Self-gravitating isothermal equilibria in Eddington-inspired Born--Infeld gravity: exact planar sheets and the Bonnor--Ebert critical mass
Abstract
We study self-gravitating fluid equilibria in the Newtonian limit of Eddington-inspired Born--Infeld (EiBI) gravity, in which the Poisson equation acquires a term proportional to the Laplacian of the density. We show that this term is equivalent, for arbitrary flows, to an effective pressure p+χρ2/8, so that equilibrium and radial stability reduce exactly to Newtonian problems with a modified equation of state. For pressure-bounded isothermal spheres we compute the EiBI generalization of the Bonnor--Ebert critical mass as a function of the single parameter ε=χPext/4cs4, and confirm each change of stability with a radial-pulsation analysis. Near ε=0 the critical mass grows as MBE(1+5.74 ε). For ε>0.0302 no isothermal sphere is radially unstable, so a positive EiBI parameter removes the Bonnor--Ebert instability; for smaller positive ε a stable high-density branch supported by the EiBI pressure follows the unstable one. For ε<−0.154 the mass limit is set instead by the vanishing of the central effective sound speed, and is a loss of equilibrium rather than an instability. In planar geometry the same reduction yields an exact first integral, closed-form isothermal sheets with a maximum column density 2cs2/√(πG|χ|) for χ<0, and a complete classification of adiabatic γ=3 sheets.
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BibTeX
@misc{chakrabarti2026selfgravitating,
title = {{Self-gravitating isothermal equilibria in Eddington-inspired Born--Infeld gravity: exact planar sheets and the Bonnor--Ebert critical mass}},
author = {Nikhil Chakrabarti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30716},
eprint = {2610.30716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30716},
}
RIS
TY - UNPB
TI - Self-gravitating isothermal equilibria in Eddington-inspired Born--Infeld gravity: exact planar sheets and the Bonnor--Ebert critical mass
AU - Nikhil Chakrabarti
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30716
UR - https://arxiv.org/abs/2610.30716
AB - We study self-gravitating fluid equilibria in the Newtonian limit of Eddington-inspired Born--Infeld (EiBI) gravity, in which the Poisson equation acquires a term proportional to the Laplacian of the density. We show that this term is equivalent, for arbitrary flows, to an effective pressure p+χρ^2/8, so that equilibrium and radial stability reduce exactly to Newtonian problems with a modified equation of state. For pressure-bounded isothermal spheres we compute the EiBI generalization of the Bonnor--Ebert critical mass as a function of the single parameter ε=χP_ext/4c_s^4, and confirm each change of stability with a radial-pulsation analysis. Near ε=0 the critical mass grows as M_BE(1+5.74 ε). For ε>0.0302 no isothermal sphere is radially unstable, so a positive EiBI parameter removes the Bonnor--Ebert instability; for smaller positive ε a stable high-density branch supported by the EiBI pressure follows the unstable one. For ε<−0.154 the mass limit is set instead by the vanishing of the central effective sound speed, and is a loss of equilibrium rather than an instability. In planar geometry the same reduction yields an exact first integral, closed-form isothermal sheets with a maximum column density 2c_s^2/√(πG|χ|) for χ<0, and a complete classification of adiabatic γ=3 sheets.
ER -