Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/0701081

Slowly Rotating Homogeneous Stars and the Heun Equation

David Petroff
View original source ↗Read source document ↗Export metadata ↓

Abstract

The scheme developed by Hartle for describing slowly rotating bodies in 1967 was applied to the simple model of constant density by Chandrasekhar and Miller in 1974. The pivotal equation one has to solve turns out to be one of Heun's equations. After a brief discussion of this equation and the chances of finding a closed form solution, a quickly converging series solution of it is presented. A comparison with numerical solutions of the full Einstein equations allows one to truncate the series at an order appropriate to the slow rotation approximation. The truncated solution is then used to provide explicit expressions for the metric.

Explore related subjects

gr-qcmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

David Petroff. 2007-02-06. Slowly Rotating Homogeneous Stars and the Heun Equation. https://doi.org/10.1088/0264-9381%2F24%2F5%2F003

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Bounds on the minimum orbital period in the background of 5-dimensional charged black holes

In this paper, we study the upper and lower bounds on the minimum orbital period of 5-dimensional charged black holes. Our results indicate that the upper bound of the minimum orbital period corresponds to non-charged black holes, while the lower bound is achieved in the case of maximally charged black holes. We further establish precise analytical expressions for the upper and lower bounds of the minimum orbital period. Our findings provide valuable insights into 5-dimensional charged black holes and help constrain theoretical gravity models.

gr-qc↗
arXiv2026

Analysis of minimum orbital periods around d-dimensional charged black holes

This paper investigates the bounds on the minimum orbital period for test objects around d-dimensional charged black holes in asymptotically flat spacetimes. We derive the exact critical radius and the minimum orbital period. We then prove analytically that the minimum orbital period decreases strictly as the charge of the black hole increases. Thus, the upper limit is reached for an uncharged black hole, while the lower limit is attained for a maximally charged one, and the two bounds take the closed form $\frac{2π(d-2)}{d-3}[(d-2)M]^{\frac{1}{d-3}}\leqslant T_{min} \leqslant 2π\sqrt{\frac{d-1}{d-3}}\,[(d-1)M]^{\frac{1}{d-3}}$. Since the minimum period equals $2π$ times the shadow radius, the upper bound is equivalently a universal upper bound on the shadow radius. These results improve our understanding of dynamics around d-dimensional black holes and impose constraints on candidate gravity theories.

gr-qc↗