Publication date: Feb 2017
Abstract:
We demonstrate that in the framework of standard general relativity,
polytropic spheres with properly fixed polytropic index n and
relativistic parameter σ , giving a ratio of the central pressure
pc to the central energy density ρc , can contain
a region of trapped null geodesics. Such trapping polytropes can exist
for n >2.138 , and they are generally much more extended and massive
than the observed neutron stars. We show that in the n – σ parameter
space, the region of allowed trapping increases with the polytropic
index for intervals of physical interest, 2.138 <n <4 . Space
extension of the region of trapped null geodesics increases with both
increasing n and σ >0.677 from the allowed region. In order to relate
the trapping phenomenon to astrophysically relevant situations, we
restrict the validity of the polytropic configurations to their
extension rextr corresponding to the gravitational mass M ̃2
M☉ of the most massive observed neutron stars. Then, for the
central density ρc̃1 015 g cm-3 , the
trapped regions are outside rextr for all values of 2.138
<n <4 ; for the central density ρc̃5 ×1 015
g cm-3 , the whole trapped regions are located inside
rextr for 2.138 <n <3.1 ; while for ρc̃1
016 g cm-3 , the whole trapped regions are inside
rextr for all values of 2.138 <n <4 , guaranteeing
astrophysically plausible trapping for all considered polytropes. The
region of trapped null geodesics is located close to the polytrope
center and could have a relevant influence on the cooling of such
polytropes or binding of gravitational waves in their interior.
Authors:
Novotný, Jan; Hladík, Jan; Stuchlík, Zdeněk;