Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond
In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in blac...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-04-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321323000597 |
| _version_ | 1797857784001200128 |
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| author | Krishnakanta Bhattacharya |
| author_facet | Krishnakanta Bhattacharya |
| author_sort | Krishnakanta Bhattacharya |
| collection | DOAJ |
| description | In the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the f(R) gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the extended phase space thermodynamics has not been studied extensively, especially in a covariant way. Since both the scalar-tensor and the f(R) gravity can be discussed in the two conformally connected frames (the Jordan and the Einstein frame respectively), the arbitrariness in the expression of pressure, will act upon the equivalence of the thermodynamic parameters in the two frames. We highlight these issues in the paper. Before that, in Einstein's gravity (GR), we obtain a general expression of the equilibrium state version of first law and the Smarr-like formula from the Einstein's equation for a general static and spherically symmetric (SSS) metric. Unlike the existing formalisms in literature which defines thermodynamic potential in order to express the first law, here we directly obtain the first law as well as the Smarr-like formula in GR in terms of the parameters present in the metric (such as mass, charge etc.). This study also shows how the extended phase space is formulated (by considering the cosmological constant as variable) and, also shows why the cosmological constant plays the role of thermodynamic pressure in GR in extended phase space. Moreover, obtaining the Smarr formula from the Einstein's equation for the SSS metric suggests that this dynamical equation encodes more information on BH thermodynamics than what has been anticipated before. |
| first_indexed | 2024-04-09T21:02:23Z |
| format | Article |
| id | doaj.art-e107954503774121bf1bc779b9eee8d6 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-09T21:02:23Z |
| publishDate | 2023-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-e107954503774121bf1bc779b9eee8d62023-03-29T09:21:06ZengElsevierNuclear Physics B0550-32132023-04-01989116130Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyondKrishnakanta Bhattacharya0IUCAA, Post Bag 4, Pune University Campus, Ganeshkhind, Pune 411 007, Maharashtra, IndiaIn the extended phase space approach, one can define thermodynamic pressure and volume that gives rise to the van der Waals type phase transition for black holes. For Einstein's GR, the expressions of these quantities are unanimously accepted. Of late, the van der Waals phase transition in black holes has been found in modified theories of gravity as well, such as the f(R) gravity and the scalar-tensor gravity. However, in the case of these modified theories of gravity, the expression of pressure (and, hence, volume) is not uniquely determined. In addition, for these modified theories, the extended phase space thermodynamics has not been studied extensively, especially in a covariant way. Since both the scalar-tensor and the f(R) gravity can be discussed in the two conformally connected frames (the Jordan and the Einstein frame respectively), the arbitrariness in the expression of pressure, will act upon the equivalence of the thermodynamic parameters in the two frames. We highlight these issues in the paper. Before that, in Einstein's gravity (GR), we obtain a general expression of the equilibrium state version of first law and the Smarr-like formula from the Einstein's equation for a general static and spherically symmetric (SSS) metric. Unlike the existing formalisms in literature which defines thermodynamic potential in order to express the first law, here we directly obtain the first law as well as the Smarr-like formula in GR in terms of the parameters present in the metric (such as mass, charge etc.). This study also shows how the extended phase space is formulated (by considering the cosmological constant as variable) and, also shows why the cosmological constant plays the role of thermodynamic pressure in GR in extended phase space. Moreover, obtaining the Smarr formula from the Einstein's equation for the SSS metric suggests that this dynamical equation encodes more information on BH thermodynamics than what has been anticipated before.http://www.sciencedirect.com/science/article/pii/S0550321323000597 |
| spellingShingle | Krishnakanta Bhattacharya Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond Nuclear Physics B |
| title | Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond |
| title_full | Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond |
| title_fullStr | Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond |
| title_full_unstemmed | Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond |
| title_short | Extended phase space thermodynamics of black holes: A study in Einstein's gravity and beyond |
| title_sort | extended phase space thermodynamics of black holes a study in einstein s gravity and beyond |
| url | http://www.sciencedirect.com/science/article/pii/S0550321323000597 |
| work_keys_str_mv | AT krishnakantabhattacharya extendedphasespacethermodynamicsofblackholesastudyineinsteinsgravityandbeyond |