Sensitivity of the scalar self-force on the compactness of anisotropic relativistic stars

Abstract

The compactness of an isotropic star is bounded above by the Buchdahl bound, which means that no isotropic stellar configurations exist that have compactnesses between the Buchdahl bound and the Schwarzschild black hole compactness. When we relax the condition for isotropy, stellar models can admit configurations whose compactnesses not only exceed the Buchdahl bound but also asymptotically approach the Schwarzschild case for increasing central pressures. This makes studying anisotropic stars a possible way towards understanding the nature of black hole mimickers. For these highly compact anisotropic configurations, the self-force on a static scalar charge in the star's exterior was found to be sensitive to small changes in compactness. In particular, we observed a possible rapid decrease in the self-force as we asymptotically approach the black hole compactness.