Stability of relativistic Bondi accretion in Schwarzschild-(anti-)de Sitter spacetimes

In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary conditions.Comment: 6 page

Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaitre-Robertson-Walker spacetimes: Stability and isoperimetric inequalities

We investigate toroidal Marginally Outer Trapped Surfaces (MOTS) and Marginally Outer Trapped Tubes (MOTT) in closed Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. They are constructed by embedding Constant Mean Curvature (CMC) Clifford tori in a FLRW spacetime. This construction is used to assess the quality of certain isoperimetric inequalities, recently proved in axial symmetry. Similarly to spherically symmetric MOTS existing in FLRW spacetimes, the toroidal ones are also unstable.Comment: 7 pages, 2 figure

Accretion of the Vlasov gas on Reissner-Nordstr\"{o}m black holes

We investigate stationary spherically symmetric accretion of the relativistic Vlasov gas on Reissner-Nordstr\"{o}m black holes. The model is based on a recent analysis done by Rioseco and Sarbach for the Schwarzschild spacetime. Both models share many common features: The gas characterized by the Maxwell-J\"{u}ttner distribution at infinity is no longer in thermal equilibrium in the vicinity of the black hole. The radial pressure at the black-hole horizon can be even an order of magnitude smaller than the tangential pressure. Quantitative characteristics of the Reissner-Nordstr\"{o}m model depend on the charge parameter. For black holes with fixed asymptotic mass, the mass accretion rate decreases with the increasing black-hole charge. The ratio of the tangential pressure to the radial pressure at the horizon also decreases with the increasing charge. On the other hand, the particle density at the horizon (normalized by its asymptotic value) grows with the black-hole charge parameter.Comment: 22 pages, 22 figure

Spherically symmetric Riemannian manifolds of constant scalar curvature and their conformally flat representations

All spherically symmetric Riemannian metrics of constant scalar curvature in any dimension can be written down in a simple form using areal coordinates. All spherical metrics are conformally flat, so we search for the conformally flat representations of these geometries. We find all solutions for the conformal factor in 3, 4 and 6 dimensions. We write them in closed form, either in terms of elliptic or elementary functions. We are particularly interested in 3-dimensional spaces because of the link to General Relativity. In particular, all 3-dimensional constant negative scalar curvature spherical manifolds can be embedded as constant mean curvature surfaces in appropriate Schwarzschild solutions. Our approach, although not the simplest one, is linked to the Lichnerowicz-York method of finding initial data for Einstein equations.Comment: 18 pages, 3 figures, to appear in Class. Quantum Gra