5.1 Addendum Chapters

              Section 5.1 gives the five chapters of the Addendum. This Addendum gives mathematical analyses to support the material presented in Universe[1] and to justify its claims. Among other things, this Addendum analyzes the Schwartzschild solution of the Einstein theory and it gives a broad theoretical discussion of the Yilmaz theory. The following is a summary of the Chapters of the Addendum.

              Chapter 1 gives an introduction to the Addendum.

              Chapter 2 discusses the Schwartzschild and isotropic solutions to the Einstein gravitational field equation. This is supplemented by material in Appendix C concerning the energy-momentum tensor.

              Chapter 3 gives the calculations to prove that the Yilmaz gravitational field equation is exactly satisfied for the static Yilmaz theory. It also discusses the Poisson equation, the Einstein pseudo-tensor for the gravitational field, and the covariant derivative. The derivation by Yilmaz is given that led to the Yilmaz theory. Einstein made an approximate calculation of the wavelength shift that is produced by a gravitational field. Yilmaz replaced this with an exact calculation, and the result led to the Yilmaz theory of gravity.

              Chapter 4 (supplemented by Appendix D) applies the geodesic equations to the Yilmaz theory. These equations are used to calculate the trajectory of a light beam, a particle, or a body. The geodesic equations give the second derivatives of the four space-time coordinates along a geodesic trajectory.

              From the basic geodesic equations, formulas for the second derivatives in spherical coordinates are calculated for the case of a gravitational field having spherical symmetry. From these general formulas, specific equations are derived for (a) the Yilmaz single star solution and (b) the Yilmaz cosmology model. The geodesic equations of the Yilmaz cosmology model are analyzed to calculate the radial velocity of a galaxy versus the true distance to the galaxy.

              The basic geodesic equations are also applied in rectangular coordinates to the general static Yilmaz solution. The resultant formulas can be used to compute the trajectories of multiple bodies, including the orbits of planets, comets, etc. in our solar system

              Chapter 5. This chapter describes the general time-varying solution of he Yilmaz theory. Particular solutions of this general theory result in the static Yilmaz solution, and two time-varying solutions that represent gravitational waves. The chapter shows how a general time-varying solution can be achieved in an iterative computer program by applying differential formulas for the theory. The chapter applies the results derived in Appendix F, which prove that the Yilmaz gravitational field equation is exactly satisfied for the general time-varying Yilmaz theory.

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