2010/04/30 by José P. S. Lemos, Vilson T. Zanchin · 37 citations
Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Charge (physics) #Classical mechanics #Cosmology and Gravitation Theories #General relativity #Gravitation #Mathematical physics #Perfect fluid #Physics #Quantum mechanics #Relativity and Gravitational Theory #Stars #astro-ph.SR #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.81.124016
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 81(12) (American Physical Society) · 16 pages, 8 figures; minor changes
openalex publication_date 2010/06/04 · arxiv created 2010/07/28 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In general relativity coupled to Maxwell's electromagnetism and charged matter, when the gravitational potential W2 and the electric potential field \ensuremathφ obey a relation of the form W2=a(\ensuremath-ϵ\ensuremathφ+b)2+c, where a, b, and c are arbitrary constants, and ϵ=\ifmmode±\else\textpm\fi1 (the speed of light c and Newton's constant G are put to one), a class of very interesting electrically charged systems with pressure arises. We call the relation above between W and \ensuremathφ, the Weyl-Guilfoyle relation, and it generalizes the usual Weyl relation, for which a=1. For both, Weyl and Weyl-Guilfoyle relations, the electrically charged fluid, if present, may have nonzero pressure. Fluids obeying the Weyl-Guilfoyle relation are called Weyl-Guilfoyle fluids. These fluids, under the assumption of spherical symmetry, exhibit solutions which can be matched to the electrovacuum Reissner-Nordstr"om spacetime to yield global asymptotically flat cold charged stars. We show that a particular spherically symmetric class of stars found by Guilfoyle has a well-behaved limit which corresponds to an extremal Reissner-Nordstr"om quasiblack hole with pressure, i.e., in which the fluid inside the quasihorizon has electric charge and pressure, and the geometry outside the quasihorizon is given by the extremal Reissner-Nordstr"om metric. The main physical properties of such charged stars and quasiblack holes with pressure are analyzed. An important development provided by these stars and quasiblack holes is that without pressure the solutions, Majumdar-Papapetrou solutions, are unstable to kinetic perturbations. Solutions with pressure may avoid this instability. If stable, these cold quasiblack holes with pressure, i.e., these compact relativistic charged spheres, are really frozen stars.