Angular momentum independence of the entropy sum and entropy product for AdS rotating black holes in all dimensions. (English) Zbl 1367.83055
Summary: In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to the Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed, but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of the entropy product only holds for the dimensions \(d > 4\) with at least one rotation parameter \(a_i = 0\), while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (\(d > 4\)) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product, but the criterion for angular momentum-independence of entropy product will be affected.
References:
| [1] | Wang, J.; Xu, W.; Meng, X. H., The “universal property” of horizon entropy sum of black holes in four dimensional asymptotical (anti-)de-Sitter spacetime background, J. High Energy Phys., 1401, Article 031 pp. (2014) |
| [2] | Zhang, Y.; Gao, S., Mass dependence of the entropy product and sum, Phys. Rev. D, 91, Article 064032 pp. (Mar. 2015) |
| [3] | Ansorg, M.; Hennig, J., The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter, Class. Quantum Gravity, 25, 22, Article 222001 pp. (2008) · Zbl 1152.83319 |
| [4] | Ansorg, M.; Hennig, J., Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory, Phys. Rev. Lett., 102, Article 221102 pp. (Jun. 2009) |
| [5] | Cvetič, M.; Gibbons, G. W.; Pope, C. N., Universal area product formulas for rotating and charged black holes in four and higher dimensions, Phys. Rev. Lett., 106, Article 121301 pp. (Mar. 2011) · Zbl 1255.83065 |
| [6] | Du, Y.-Q.; Tian, Y., The universal property of the entropy sum of black holes in all dimensions, Phys. Lett. B, 739, 250-255 (2014) · Zbl 1306.83043 |
| [7] | Wang, J.; Xu, W.; Meng, X.-h., Entropy relations of black holes with multihorizons in higher dimensions, Phys. Rev. D, 89, Article 044034 pp. (Feb. 2014) |
| [8] | Kastor, D.; Ray, S.; Traschen, J., Enthalpy and the mechanics of AdS black holes, Class. Quantum Gravity, 26, Article 195011 pp. (2009) · Zbl 1178.83030 |
| [9] | Dolan, B. P., Pressure and volume in the first law of black hole thermodynamics, Class. Quantum Gravity, 28, Article 235017 pp. (2011) · Zbl 1231.83020 |
| [10] | Cvetic, M.; Gibbons, G. W.; Kubiznak, D.; Pope, C. N., Black hole enthalpy and an entropy inequality for the thermodynamic volume, Phys. Rev. D, 84, Article 024037 pp. (2011) |
| [11] | Dolan, B. P.; Kastor, D.; Kubiznak, D.; Mann, R. B.; Traschen, J., Thermodynamic volumes and isoperimetric inequalities for de Sitter black holes, Phys. Rev. D, 87, 10, Article 104017 pp. (2013) |
| [12] | Altamirano, N.; Kubiznak, D.; Mann, R. B.; Sherkatghanad, Z., Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume, Galaxies, 2, 89 (2014) |
| [13] | Xu, W.; Wang, J.; Meng, X. he, Entropy relations and the application of black holes with the cosmological constant and Gauss-Bonnet term, Phys. Lett. B, 742, 225-230 (2015) · Zbl 1345.83021 |
| [14] | Dolan, B. P., Thermodynamic stability of asymptotically anti-de Sitter rotating black holes in higher dimensions (2014) · Zbl 1298.83078 |
| [15] | Gibbons, G.; Lu, H.; Page, D. N.; Pope, C., The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys., 53, 1, 49-73 (2005) · Zbl 1069.83003 |
| [16] | Meng, X.-H.; Xu, W.; Wang, J., A note on entropy relations of black hole horizons, Int. J. Mod. Phys. A, 29, 18, Article 1450088 pp. (2014) · Zbl 1294.83059 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
