Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes

@article{57443,
   author = {Stuchlík, Zdeněk and Vrba, Jaroslav},
   article_number = {9},
   doi = {http://dx.doi.org/10.1140/epjp/s13360-021-01890-2},
   keywords = {NEUTRON-STARS;FIELD;CONSTANT;DENSITY;SPHERES},
   language = {eng},
   issn = {2190-5444},
   journal = {European Physical Journal Plus},
   title = {Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes},
   url = {https://epjplus.epj.org/articles/epjplus/abs/2021/09/13360_2021_Article_1890/13360_2021_Article_1890.html},
   volume = {136},
   year = {2021}
}

TY  - JOUR
ID  - 57443
AU  - Stuchlík, Zdeněk - Vrba, Jaroslav
PY  - 2021
TI  - Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes
JF  - European Physical Journal Plus
VL  - 136
IS  - 9
SP  - "977-1"-"977-34"
EP  - "977-1"-"977-34"
SN  - 21905444
KW  - NEUTRON-STARS;FIELD;CONSTANT;DENSITY;SPHERES
UR  - https://epjplus.epj.org/articles/epjplus/abs/2021/09/13360_2021_Article_1890/13360_2021_Article_1890.html
N2  - Region of trapped null geodesics hidden inside of extremely compact objects is of astrophysical importance because of trapping of gravitational waves, or neutrinos. The trapping effect of null geodesics was extensively studied for spherically symmetric extremely compact objects. Recently, influence of rotation of the extremely compact objects on the trapping of null geodesics was treated in the simplest possible model of internal linearized Hartle-Thorne spacetime with uniform energy density distribution and uniform emissivity distribution of null geodesics. Here, we extend the study of the rotation influence on the trapping effect in the case of linearized Hartle-Thorne spacetimes based on the Tolman VII spherically symmetric solutions, where we assume the emissivity of the null geodesics proportional to the energy density of the Tolman VII object having quadratic radial profile. We demonstrate enhancement (suppression) of the trapping effect in the case of counter-rotating (co-rotating) null geodesics due to the behavior of the effective potentials and escape cones of the null geodesics in the linearized Hartle-Thorne-Tolman VII spacetimes. In dependence on the parameters of these spacetimes, we determine the "local" and "global" coefficients of efficiency of the trapping and compare the results to those related to the rotating spacetimes based on the internal Schwarzschild spacetimes. We demonstrate that in the Tolman VII spacetimes the trapping is more efficient, being allowed in objects with radii larger than those of the trapping internal Schwarzschild spacetimes, occurring even for R > 3.3 M.
ER  - 

STUCHLÍK, Zdeněk a Jaroslav VRBA. Trapping of null geodesics in slowly rotating extremely compact Tolman VII spacetimes. \textit{European Physical Journal Plus}. 2021, roč.~136, č.~9, s.~''977-1''-''977-34'', 34 s. ISSN~2190-5444. Dostupné z: https://dx.doi.org/10.1140/epjp/s13360-021-01890-2.