Scalar Perturbations of Gravitational Collapse under Homotopy Perturbation Method: A Critical Study on the Rectangular and Price Potential

In order to unveil different features of gravitational waves due to massive objects like black hole etc., researchers primarily attempt to find the corresponding quasi normal modes from the relevant wave equations. In the present article, homotopy perturbation method (HPM) is employed to obtain the wave functions by solving wave equations for one-dimensional potential barriers. Under this scheme (i) for constant potential barrier a generalized solution which reduces to the known solution as done by Chandrasekhar and Detweiler [Proc. R. Soc. Lond. A 344 (1975) 441] is produced, (ii) the wave equation for the Price potential [Phys. Rev. D 5 (1972) 2419; Phys. Rev. D 5 (1972) 2439] by HPM is solved. The wave functions (graphically) as well as quasi-normal modes to those of the Press solution (1973) are compared. The present investigation is important in connection to further study related to the Zerilli potential and Regge-Wheeler potential in case of black hole.