Find the attached file.

Dear Prof. Herrera, since $p_t$ acts perpendicular to $p_r$, does it mean that $p_t$ will produce a rotational motion on the particles at interior? What will be the effect of anisotropy on a collapsing star?

No, rotations are excluded by the spherical symmetry. (in the case you are considering such a case.  The effect of anisotropy consists in the appearance of an additional "force" term, besides the pressure gradient.

The above mentioned force term, of course, is directed along the radial direction.

THANKS  Prof Herrera for your prompt reply !

Prof. Herrera, that means, due to the presence of anisotropy, the collapse will be delayed ? 

It might be. It will depend on the type of anisotropy.

Thank you so much Prof. Herrera. This idea seems to agree with our new solution that represents a collapsing star with non-zero anisotropy. We have analysed the time evolution of all the physical quantities and found to delayed due to anisotropy. Again we found more anisotropy implies more delayed.

Dear sir, anisotropy may or may not delay the collapse rate it depends on type of anisotropy as said by Prof. Herrera i.e. radial pressure is greater or less than the tangential pressure.

Here pr 0 and thus exert an outward force. Therefore it is clearly seen that positive anisotropy force will delay the collapsing possess. 

I think everyone is forgetting that the interior of stars represents a complex plasma in its physics more than an ideal gas under hydrostatic equilibrium.  Yes there is no LARGE SCALE asymmetry but there are important small scale effects.

1.  We do know something about seismicity in the solar fluid through the solar helioseismology project.  Bulk internal movements, which can move significant amounts of mass, can produce temporal anisotropies.

2.  The role that magnetic fields play in the internal structures of stars is virtually unknown and may cause important effects

Also, in the latter part of stellar evolution when the core is degenerate there may be some important effects as well

yes

Following.