Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · gr-qc/0003029

A New Way to Make Waves

Jeffrey Winicour
View original source ↗Read source document ↗Export metadata ↓

Abstract

I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other systems described by second differential order hyperbolic equations. The basic ideas should also be applicable to hydrodynamics. It is an especially accurate and efficient way for simulating waves in regions where the characteristics are well behaved. A prime application of the algorithm is to Cauchy-characteristic matching, in which this new approach is matched to a standard Cauchy evolution to obtain a global solution. In a model problem of a nonlinear wave, this proves to be more accurate and efficient than any other present method of assigning Cauchy outer boundary conditions. The approach was developed to compute the gravitational wave signal produced by collisions of two black holes. An application to colliding black holes is presented.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jeffrey Winicour. 2000-03-08. A New Way to Make Waves. https://arxiv.org/abs/gr-qc/0003029

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↗