Eur. Phys. J. Plus (2013) 128: 83
https://doi.org/10.1140/epjp/i2013-13083-3

Regular Article

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

¹ Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran
² Department of Basic Sciences, Shahrood Branch, Islamic Azad University, Shahrood, Iran

^* e-mail: zarrinkamar.s@gmail.com

Received: 9 April 2013
Revised: 10 June 2013
Accepted: 29 June 2013
Published online: 5 August 2013

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.