Universality of isothermal fluid spheres in Lovelock gravity

TL;DR

This paper demonstrates that isothermal fluid spheres in pure Lovelock gravity exhibit a universal form across all dimensions greater than or equal to 2N+2, characterized by a specific equation of state and metric properties.

Contribution

It establishes the universality of isothermal fluid spheres in pure Lovelock gravity and characterizes their metrics as conformal to massless global monopole or solid angle deficit metrics.

Findings

Isothermal spheres exist only for pure Lovelock equations.

The form of isothermal solutions is universal across dimensions ≥ 2N+2.

The metric is conformal to a massless global monopole or solid angle deficit metric.

Abstract

We show universality of isothermal fluid spheres in pure Lovelock gravity where the equation of motion has only one $N$th order term coming from the corresponding Lovelock polynomial action of degree $N$. Isothermality is characterized by the equation of state, $p = \alpha \rho$ and the property, $\rho \sim 1/r^{2N}$. Then the solution describing isothermal spheres, which exist only for the pure Lovelock equation, is of the same form for the general Lovelock degree $N$ in all dimenions $d \geq 2N+2$. We further prove that the necessary and sufficient condition for the isothermal sphere is that its metric is conformal to the massless global monopole or the solid angle deficit metric, and this feature is also universal.