Particle Motion in the Rotating Black Ring Metric

Abstract

In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic equations can be examined analytically - specifically geodesics confined to the axis of rotation, geodesics restricted to the equatorial plane, and geodesics that circle through the centre of the ring. The geodesics on the rotational axis behave like a particle in a potential well, while the geodesics confined to the equatorial plane mimic those of the Schwarzschild metric. It is shown that it is impossible to have circular orbits that pass through the ring, but some numerical results are presented which suggest that it is possible to have bound orbits that circle through the ring.

36 pages, 19 figures, updated references, section 5 modified to remove ambiguity in discussion

References in corpus (12)

• New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
• The holographic principle
• A rotating black ring in five dimensions
• Black Rings
• Particle and light motion in a space-time of a five-dimensional rotating black hole
• Exact Standard model Structures from Intersecting D5-Branes
• Black Rings, Supertubes, and a Stringy Resolution of Black Hole Non-Uniqueness
• Black ring with two angular momenta
• Dynamics and Stability of Black Rings
• Energy Extraction from Higher Dimensional Black Holes and Black Rings
• Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions
• Brane World Black Rings

Cited by in corpus (15)

• Black holes die hard: can one spin-up a black hole past extremality?
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Geodesic Motion in the Singly Spinning Black Ring Spacetime
• Geodesics and Symmetries of Doubly-Spinning Black Rings
• Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime
• Stable Bound Orbits of Massless Particles around a Black Ring
• Chaos in Geodesic Motion around a Black Ring
• Stable Bound Orbits around Black Rings
• The Stable Trapping Phenomenon for Black Strings and Black Rings and its Obstructions on the Decay of Linear Waves
• Stable circular orbits in higher-dimensional multi-black hole spacetimes
• Stable circular orbits in caged black hole spacetimes
• Particle dynamics in the Newtonian potential sourced by a homogeneous circular ring
• Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring
• Chaotic particle motion around a homogeneous circular ring
• Hidden Symmetries and Black Holes