Journal of Modern Physics, 2011, 2, 370-373

doi:10.4236/jmp.2011.25045 Published Online May 2011 (http://www.SciRP.org/journal/jmp)

Copyright © 2011 SciRes. JMP

Using of the Generalized Special Relativity in Deriving the

Equation of the Gravitational Red-Shift

Mahmoud Hamid Mahmoud Hilo1,2

1Department of Physics, Faculty of Education, Al-Zaiem Al-Azhari University, Omdurman, Sudan

2Department of Physics, Faculty of Science and Arts at Al-Rass, Qassim University, KSA

E-mail: mhhlo@qu.edu.sa

Received January 9, 2011; revised March 10, 2011; accepted March 21, 2011

Abstract

In this work we present a study of a new method to prove the equation of the gravitational red shift of spec-

tral lines. That’s according to the generalized special relativity theory. The equation of the gravitational red

shift of spectral lines has been studied in many different works, using different methods depending on the

Newtonian mechanics, and other theories. Although attention was drawn to the fact that the well-known ex-

pression of the gravitational Red-Shift of spectral lines may be derived with no recourse to the general rela-

tivity theory! In this study a unique derivation has been done using the Generalized Special Relativity (GSR)

and the same result obtained.

Keywords: Generalized, Red-Shift, GSR, Approximations, Gravitational

1. Introduction

In physics, light or other forms of electromagnetic radia-

tions of a certain wavelength originating from a source

placed in a region of strong gravitational field (and

which could be said to have climbed “uphill” out of the

gravity well) will be found to be longer wavelength when

received by observer in a region of weak gravitational

field [1]. If we apply to optical wave-lengths this mani-

fests itself as a change in the color of the light, the wave-

length is shifted towards the red (making it less energetic,

longer in wavelength, and lower in frequency) part of the

spectrum. This effect is called the gravitational red shift,

and the other spectral lines found in the light, will also be

shifted towards the longer wavelength, or red end of the

spectrum. This shift can be observed along the entire

electromagnetic spectrum [2].

In all basic studies involved in the theory of general

relativity, attention was drawn to the three main prob-

lems related to it, those are Well-Known advance of the

perihelion of the planet Mercury, the Gravitational De-

flection of Light Rays and the Gravitational Red-Shift of

Spectral Lines. The gravitational red-shift discussed within

the emitted rays from a particle that located in the field

of another rest particle due to a spherical symmetry (such

as Solar field), the atoms that compose the gases edges of

a rest star forms light sources in the star field, and ac-

cording to this information the Gravitational Red-Shift

obtained [3]. This study introduces a new method to ob-

tain the same result of the Gravitational Red-Shift using

the Generalized Special Relativity theory, (GSR) by

adopting the approximation of the gravitational potential.

2. Objective

Objective of this work is to prove the equation of the gra-

vitational redshift as well as to test the theory of the gen-

eralized special relativity.

3. Generlized Special Relativity (GSR)

Theory

The Generalized Special Relativity theory is a new form

of the special relativity theory that adopts the gravita-

tional potential, and it gives the formula of relative mass

to be as follows [4]:

00 0

2

00 2

v

m

m

gc

(1)

where, 00 2

2

1gc

and

denotes the gravitational po-

tential, or the field in which the mass is measured.

The derivation of the mass Equation 1 using the Gen-