Abstract
We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume. When the energy of the particle is considered to contribute to the internal energy of the black hole, the variation exactly corresponds to the prediction of the first law of thermodynamics. Nevertheless, we find the decrease of the Bekenstein-Hawking entropy for extremal and near-extremal black holes under the absorption, which is an irreversible process. This violation of the second law of thermodynamics is only found when considering thermodynamic volume. We test the weak cosmic censorship conjecture affected by the violation. Fortunately, the conjecture is still valid, but extremal and near-extremal black holes do not change their configurations when any particle enters the black hole. This result is quite different from the case in which thermodynamic volume is not considered.
Highlights
JHEP11(2017)129 conducted on the conjecture for black holes of Einstein’s theory of gravity, and anti-de Sitter (AdS), lower-dimensional, and higher-dimensional black holes [18,19,20,21,22,23,24,25,26,27,28,29,30]
We investigate the variation of the charged anti-de Sitter black hole under charged particle absorption by considering thermodynamic volume
We prove that the variation in the D-dimensional charged AdS black hole including four dimensions due to charged particle absorption follows the first law of thermodynamics in consideration the thermodynamic volume term
Summary
Where the spacetime dimensions are denoted as D ≥ 4. When the black hole absorbs the particle, the conserved quantities of the particle can perturb both the mass and charge of the black hole, and the AdS radius is affected by these changes owing to the contribution of thermodynamic pressure and volume. By absorbing the charged particle, the black hole is varied by as much as the variation in the particle, assuming no loss of conserved quantities in this process This is supported by the change in the black hole following the first law of thermodynamics. The charge in the particle q is coincident to the change of the charge of the black hole dQb. Because the energy of the particle is only given as q and |pr| at the horizon in eq (3.8), we must find a thermodynamic potential of which the variables change by q and |pr|. This implies that the entropy needs a correction term to resolve the violation when we consider thermodynamic pressure and volume
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