Gravitational collapse of relativistic compact objects in higher dimension

In this work, we present an iterative method for gravitational collapse in higher dimensions. A framework is developed in a post-quasi-static regime with non-comoving coordinates. The internal five-dimensional system is smoothly matched with the corresponding outer Vaidya space-time over the boundary surface (BS). This correspondence provides a set of dimensionless surface equations in higher dimensions. The physical quantities such as Doppler shift, luminosity, and redshift at the BS of gravitating systems can be described through these surface equations. This procedure offers valuable insights that facilitate comprehension of the behavior of compact objects.