General Relativistic Behaviour of a Test Particle and Doppler’s Effect in a Model
Exploring the General Relativistic Behavior of Test Particles and Doppler's Effect in a Model
by Dr. Kamlesh Kumar*,
- Published in Journal of Advances and Scholarly Researches in Allied Education, E-ISSN: 2230-7540
Volume 15, Issue No. 1, Apr 2018, Pages 1200 - 1201 (2)
Published by: Ignited Minds Journals
ABSTRACT
The present paper provides the behaviour of a test particle and Doppler’s effect by considering suitable model.
KEYWORD
general relativistic, test particle, Doppler's effect, model, behaviour
1. INTRODUCTION
Taking an anisotropic magneto hydrodynamic cosmological model in general relativity. Roy and Prtakash (1) have discussed the behaviour of a test particle and Doppler‘s effect following Tolman‘s technique (2). This discussion has been further extended by Singh and Yadav & Yadav & Purushottam (3, 4) for non-static cylindrically cosmological model which is spatially homogenous non-degenerate petrov type-1. In this paper we have also investigated the behaviour of a test particle and red shift (Doppler‘s effect) for the model given by line element. which is of the form where A.B. = C are functions of t only Clearly
2. BEHAVIOUR OF A TEST PARTICLE IN THE MODEL
The equation of geodesic viz. For the metric (1.1) when i = 2, 3, 4 are given by If a particle is initially at rest, that is, if The from equations of geodesic we find that for all such particles the components of spatial acceleration would vanish, namely. and the particle would remain permanently at rest.
3. THE DOPPLER EFFECT IN THE MODEL
The track of a light pulse in the model is obtained by setting For the case when velocity is along z axis equation (3.1) gives
Hence the light pulse leaving a particle at (0, 0, z) at time t1 would arrive at a later time t2 given by where zdzUdt is the z-component of the velocity of the particle at the time of emission, 12(t)and(t) are the value of (t) for t = t1 and t = t2 respectively. From the above equation we get The proper time interval 01tbetween the successive wave crests as measured by the local observer moving with the source is given by This can be written as where U is the velocity of the source at the time of emission, similarly we may write. as the proper time interval between the reception of two successive wave crests by an observer at rest at the origin. Hence following Tolman (2) the red shift in this case is given by
4. REFERENCES
1. Roy. S.R. and Prakash. S. (1978). Indian J. Phys., 52 B, pp. 47. 3. Singh. T. and Yadav, R.B.S. (1980); Indian J. Pure Appl. Maths, 11 (7), pp. 917. 4. Yadav, R.B.S. & Purushottam (2004); Acta Ciencia Indica, 30, pp. 629.
Corresponding Author Dr. Kamlesh Kumar*
+ 2 B.N. High School Agandha, Shabpur, Belaganj, Gaya
