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FLAT SPACE

space that has a linear characteristic

planck's constant, the speed of light and gravity can be called flat space absolutes |

^{ }), appears to be the constant temperature for the infinite distances that exist surrounding the straight line and gives rise to a physics maxim... the higher the stationary state the lower the temperature

5th april 2009

NEW RESULTS OF FLAT SPACE-TIME

THEORY OF GRAVITATION

Walter Petry

Mathematisches Institut der Universitaet Duesseldorf

D – 40225 Duesseldorf

Abstract: An explanation of the anomalous acceleration of spacecrafts in the solar system is given

A new explanation of the observed superluminal velocities at extragalactic objects is stated

The extension of quasars can be larger than generally assumed, i.e. quasars must not be very compact objects

The high energy loss per unit time of quasars can be explained

The virial theorem implies for large galaxies in addition to the law of Newton a further expression

A relation between the measured redshifts of stars rotating about the center of the galaxy and their velocities is derived

An upper bound for the radius of rotating galaxies is given

The upper bound for the structures in the cosmic microwave background stated by the satellite WMAP can be explained

All these results are received from cosmological models studied by flat space-time theory of gravitation and by use of post-Newtonian approximations of perfect fluid in these cosmological models where clocks at earlier times go faster than at present implying that the light velocity at distant objects is greater that the vacuum light velocity measured locally by the observer.

1. Introduction

NEW RESULTS OF FLAT SPACE-TIME It gives the same results as the general theory of relativity to the accuracy needed by the experiment such as: gravitational redshift, light deflection, perihelion precession, radar time delay, post-Newtonian approximation, gravitational radiation, and the precession of the spin axis of a gyroscope in the orbit of a rotating body

Birkhoff’s theorem is not valid by this gravitational theory

A summary of flat space-time theory of gravitation with these results can be found in paper [2] where references to detailed studies are given

The theory is also applied to homogeneous, isotropic cosmological models in several papers (see e.g. [3] where further references can be found)

There exist non-singular cosmological models in contrast to Einstein’s general theory of relativity

Entropy is produced and the space must be flat as recently observed

In these cosmological models a perfect fluid is considered and post-Newtonian approximations are derived [4].

In this paper the post-Newtonian approximation of a perfect fluid in the universe is used to derive several results:

(1) An explanation of the anomalous acceleration of spacecrafts in the solar system is given

This acceleration is opposite to the direction of the velocity of the spacecraft. In particular, for objects moving radially away from the Sun it is in the direction to the Sun

The study of the radio Doppler data of spacecrafts, in particular of Pioneer 10 and 11 by Anderson et al. [5] yields an anomalous acceleration of spacecrafts of about in the direction to the Sun

The effect was also confirmed by Markwardt [6]

Several explanations of this anomalous acceleration have been given (see e.g. [5] and the cited literature therein) but Anderson et al [5] conclude that no mechanism or theory can explain this anomalous acceleration

In the meantime new explanations of this effect appeared. Scheffer [7] explains the effect as the sum of several small accelerations which already have been studied by other authors and Marmet [8] illustrates the anomalous acceleration by the variation of the momentum of Pioneer 10 due to the collision with dust in the Kuiper belt.

_________

e-mail:

__wpetry@meduse.de__ (private)

__petryw@uni-duesseldorf.de__

(2) Flat space-time theory of gravitation implies that in the universe clocks at earlier times go

faster than clocks at present in contrast to those of Einstein’s theory

Therefore, an observer states that the light velocity at distant objects is greater than the measured local vacuum light velocity

This gives a new explanation of the observed superluminal velocities in extragalactic objects

This result was already stated in the paper [3]

It also yields that the estimated upper bounds of quasars are too small and the extension of the quasars can be larger, i.e. quasars must not be as compact as generally assumed.

(3) For spherically symmetric objects the virial theorem is derived from the post-Newtonian approximation in the universe

The connection between the measured shift of spectral lines of stars moving around the center of the galaxy and their velocities is given

For small galaxies the virial theorem in the universe implies Newton’s law but for large objects in addition to the Newton law a repulsive force acts. Under certain assumptions on the density of the matter distribution in the galaxy flat rotation curves can arise.

(4) An upper bound of the radius of rotating galaxies is received by considering the virial theorem on large scales using the density distribution which implies flat rotation curves.

(5) Considerations on the attractive Newton force and the repulsive force acting on matter from the beginning of the universe till the time of decoupling of matter and radiation (recombination epoch) give an estimate of the upper bound of the structures in the cosmic microwave background which is stated by the satellite WMAP.

(6) The electromagnetic radiation of moving charges in the gravitational field of a distant object is calculated implying that the high energy loss per unit time of quasars can be explained without the assumption of a black hole.