Testing thermodynamic laws and weak cosmic censorship conjecture of conformal anomaly corrected AdS black hole

TL;DR

This study tests thermodynamic laws and the weak cosmic censorship conjecture for a conformal anomaly corrected AdS black hole, confirming their validity in various phase spaces through particle infall analysis.

Contribution

It provides a detailed verification of thermodynamic laws and censorship conjecture for this specific black hole model, including extended phase space considerations.

Findings

First law of thermodynamics holds in both phase spaces.

Second law is valid under certain conditions in extended phase space.

Weak cosmic censorship conjecture remains valid, horizons are preserved.

Abstract

By dropping particles into black hole, we have employed the recently new assumption [1] that the change of the black hole mass(enthalpy) should be the same amount as the energy of an infalling particle($\omega = dM$), to carefully test the laws of thermodynamics and the weak cosmic censorship conjecture of a conformal anomaly corrected AdS black hole in different phase spaces. Using the energy-momentum relation, the result shows that the first law, second law and weak cosmic censorship conjecture of black hole are all valid in the normal phase space, no violations occur. In the extended phase space, it firstly shows that the first law of black hole thermodynamics is always true in our case. Then, we interestingly find that if the condition ${d\ell} > -\left(P^r \ell^3\right)/{r_+^3}$ satisfied the variation of entropy is always positive, which means there would be no violation of the second law in the extend phase spaces. Also, it is true that there are always horizons by which the singularity is also covered. So, the configurations of the extremal and near-extremal black holes will not be changed, and there has no violation of the weak cosmic censorship conjecture. Finally, all of those conclusions are independent of the scalar curvature parameter $k$ and the conformal anomaly parameter $\tilde{\alpha}$