An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges
In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional...
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MDPI AG
2022-08-01
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| Online Access: | https://www.mdpi.com/1099-4300/24/9/1197 |
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| author | Rodrigo Aros Milko Estrada Pablo Pereira |
| author_facet | Rodrigo Aros Milko Estrada Pablo Pereira |
| author_sort | Rodrigo Aros |
| collection | DOAJ |
| description | In this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mover accent="true"><mi>δ</mi><mo stretchy="false">^</mo></mover><mo form="prefix">ln</mo><mrow><mo>(</mo><mi>l</mi><mo>/</mo><mo>ℓ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, with <i>l</i> the AdS radius and <i>ℓ</i> a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry. |
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| format | Article |
| id | doaj.art-839d1b0941b349abb4848961329e8feb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T00:06:21Z |
| publishDate | 2022-08-01 |
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| spelling | doaj.art-839d1b0941b349abb4848961329e8feb2023-11-23T16:07:36ZengMDPI AGEntropy1099-43002022-08-01249119710.3390/e24091197An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved ChargesRodrigo Aros0Milko Estrada1Pablo Pereira2Departamento de Ciencias Fisicas, Universidad Andres Bello, Av. Republica 252, Santiago 8370134, ChileFacultad de Ingeniería, Ciencia y Tecnología, Universidad Bernardo O’Higgins, Av. Viel 1497, Santiago 8370993, ChileDepartamento de Fisica, Universidad del Biobio, Av. Collao 1202, Concepcion 4051381, ChileIn this work, we introduce an extension of the study of the first law of thermodynamics of black holes based on the geometry of the extended phase space for AdS Lovelock gravities, which includes changes in scales. As expected, the result obtained coincides with the previously known four-dimensional case. For higher dimensions, the result is the rise of two new contributions to the first law of thermodynamics. The first term corresponds to corrections of the usual definition of thermodynamic volumes at the horizon due to the presence of the higher curvature terms. The second term arises in odd dimensions, comes from the asymptotic region, and corresponds to a scale transformation of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∝</mo><mover accent="true"><mi>δ</mi><mo stretchy="false">^</mo></mover><mo form="prefix">ln</mo><mrow><mo>(</mo><mi>l</mi><mo>/</mo><mo>ℓ</mo><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, with <i>l</i> the AdS radius and <i>ℓ</i> a parameter. A particularly interesting case corresponds to the Chern Simons gravity where the change scale does not generate a contribution at the asymptotic region, likely due to the Chern Simons AdS local symmetry.https://www.mdpi.com/1099-4300/24/9/1197black holes thermodynamicshigher curvature gravityhigher dimensional gravity |
| spellingShingle | Rodrigo Aros Milko Estrada Pablo Pereira An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges Entropy black holes thermodynamics higher curvature gravity higher dimensional gravity |
| title | An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges |
| title_full | An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges |
| title_fullStr | An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges |
| title_full_unstemmed | An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges |
| title_short | An Alternative Study about the Geometry and the First Law of Thermodynamics for AdS Lovelock Gravity, Using the Definition of Conserved Charges |
| title_sort | alternative study about the geometry and the first law of thermodynamics for ads lovelock gravity using the definition of conserved charges |
| topic | black holes thermodynamics higher curvature gravity higher dimensional gravity |
| url | https://www.mdpi.com/1099-4300/24/9/1197 |
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