CONTRIBUTION OF VACUUM FIELD TO ANGULAR DEVIATION OF LIGHT PATH AND RADAR ECHO DELAY

Abstract

The discovery of ‘twin quasistellar objects’ arose interests among astronomers and astrophysicists to study gravitational lensing problems. The deviation of light from its straight line path is caused by two sources according to the general theory of relativity: (i) the presence of massive objects, i.e. the presence of gravitational field and (ii) the presence of a ‘vacuum field’ which arises because there is a non-zero cosmological vacuum energy. Recently, the research on the relationship between cosmological constant and gravitational lensing process is rather active (see reference [1, 2, 3]. According to the Kottler space time metric, we have deduced an explicit representation of the angular deviation of light path. The deviation term is found to be simply \( - \frac{{4GM}}{{r_{{\text{min}}} c^2 }}\left( {\frac{\Lambda }{6}r_{_{{\text{min}}} }^2 } \right)\), where M is the mass of the ‘astronomical lens’, rmin is the distance between the point of nearest approach and the centre of M, other symbols have their usual meaning. The presence of this term may be meaningful to the study of cosmological constant using the concept of gravitational lensing; however more sophisticated analysis awaits. Consider a signal radar to be sent from one planet to another. We have found that the radar echo delay contributed by the existence of the cosmological constant Λ is expressible as \(\frac{{2\Lambda }}{{9c}}\left( {r_{_A }^3 + r_{_B }^3 } \right)\left[ {1 - \frac{{r_{_{{\text{min}}} }^2 }}{{2r^2 _A }} + \frac{{r_{_{{\text{min}}} }^2 }}{{2r^2 _B }}} \right]\)