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<p>We explore the thermodynamics and geothermodynamics of black holes with the Barrow entropy&#xa0;in a brane-world scenario, where the horizon geometry of the black hole is regarded as a fractal structure. Our analysis reveals the behavior of heat capacity, identifying both bound and divergence points. For the Bekenstein-Hawking entropy, the divergence point exhibits smooth behavior, indicating no phase transition. In contrast, we observe divergence with Barrow entropy as the deformation parameter increases, confirming the presence of a zero point in heat capacity through various thermodynamic geometry formalisms. Additionally, we delve into thermodynamic topology, detailing the classification of black holes in the brane-world context and comparing their characteristics determined from the Bekenstein-Hawking and the Barrow entropy. Notably, fixing the deformation and cosmological parameters results in a topological charge <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> predominately by the dark matter parameter, which remains unaffected despite variations in other parameters. In the dS model, the cosmological horizon prevents stable photon spheres, making topological charges of 0 and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(+1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>+</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> unattainable. Incremental increases in the cosmological parameter reduce the dark matter parameter-dominated region.</p>

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Thermodynamic topology and photon spheres analysis of black holes in brane-world: insights from Barrow entropy

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月22日

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  • Usman Zafar,
  • Abdul Jawad,
  • Kazuharu Bamba,
  • Mohammad Ali S. Afshar,
  • Mohammad Reza Alipour,
  • Saeed Noori Gashti,
  • Jafar Sadeghi

摘要

We explore the thermodynamics and geothermodynamics of black holes with the Barrow entropy in a brane-world scenario, where the horizon geometry of the black hole is regarded as a fractal structure. Our analysis reveals the behavior of heat capacity, identifying both bound and divergence points. For the Bekenstein-Hawking entropy, the divergence point exhibits smooth behavior, indicating no phase transition. In contrast, we observe divergence with Barrow entropy as the deformation parameter increases, confirming the presence of a zero point in heat capacity through various thermodynamic geometry formalisms. Additionally, we delve into thermodynamic topology, detailing the classification of black holes in the brane-world context and comparing their characteristics determined from the Bekenstein-Hawking and the Barrow entropy. Notably, fixing the deformation and cosmological parameters results in a topological charge \(-1\) - 1 predominately by the dark matter parameter, which remains unaffected despite variations in other parameters. In the dS model, the cosmological horizon prevents stable photon spheres, making topological charges of 0 and \(+1\) + 1 unattainable. Incremental increases in the cosmological parameter reduce the dark matter parameter-dominated region.