Energy Balance of a Bose Gas in Curved Spacetime
Tonatiuh Matos, Ana Avilez, Tula Bernal, Pierre-Henri Chavanis
TL;DR
This paper develops an energy balance equation for a zero-temperature Bose gas in curved spacetime, advancing the understanding of thermodynamics for scalar fields in general relativity.
Contribution
It introduces a hydrodynamic formulation of the Klein-Gordon-Maxwell equations in curved spacetime, identifying various energy contributions.
Findings
Derived a general energy balance equation for a Bose gas in curved spacetime
Reformulated Klein-Gordon-Maxwell equations into hydrodynamic form
Separated energy contributions into kinetic, quantum, electromagnetic, and gravitational
Abstract
We derive a general energy balance equation for a self-interacting boson gas at vanishing temperature in a curved spacetime. This represents a first step towards a formulation of the first law of thermodynamics for a scalar field in general relativity. By using a foliation of the spacetime and performing a Madelung transformation, we rewrite the Klein-Gordon-Maxwell equations in a general curved spacetime into its hydrodynamic version where we can identify the different energy contributions of the system and separate them into kinetic, quantum, electromagnetic, and gravitational.
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