Journal of Applied Mathematics and Physics, 2014, 2, 50-54

Published Online April 2014 in SciRes. http://www.scirp.org/journal/jamp

http://dx.doi.org/10.4236/jamp.2014.25007

How to cite this paper: Petry, W. (2014) Gravitation in Flat Space-Time and General Relativity. Journal of Applied

Mathematics and Physics, 2, 50-54. http://dx.doi.org/10.4236/jamp.2014.25007

Gravitation in Flat Space-Time and General

Relativity

Walter Petry

Mathematical Institute of the University Duesseldorf, Duesseldorf, Germany

Email: wpetr y @med use.d e, petryw@uni-duesseldorf.de

Received January 2014

Abstract

A covariant theory of gravitation in flat space-time is stated and compared with general relativity.

The results of the theory of gravitation in flat space-time and of general relativity agree for weak

gravitational fields to low approximations. For strong fields the results of the two theories deviate

from one another. Flat space-time theory of gravitation gives under some natural assumptions

non-singular cosmological models with a flat space. The universe contracts to a positive minimum

and then it expands for all times. Shortly, after the minimum is reached, the cosmological models

of two theories approximately agree with one another if models in general relativity with z ero

curvature are considered. A flat space is proved by experiments.

Keywords

Gravi tati on , Flat Space-Ti me, Cosmology, Big Bounce, No Big Bang, Flat Space

1. Introduction

A previously studied covariant theory of gravitation in flat space-time is stated [1]. The energy-momentum of

the gravitational field is a tensor. The source of the gravitational field is the total energy-momentum of all the

fields inclusive that of gravitation. This is quite different from general relativity for which the energy-mo men-

tum of gravitation is not a tensor. Hence, the energy-momentum of the gravitational field cannot explicitly ap-

pear as source by virtue of the covariance of general relativity. Therefore, the Ricci tensor is used as differential

operator yielding a non-Euclidean geometry. An extensive study exists of flat space-time theory of gra vitation. It

follows that the results of the two theories agree with one another for weak field approximations but there are

differences if the gravitational fields are strong. Therefore, the theory of flat space-time theory is applied to ho-

mogeneous, isotropic cosmological models where only matter and radiation are considered. A cosmological

constant could also be included [2]. The universe is non-singular under the assumption that the sum of the den-

sity parameters is a little bit greater than one. In the beginning of the universe there is no matter and no radiation.

The universe contacts to a small minimum creating matter and radiation with very high temperature. All the

densities of matter and radiation are always finite. After the minimum is reached the universe expands for all

times. Shortly after the time when the minimum is reached the results of the two theories approximately agree if

a vanishing curvature of general relativity is assumed. The space of flat space-time theory of gravitation is flat,

i.e. there is no necessity of inflation in the beginning of the universe in contrast to general relativity where strong