Spherical solutions in Einstein-aether theory: static aether and stars

Abstract

The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness restricts to two parameters, and requiring that the aether be aligned with the timelike Killing field further restricts to one parameter, the total mass. These "static aether" solutions are given analytically up to solution of a transcendental equation. The positive mass solutions have spatial geometry with a minimal area 2-sphere, inside of which the area diverges at a curvature singularity occurring at an extremal Killing horizon that lies at a finite affine parameter along a radial null geodesic. Regular perfect fluid star solutions are shown to exist with static aether exteriors, and the range of stability for constant density stars is identified.

Solutions with throats in Hořava gravity with cosmological constant

“…We give in advance that the asymptotia we find (at one of the sides of the throat) is not exactly anti-de Sitter, but rather a deformation of it. At the other side there is an essential singularity similar to the one found in the inner side of the Λ = 0 case [15,21].…”

“…N diverges and h goes to zero at χ → −∞ (r → 0); whereas N and h diverge as χ → χ sential singularity. The behavior of N 2 and h at this asymptotic limit is completely equivalent to what happens in the infinite boundary of the inner side of the Λ = 0 solution [15,21].…”

“…Actually, the solutions of Ref. [15] were found in the context of the Einstein-aether theory [17]. The correspondence comes from the equivalence this theory has with the second-order effective action of the Hořava theory [12,18,19].…”

“…[21] we recovered the same solutions of Ref. [15] but explicitly on a coordinate system valid at the throat. In particular this allows to show directly that the physical radius r has a minimum at the throat.…”

A cyclic universe with colour fields

“…a sphere), ∈ {S 3 }, of radius R ∈ (−∞ +∞) formed of a massless elastic fluid -a collection of worldlines of test particles. The rotation of corresponds to a 4-velocity u of the fluid in all possible directions through each point of the spatial slice of the manifold (for a discussion of spinning 3-manifolds see, e.g., [126][127][128][129][130][131]). Let the manifold be punctured, → \{0}, that is, containing a point-like discontinuity σ , which we shall use to represent a singularity ( Fig.…”