Approximate analytical treatment of gravitational potential with relativistic correction in Bianchi type-I cosmology

Abstract

As the theory of general relativity implies corrections to the classical gravitational potential, we consider the Wheeler-DeWitt equation for anisotropically expanding homogeneous high-dimension spaces with a modified gravitational potential which includes a relativistic correction indicating the Schwarzschild radii of heavy objects. By proposing an approximation scheme, we report the wave function in terms of the Jacobi polynomial. The eigenvalue equation is reported as well.