By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solut

We perform a careful investigation of the problem of physically realistic gravitational collapse of massive stars in $f(R)$ gravity. We show that the extra matching conditions that arise in the modified gravity impose strong constraints on the stellar structure and thermodynamic properties. In our opinion these constraints are unphysical. We prove that no homogeneous stars with nonconstant Ricci scalar can be matched smoothly with a static exterior for any nonlinear function $f(R)$. Therefore, these extra constraints make classes of physically realistic collapse scenarios in general relativity, nonadmissible in these theories. We also find an exact solution for an inhomogeneous collapsing star in the Starobinski model that obeys all the energy and matching conditions. However, we argue that such solutions are fine-tuned and unstable to matter perturbations. Possible consequences on black hole physics and the cosmic censorship conjecture are also discussed.

We derive a radiating regular rotating black hole solution, radiating Kerr-like regular black hole solution. We achieve this by starting from the Hayward regular black hole solution via a complex transformation suggested by Newman–Janis. The radiating Kerr metric, the Kerr-like regular black hole and the standard Kerr metric are regained in the appropriate limits. The structure of the horizon-like surfaces are also determined.