States in Quantum Gravity can be defined by a partition function (analogous to statistical mechanics). In Gravity, this partition function is defined to be a path integral over all metrics that obey certain boundary conditions. In Euclidean Quantum Gravity the partition function is dominated by solutions that obey the Principle of least action. Accordingly, the dominating state will be the one minimizing the action. The action depends on the temperature and changes for different metrics. This enabled Hawking and Page to show that the spacetime will undergo a first-order phase transition at a specific temperature. In my research, I firstly reproduced results for the temperature of the phase transition for charged black holes in (d+1) spacetime dimensions. Later on, I analyzed the stability of a state in the microcanonical ensemble. Professor Marolf found an operator that projected a state into a microcanonical ensemble, fixing the energy. Our concern was that this state might be unstable. My calculations aim to research the impact of those perturbations on the action to determine if the state is stable.
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