Buchdahl-Vaidya-Tikekar model for stellar interior in pure Lovelock gravity - II

TL;DR

This paper explores static stellar interior solutions in pure Lovelock gravity across various dimensions, revealing universal behaviors and establishing bounds on stellar compactness using the Buchdahl metric ansatz.

Contribution

It introduces a unified framework for modeling stellar interiors in pure Lovelock gravity, extending known solutions and identifying universal properties across dimensions.

Findings

Universal behavior of solutions in dimensions n ≥ 2N+2

Constant density star as the most compact configuration

All physically acceptable models lie between Schwarzschild and Finch-Skea solutions

Abstract

For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior solution, defines the most compact state of distribution while the other end is marked by the Finch-Skea model, and all the other physically tenable models lie in between these two limiting distributions.