Stability of Quantum Isolated Horizon : A Local Observer's View

It is shown that a Quantum Isolated Horizon(QIH), as observed by a local observer, is locally unstable as a thermodynamic system. The result is derived in two different ways. Firstly, the specific heat of the QIH is shown to be negative definite through a quantum statistical analysis. Then, it is shown, in the thermal holographic approach, that the canonical partition function of the QIH diverges under Gaussian thermal fluctuations of such energy spectrum, implying local instability of such a QIH as a thermodynamic system.