Interior solution for the Kerr metric
arXiv:1701.02098 · doi:10.1103/PhysRevD.95.024003
Abstract
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution, which is generated by an anisotropic fluid, verifies the energy conditions for a wide range of values of the parameters, and matches smoothly to the Kerr solution, thereby representing a globally regular model describing a non spherical and rotating source of gravitational field. In the spherically symmetric limit, our model converges to the well known incompressible perfect fluid solution.The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. The physical variables of the energy-momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments.
10 pages, 7 figures and 1 table. Published in Physical Revew D. arXiv admin note: substantial text overlap with arXiv:1607.02315
References in corpus (9)
- Quadrupole moments of rotating neutron stars
- From static to rotating to conformal static solutions: Rotating imperfect fluid wormholes with(out) electric or magnetic field
- The Application of the Newman-Janis Algorithm in Obtaining Interior Solutions of the Kerr Metric
- Axially symmetric static sources: A general framework and some analytical solutions
- Frame dragging, vorticity and electromagnetic fields in axially symmetric stationary spacetimes
- Axially symmetric static sources of gravitational field
- Interior Kerr solutions with the Newman-Janis algorithm starting with static physically reasonable space-times
- Generating anisotropic fluids from vacuum Ernst equations
- Family Of Rotating Anisotropic Fluid Solutions which Match to Kerr's Solution
Cited by in corpus (16)
- Rotating black holes with an anisotropic matter field
- Approximate perfect fluid solutions with quadrupole moment
- Normal gravity field in relativistic geodesy
- Physical properties of a source of the Kerr metric: Bound on the surface gravitational potential and conditions for the fragmentation
- An Exact Interior Kerr Solution
- An algorithm to generate anisotropic rotating fluids with vanishing viscosity
- Connecting the exterior gravitational field with the energy momentum tensor of axially symmetric compact objects
- An Interior Solution for the Kerr Metric: A Novel Approach
- Whom actually do multipole moments belong to?
- Deconstructing Frame Dragging
- Compact regular objects from an electrified Tolman-like density: A new interior region for the Kerr-Newman spacetime
- Physically viable rotating mass solutions surrounding Kerr black hole
- Regular Interior Solutions to the Solution of Kerr which Satisfy the Weak and the Strong Energy Conditions
- On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
- Regular Kerr black holes: Junction conditions and the matter content across the ring
- The no-hair theorems at work in the tidal disruption event AT2020afhd