Papers by Ranchhaigiri Brahma
Cornell University - arXiv, Oct 21, 2022
In this paper, we solved the Einstein's field equation and obtained a line element for static, el... more In this paper, we solved the Einstein's field equation and obtained a line element for static, ellipsoidal objects characterized by the linear eccentricity (η) instead of quadrupole parameter (q). This line element recovers the Schwarzschild line element when η is zero. In addition to that it also reduces to the Schwarzschild line element, if we neglect terms of the order of r −2 or higher which are present within the expressions for metric elements for large distances. Furthermore, as the ellipsoidal character of the derived line element is maintained by the linear eccentricity (η), which is an easily measurable parameter, this line element could be more suitable for various analytical as well as observational studies.
Deflection of light due to massive objects was predicted by Einstein in his General Theory of Rel... more Deflection of light due to massive objects was predicted by Einstein in his General Theory of Relativity. This deflection of light has been calculated by many researchers in past, for spherically symmetric objects. But, in reality, most of these gravitating objects are not spherical instead they are ellipsoidal ( oblate) in shape. The objective of the present work is to study theoretically the effect of this ellipticity on the trajectory of a light ray. Here, we obtain a converging series expression for the deflection of a light ray due to an ellipsoidal gravitating object, characterised by an ellipticity parameter. As a boundary condition, by setting the ellipticity parameter to be equal to zero, we get back the same expression for deflection as due to Schwarzschild object. It is also found that the additional contribution in deflection angle due to this ellipticity though small, but could be typically higher than the similar contribution caused by the rotation of a celestial objec...
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Papers by Ranchhaigiri Brahma