Mechanics of geodesics in Information geometry and Black Hole Thermodynamics

TL;DR

This paper explores the mechanics of geodesics in information geometry, applying the theory to astrophysical models including black hole thermodynamics, and introduces a framework connecting gradient flows, Finsler metrics, and Hamiltonian mechanics.

Contribution

It develops a novel approach linking information geometry geodesics with black hole thermodynamics, incorporating deformations and constraints to unify various geometric and physical concepts.

Findings

Gradient flows describe geodesics in information geometry.

Deformation leads to Randers-Finsler metrics.

Application to black hole thermodynamics and Gaussian models.

Abstract

In this article we shall discuss the theory of geodesics in information geometry, and an application in astrophysics. We will study how gradient flows in information geometry describe geodesics, explore the related mechanics by introducing a constraint, and apply our theory to Gaussian model and black hole thermodynamics. Thus, we demonstrate how deformation of gradient flows leads to more general Randers-Finsler metrics, describe Hamiltonian mechanics that derive from a constraint, and prove duality via canonical transformation. We also verified our theories for a deformation of the Gaussian model, and described dynamical evolution of flat metrics for Kerr and Reissner-Nordstr\"om black holes.