strings surrounded by a uniform magnetic field. For the zero rotation case, the space-time reduces to the Schwarzschild-Bertotti-Robinson black hole with a cloud of strings. Moreover, for zero magnetic field, the metrics simplify to a Kerr-like black hole surrounded by a cloud of strings, and its static counterpart reduces to the Schwarzschild black hole with a cloud of strings.

Paper Structure

This paper contains 3 sections, 37 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. KBR BH surrounded by CoS
  3. Conclusion

Figures (3)

  • Figure 1: Variation of $\Delta$ (rotating BH) and $f(r)=\left(1-\alpha- B^{2}m^{2}- \frac{2m}{r}\right)$ (non-rotating BH) as a function of the radial coordinate $r$ for various combination of $(\alpha, B)$. Here, $m=1$
  • Figure 2: Behavior of the horizon radius $r_h=r_{+}$ using Eq. (\ref{['bb6']}) as a function of the magnetic field strength $B$ with and without string clouds parameters $\alpha$.
  • Figure 3: Behavior of the surface gravity $\kappa$ for non-rotating and rotating BHs as a function of the magnetic field $B$ with and without string cloud parameter $\alpha$.