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Thermodynamical properties of a deformed Schwarzschild black hole via Dunkl generalization

P. Sedaghatnia, H. Hassanabadi, A. A. Araújo Filho, P. J. Porfírio, W. S. Chung

TL;DR

The paper develops a Dunkl-generalized Schwarzschild black hole within a de Sitter gauge gravity framework, deriving metric coefficients that depend on Dunkl parameters and parity operators and ensuring consistency with known limits. By implementing a diagonal tetrad ansatz and solving the gauge field equations, it computes curvature tensors and thermodynamic quantities, revealing parity-specific modifications. A key finding is the emergence of a phase transition in the odd-parity case manifested in the heat capacity, while even parity remains without such a transition. The results highlight how reflection symmetries encoded by Dunkl operators can qualitatively alter horizon structure and black hole thermodynamics with potential implications for quantum gravity phenomenology.

Abstract

In this paper, we construct a deformed Schwarzschild black hole from the de Sitter gauge theory of gravity within Dunkl generalization and we determine the metric coefficients versus Dunkl parameter and parity operators. Since the spacetime coordinates are not affected by the group transformations, only fields are allowed to change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed as well. Additionally, we analyze the modifications on the thermodynamic properties to a spherically symmetric black hole due to Dunkl parameters for even and odd parities. Finally, we verify a novel remark highlighted from heat capacity: the appearance of a phase transition when the odd parity is taken into account.

Thermodynamical properties of a deformed Schwarzschild black hole via Dunkl generalization

TL;DR

The paper develops a Dunkl-generalized Schwarzschild black hole within a de Sitter gauge gravity framework, deriving metric coefficients that depend on Dunkl parameters and parity operators and ensuring consistency with known limits. By implementing a diagonal tetrad ansatz and solving the gauge field equations, it computes curvature tensors and thermodynamic quantities, revealing parity-specific modifications. A key finding is the emergence of a phase transition in the odd-parity case manifested in the heat capacity, while even parity remains without such a transition. The results highlight how reflection symmetries encoded by Dunkl operators can qualitatively alter horizon structure and black hole thermodynamics with potential implications for quantum gravity phenomenology.

Abstract

In this paper, we construct a deformed Schwarzschild black hole from the de Sitter gauge theory of gravity within Dunkl generalization and we determine the metric coefficients versus Dunkl parameter and parity operators. Since the spacetime coordinates are not affected by the group transformations, only fields are allowed to change under the action of the symmetry group. A particular ansatz for the gauge fields is chosen and the components of the strength tensor are computed as well. Additionally, we analyze the modifications on the thermodynamic properties to a spherically symmetric black hole due to Dunkl parameters for even and odd parities. Finally, we verify a novel remark highlighted from heat capacity: the appearance of a phase transition when the odd parity is taken into account.
Paper Structure (8 sections, 54 equations, 5 figures)

This paper contains 8 sections, 54 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Dunkl operator in Spherical coordinates
  3. The deformed Schwarzschild spacetime in the presence of Dunkl operators
  4. Thermodynamics
  5. Conclusion
  6. The relations of the Einstein field equations (9-14)
  7. The Riemann tensor in the presence of Dunkl operator
  8. Data Availability Statement

Figures (5)

  • Figure 1: Function $f(r)$ with respect to $r$ for (a) $\mathcal{R}=-1$ (odd parity) with different values of $\alpha=1/2,3/2,4$, and (b) $\mathcal{R}=+1$ (even parity) with different values of $\Lambda=0,-30,-60$. Here, we set $M = 1$.
  • Figure 2: Plot of temperature $T$ as the function of horizon radius $r$ for (a) $\mathcal{R}=-1$ (odd parity) with different values of $\alpha=0.5,0.75,0.95$, and (b) $\mathcal{R}=+1$ (even parity) with different values of $\Lambda=0,-30,-60$.
  • Figure 3: Entropy $S$ as a function of radius $r$ for (a) $\mathcal{R}=-1$ (odd parity) with different values of $\alpha=0.5,0.75,0.95$, and (b) $\mathcal{R}=\pm1$ (even and parity) with $\alpha=0.95$.
  • Figure 4: Helmholtz free energy $F$ as the function of radius $r$ for (a) $\mathcal{R}=-1$ (odd parity) with different values of $\alpha=0.5,0.75,0.95$, and (b) $\mathcal{R}=+1$ (even parity) with $\Lambda=0,-30,-60$.
  • Figure 5: Heat capacity vs $r$ for (a) $\mathcal{R}=-1$ (odd parity) with different values of $\alpha=0.5,0.75,0.95$, and (b) $\mathcal{R}=+1$ (even parity) with $\Lambda=0,-0.3,-0.6$.