Journal of Holography Applications in Physics

Hayward-Kalb-Ramond AdS Black Holes with a Cloud of Strings: Geometry, Thermodynamic Topology, Photon-Sphere Observables, and Wave Dynamics

Document Type : Regular article

Author

Physics Department, Eastern Mediterranean University, Famagusta 99628, North Cyprus via Mersin 10, Turkiye

Abstract

We construct a static spherically symmetric black hole (BH) solution in Kalb-Ramond (KR) gravity that simultaneously hosts a Hayward magnetic-monopole regular core, a Letelier cloud of strings (CoS), and an anti-de Sitter (AdS) asymptote with the cosmological constant identified as thermodynamic pressure. The lapse function $f(r)=(1-\alpha_{s})/(1-\ell)-2Mr^{2}/[(1-\ell)(r^{3}+g^{3})]+8\pi P r^{2}/[3(1-\ell)]$ carries four independent parameters with transparent physical roles: the KR Lorentz-violation (LV) parameter $\ell$ rescales the asymptotic potential, the Hayward length $g$ removes the central singularity, the CoS deficit $\alpha_{s}$ deforms the solid angle, and $P=-\Lambda/8\pi$ sets the AdS curvature. Symbolic verification confirms regularity of every curvature invariant at $r=0$, with $f(r)$ admitting a finite limit and reducing to the Ditta {\it et al.} (JHEAP 2025) solution as $g\to 0$, $\alpha_{s}\to 0$. We work out the horizon structure, photon sphere $r_{\rm ph}$ and shadow radius $r_{\rm sh}$, weak-deflection lensing via the Gauss-Bonnet theorem (GBT), innermost stable circular orbits (ISCO), Hawking temperature, Bekenstein-Hawking entropy, heat capacity, Gibbs free energy, $P$-$V$ criticality, Joule-Thomson (JT) inversion, and the eikonal quasinormal-mode (QNM) spectrum. The Van der Waals (VdW) critical point exists across the whole window of $g$ tested above $g\to 0$, with the universal ratio $\rho_{c}\equiv P_{c}v_{c}/T_{c}$ depending on $\ell$ alone through the factorisation $\rho_{c}=(1-\ell)\,\rho_{c}^{\rm Hay\text{-}AdS}$ with $\rho_{c}^{\rm Hay\text{-}AdS}=0.39303$, so that the reference $(\alpha_{s},\ell)=(0.05,0.10)$ configuration gives $\rho_{c}=0.354$, $5.6\%$ below the standard $3/8$ value of the charged-AdS class. The Wei-Liu-Mann thermodynamic-topology classification places the solution in the $W=+1$ topological class, the same as Reissner-Nordstr\"om-AdS (RN-AdS): three BH branches appear below $\tau_{c}$ with windings $\{+1,-1,+1\}$, merge at $\tau_{c}$, and reduce to one $W=+1$ branch above $\tau_{c}$. The numerical analysis shows that $\alpha_{s}$ and $\ell$ act on photon and scalar-wave barriers in opposite directions. The combined dependence makes the four parameters separately identifiable in principle from a joint shadow-ringdown measurement at Event Horizon Telescope (EHT) angular resolution and LIGO/Virgo ringdown sensitivity.

Keywords

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Journal of Holography Applications in Physics
Volume 7, Issue 1
July 2026
Pages 15-39
  • Receive Date: 26 May 2026
  • Revise Date: 19 June 2026
  • Accept Date: 27 June 2026