Constructing a family of probability distributions with Schwarzschild as information metric

Abstract

We explore the inverse problem in information geometry. A family of probability distributions with the (Euclidean) Schwarzschild metric as the Fisher information metric is constructed using the method developed by Clingman, Murugan, and Shock and the Fronsdal embedding of Schwarzschild into flat space. We study the fate of the isometries of Schwarzschild under this mapping. We provide a potential connection with a thermodynamic system described by a Hamiltonian in the presence of a gauge field.