Year: 2017
Type: article
Abstract: We derive spherically symmetric solutions of the classical $\ensuremath{\lambda}\text{\ensuremath{-}}R$ model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a $3+1$ decomposition of the four-metric in a general spherically symmetric ansatz, we perform a phase space analysis of the reduced model. We show that its constraint algebra is consistent with that of the full $\ensuremath{\lambda}\text{\ensuremath{-}}R$ model, and also yields a constant mean curvature or maximal slicing condition as a tertiary constraint. Although the solutions contain the standard Schwarzschild geometry for the general relativistic value $\ensuremath{\lambda}=1$ or for vanishing mean extrinsic curvature $K$, they are in general nonstatic, incompatible with asymptotic flatness, and parametrized not only by a conserved mass. We show by explicit computation that the four-dimensional Ricci scalar of the solutions is in general time dependent and nonvanishing.
Institution: Radboud University Nijmegen
Language: Latvian
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3170399729