A biorthogonal alpha-deformed Fubini-Study geometry is constructed, giving dual connections and a four-way classification of metric and Berry-curvature tensors for non-Hermitian quantum systems.
On the Thermodynamic Geometry of BTZ Black Holes
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abstract
We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.
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Generalised state space geometry in Hermitian and non-Hermitian quantum systems
A biorthogonal alpha-deformed Fubini-Study geometry is constructed, giving dual connections and a four-way classification of metric and Berry-curvature tensors for non-Hermitian quantum systems.