Thermodynamics and Optical Properties of Phantom AdS Black Holes in Massive Gravity

Thermodynamics and Optical Properties of Phantom AdS Black Holes in Massive Gravity

13 Feb 2024 | Kh. Jafarzade, B. Eslam Panah, and M. E. Rodrigues
This paper presents an exact solution for a phantom AdS black hole in the context of dRGT massive gravity, and investigates its thermodynamic and optical properties. The black hole solution is derived in four-dimensional spacetime with a specific metric form, and the reference metric is chosen to ensure the theory is ghost-free. The solution includes a phantom Maxwell field and a cosmological constant, and the thermodynamic quantities such as mass, temperature, entropy, and electric charge are calculated. The first law of thermodynamics and the Smarr relation are verified in the extended phase space, where the cosmological constant is treated as a thermodynamic variable. The local and global stability of the black hole is analyzed using heat capacity and Gibbs free energy, revealing phase transitions and stability regions. The optical properties of the black hole, including the shadow geometry, energy emission rate, and deflection angle, are also studied. Additionally, the quasinormal modes (QNMs) of the black hole are examined using the WKB approximation. The results show that the massive parameters significantly affect the stability and optical properties of the black hole, and that the black hole can exhibit different thermodynamic behaviors depending on the values of these parameters. The study highlights the importance of dRGT massive gravity in understanding the thermodynamics and optical properties of black holes in the context of phantom AdS spacetime.This paper presents an exact solution for a phantom AdS black hole in the context of dRGT massive gravity, and investigates its thermodynamic and optical properties. The black hole solution is derived in four-dimensional spacetime with a specific metric form, and the reference metric is chosen to ensure the theory is ghost-free. The solution includes a phantom Maxwell field and a cosmological constant, and the thermodynamic quantities such as mass, temperature, entropy, and electric charge are calculated. The first law of thermodynamics and the Smarr relation are verified in the extended phase space, where the cosmological constant is treated as a thermodynamic variable. The local and global stability of the black hole is analyzed using heat capacity and Gibbs free energy, revealing phase transitions and stability regions. The optical properties of the black hole, including the shadow geometry, energy emission rate, and deflection angle, are also studied. Additionally, the quasinormal modes (QNMs) of the black hole are examined using the WKB approximation. The results show that the massive parameters significantly affect the stability and optical properties of the black hole, and that the black hole can exhibit different thermodynamic behaviors depending on the values of these parameters. The study highlights the importance of dRGT massive gravity in understanding the thermodynamics and optical properties of black holes in the context of phantom AdS spacetime.
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