Relativistic Dyson Rings and Their Black Hole Limit
arXiv:gr-qc/0211040 · doi:10.1086/367632
Abstract
In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.
13 pages, 1 table, 5 figures, v2: some discussion and two references added, accepted for publication in Astrophys. J. Lett
References in corpus (1)
Cited by in corpus (30)
- A single-domain spectral method for black hole puncture data
- Spectral Methods for Numerical Relativity
- Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods
- Black Holes Surrounded by Uniformly Rotating Rings
- Differentially-rotating neutron star models with a parametrized rotation profile
- On the Solution Space of Differentially Rotating Neutron Stars in General Relativity
- Gravitating discs around black holes
- Equilibrium configurations of fluids and their stability in higher dimensions
- A double-domain spectral method for black hole excision data
- Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes
- On Axisymmetric and Stationary Solutions of the Self-Gravitating Vlasov System
- On the black hole limit of rotating fluid bodies in equilibrium
- Equilibrium Configurations of Homogeneous Fluids in General Relativity
- Uniformly Rotating Rings in General Relativity
- On the black hole limit of electrically counterpoised dust configurations
- Cosmic String and Black Hole Limits of Toroidal Vlasov Bodies in General Relativity
- Maximal mass of uniformly rotating homogeneous stars in Einsteinian gravity
- Orbital perturbations due to massive rings
- On the black hole limit of rotating discs and rings
- Uniformly Rotating Homogeneous and Polytropic Rings in Newtonian Gravity
- On the bound states of the Dirac equation in the extreme Kerr metric
- Uniformly Rotating Polytropic Rings in Newtonian Gravity
- The Dirac propagator in the extreme Kerr metric
- The Parametric Transition of Strange Matter Rings to a Black Hole
- Post-Newtonian expansion of a rigidly rotating disc of dust with a constant specific charge
- Uniformly Rotating Homogeneous Rings in post-Newtonian Gravity
- Ergoregion instability in bosonic stars: scalar mode structure, universality, and weakly nonlinear effects
- Gravitational collapse in the vicinity of the extremal black hole critical point
- Bäcklund transforms of the extreme Kerr near-horizon geometry
- On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric