10. Chifu Ebenezer Ndikilar, Samuel Xede Kofi Howusu, Gravitational radiation and propagation field equation exterior to astrophysically real or hypothetical time varying distributions of mass within regions of spherical geometry

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Volume 22: Pages 73-77, 2009

Gravitational radiation and propagation field equation exterior to astrophysically real or hypothetical time varying distributions of mass within regions of spherical geometry

Chifu Ebenezer Ndikilar 1, Samuel Xede Kofi Howusu 2

1Physics Department, Gombe State University, P.M.B 127, Gombe State, Nigeria

2Physics Department, Kogi State University, Anyigba, Kogi State, Nigeria

In this article, we introduce an alternative method to obtain Schwarzschild’s solution to Einstein’s gravitational field equation. We then extend Schwarzschild’s solution to obtain a generalized metric exterior to all possible distributions of mass or pressure within spherical regions. The spherical gravitational radiation and propagation field equation exterior to physically real or imaginary time varying distributions of mass within spherical regions is derived. To the order of c0, c being the speed of light in vacuum, the geometrical wave equation obtained admits a solution with imaginary phase velocity of magnitude one. To the order of c2, the wave admits an imaginary speed ic in vacuum.

Keywords: Time Varying, Gravitation, Spherical Bodies, Einstein’s Field Equations, Radiation, Propagation, Schwarzschild’s Metric, General Relativity, Gravitational Waves, Generalized Exterior Metric Tensor

Received: July 28, 2008; Accepted: January 6, 2009; Published Online: February 25, 2009