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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.02768 |
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| _version_ | 1866916884726677504 |
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| author | Kumar, Arun Wu, Qiang Zhu, Tao Ghosh, Sushant G. |
| author_facet | Kumar, Arun Wu, Qiang Zhu, Tao Ghosh, Sushant G. |
| contents | We investigate Schwarzschild black holes in anti-de Sitter (AdS) spacetimes surrounded by a cloud of strings (BH-AdS-CoS), incorporating both electric- and magnetic-like components of the string bi-vector. Thermodynamically, these systems exhibit small/intermediate/large black hole phases with first- and second-order transitions governed by the string parameter $c_0$. Dynamically, we probe the phase structure using Lyapunov exponents $λ$ from unstable circular geodesics. For massless particles ($δ= 0$), analytical expressions $λ$ reveal multivalued behavior in first-order transition regimes ($c_0 < c_{\text{cri}}$), with branches mapping to thermodynamic phases ($λ_{\text{SBH}}, λ_{\text{IBH}}, λ_{\text{LBH}}$). The discontinuity $Δλ= λ_{\text{SBH}} - λ_{\text{LBH}}$ at $T_p$ follows mean-field scaling: $Δλ/ λ_{\text{cri}} \propto (T_\text{cri} - T)^{1/2} \quad (β= 1/2)$. For massive particles ($δ= 1$), numerical computation of timelike geodesics confirms $λ$ as an order parameter, with critical exponent $β= 1/2$ universally. Key distinctions emerge: $λ\to 1$ asymptotically for photons, while $λ\to 0$ in the significant black hole phase for massive particles due to vanishing unstable orbits. The transition of $λ$ from multivalued to single-valued at $c_0 = c_{\text{cri}}$ establishes it as a universal dynamical probe of black hole criticality. The universal critical exponent of 1/2 for \(Δλ\) further reinforces the analogy with conventional thermodynamic systems. Our results confirm a direct connection between the thermodynamic phase structure of BH-AdS-CoS and the dynamics of test particles, with the Lyapunov exponent emerging as a sensitive diagnostic of black hole criticality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lyapunov Exponent Approach to Phase Structure of Schwarzschild AdS Black Holes Surrounded by a Cloud of Strings Kumar, Arun Wu, Qiang Zhu, Tao Ghosh, Sushant G. General Relativity and Quantum Cosmology We investigate Schwarzschild black holes in anti-de Sitter (AdS) spacetimes surrounded by a cloud of strings (BH-AdS-CoS), incorporating both electric- and magnetic-like components of the string bi-vector. Thermodynamically, these systems exhibit small/intermediate/large black hole phases with first- and second-order transitions governed by the string parameter $c_0$. Dynamically, we probe the phase structure using Lyapunov exponents $λ$ from unstable circular geodesics. For massless particles ($δ= 0$), analytical expressions $λ$ reveal multivalued behavior in first-order transition regimes ($c_0 < c_{\text{cri}}$), with branches mapping to thermodynamic phases ($λ_{\text{SBH}}, λ_{\text{IBH}}, λ_{\text{LBH}}$). The discontinuity $Δλ= λ_{\text{SBH}} - λ_{\text{LBH}}$ at $T_p$ follows mean-field scaling: $Δλ/ λ_{\text{cri}} \propto (T_\text{cri} - T)^{1/2} \quad (β= 1/2)$. For massive particles ($δ= 1$), numerical computation of timelike geodesics confirms $λ$ as an order parameter, with critical exponent $β= 1/2$ universally. Key distinctions emerge: $λ\to 1$ asymptotically for photons, while $λ\to 0$ in the significant black hole phase for massive particles due to vanishing unstable orbits. The transition of $λ$ from multivalued to single-valued at $c_0 = c_{\text{cri}}$ establishes it as a universal dynamical probe of black hole criticality. The universal critical exponent of 1/2 for \(Δλ\) further reinforces the analogy with conventional thermodynamic systems. Our results confirm a direct connection between the thermodynamic phase structure of BH-AdS-CoS and the dynamics of test particles, with the Lyapunov exponent emerging as a sensitive diagnostic of black hole criticality. |
| title | Lyapunov Exponent Approach to Phase Structure of Schwarzschild AdS Black Holes Surrounded by a Cloud of Strings |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.02768 |