Ideal Fluids In Born-Infeld Inspired Gravity

TL;DR

This work develops a Palatini formulation of Born-Infeld Inspired Gravity (BIMG) and its coupling to matter currents, deriving the complete set of equations of motion for the metric, connection, and current. By introducing an auxiliary metric and a Brown-type perfect-fluid action, it demonstrates current conservation $\nabla_\mu j^\mu = 0$ and a conserved stress-energy tensor that reduces to the ideal-fluid form under Brown identifications, yielding a GR-like gravitational dynamics with Born-Infeld corrections. It also shows an alternative current-coupling construction that is dynamically equivalent to the original BIMG when appropriate field redefinitions are performed. Finally, the canonical (Hamiltonian) formulation is developed, obtaining a diffeomorphism-invariant action with four constraints after eliminating non-dynamical fields, providing a robust framework for exploring BI corrections in cosmological and gravitational contexts with matter currents.

Abstract

In this short note we study Born-Infeld Inspired Gravity together with an action functional for ideal fluid. We obtain corresponding equations of motion and also determine canonical form of this action.