Overturning and cracking of stellar objects in modified $$f(R, \varphi )$$ gravity

Abstract This study extends the concept of cracking to self-gravitating, spherically symmetric compact objects in modified $$f(R, \varphi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>φ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory of gravity, where R represents the Ricci scalar, and $$\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> is the scalar potential. In this regard, we consider spherically symmetric spacetime characterized with an anisotropic matter to detect the instabilities of self-gravitating compact objects via cracking and overturning. Further, we construct the general framework to observe the cracking and overturning points by applying the local density perturbation technique to the configuration governed by barotropic equation of state. The effectiveness of this approach is assessed by analyzing its results on the data of Her X-1, SAX J1808.4-3658, and 4U 1820-30 respectively. It is concluded that cracking points appear in the different interior regions of these three stars. Significantly, this study illustrates the effectiveness of the cracking approach by highlighting the regions sensitive to localized density disruptions, offering valuable insights into the structural behavior of compact stars within a modified gravity framework.