General relativistic study of the neutrino path and calculation of the minimum photosphere for different stars

A detailed general relativistic (GR) calculation of the neutrino path for a general metric describing a rotating star is studied. We have calculated the neutrino path along the equatorial and polar plane. The expression for the minimum photosphere radius (MPR) is obtained and matched with the Schwarzschild limit. The MPR is calculated for the stars with two different equations of state (EOS) each rotating with two different velocities, to analyze the dependence of EOS and rotational velocity on the MPR. The results show that the MPR for the hadronic star is much greater than the quark star and the MPR increases as the rotational velocity of the star decreases. The MPR along the polar plane is larger than that along the equatorial plane.

Figure 1

Variation of pressure with energy density for quark and hadronic matter EOS.

Figure 2

Variation of pressure along the radial direction of the star for two different rotational velocities each with two different values of $\chi$ for the quark matter EOS.

Figure 3

Variation of pressure along the radial direction of the star for two different rotational velocities each with two different values of $\chi$ for the hadronic matter EOS.

Figure 4

Variation of energy density along the radial direction of the star for two different rotational velocities each with two different values of $\chi$ for the quark matter EOS.

Figure 5

Variation of energy density along the radial direction of the star for two different rotational velocities each with two different values of $\chi$ for the hadronic matter EOS.