Abstract
Static spherically symmetric solutions to the Einstein–Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the latter case, the matter extends globally with the density approaching zero at infinity. The asymptotic behavior largely depends on the equation of state of the fluid and is still poorly understood. While a few such unbounded solutions are known to be asymptotically flat with finite ADM mass, the vast majority are not. We provide a full geometric description of the asymptotic behavior of static spherically symmetric perfect fluid solutions with linear equations of state and polytropic-type equations of state with index n>5. In order to capture the asymptotic behavior, we introduce a notion of scaled quasi-asymptotic flatness, which encompasses the notion of asymptotic conicality. In particular, these spacetimes are asymptotically simple.
Highlights
Perfect fluids in general relativity are described by the Einstein–Euler equations, i.e., Gαβ = 8πTαβ, ∇αT αβ = 0, (1.1)
We provide a geometric description of the asymptotic behavior of solutions to (1.4) with linear equation of state (1.6) and power-law polytropic equation of state (1.9) with index n > 5
We show that spherically symmetric static perfect fluids with linear equation of state are so-called quasiasymptotically flat, a concept developed by Nucamendi and Sudarsky [60] which generalizes the notion of asymptotic flatness and at the same time admits conformal compactifications
Summary
Perfect fluids in general relativity are described by the Einstein–Euler equations, i.e., Gαβ = 8πTαβ, ∇αT αβ = 0,. Tαβ = (ρ + p)uαuβ + p gαβ, where ρ denotes the proper energy density, p the pressure and uα the velocity vector normalized to uαuα = −1. The gravitational constant and the speed of light are normalized, i.e., G = c = 1. Y. Burtscher Ann. Henri Poincare unless we prescribe a so-called equation of state, p = p(ρ), relating the pressure and proper energy density
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
