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

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)=(۱-\alpha_{s})/(۱-\ell)-۲Mr^{۲}/[(۱-\ell)(r^{۳}+g^{۳})]+۸\pi P r^{۲}/[۳(۱-\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/۸\pi sets the AdS curvature. Symbolic verification confirms regularity of every curvature invariant at r=۰, with f(r) admitting a finite limit and reducing to the Ditta {\it et al.} (JHEAP ۲۰۲۵) solution as g\to ۰, \alpha_{s}\to ۰. 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 ۰, with the universal ratio \rho_{c}\equiv P_{c}v_{c}/T_{c} depending on \ell alone through the factorisation \rho_{c}=(۱-\ell)\,\rho_{c}^{\rm Hay\text{-}AdS} with \rho_{c}^{\rm Hay\text{-}AdS}=۰.۳۹۳۰۳, so that the reference (\alpha_{s},\ell)=(۰.۰۵,۰.۱۰) configuration gives \rho_{c}=۰.۳۵۴, ۵.۶\% below the standard ۳/۸ value of the charged-AdS class. The Wei-Liu-Mann thermodynamic-topology classification places the solution in the W=+۱ topological class, the same as Reissner-Nordstr\"om-AdS (RN-AdS): three BH branches appear below \tau_{c} with windings \{+۱,-۱,+۱\}, merge at \tau_{c}, and reduce to one W=+۱ 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.

کلیدواژه ها:

Lorentz-symmetry breaking ، Nonlinear electrodynamics ، Gravitational lensing ، Van der Waals criticality ، Joule-Thomson expansion ، quasinormal modes ، greybody factor