The present research paper derives a formula for gravitational force acting between the black hole and light particle passing near the radius of event horizon of black holes and calculates also their values of different test black holes existing in only X-ray binaries (XRBs). 1. Introduction The English physicist Isaac Newton proposed Universal law of Gravitation in 1687, which states that every particle in the universe exerts a force on every particle along the line joining their centres. The magnitude of the force is directly proportional to the product of the masses of two particles and inversely proportional to the square of distance between them , which was successively explained by the observation on the planetary movements made by the German astronomer Kepler (1571–1630). It works perfectly well in the world of ordinary experience and has dominated for about 250 years. It, however, shows its shortcoming when explaining the unusual orbit of Mercury around the sun. It breaks down when the gravitational forces get very strong or involving bodies moving at speed near that of light (http://library.thinkquest.org/C007571/english/printback.htm). In 1915, Albert Einstein demonstrated better theory of gravitation on the basis of general relativity, which has overcome the limitations of Newton’s law of universal gravitation . In 1997, Lerner discussed the problem of the deflection of light in a medium with varying refractive index applied to the motion of light in a weak Schwarzschild gravitational field . In 1999-2000, Mario presented a theory which introduces new unknown relationships that may shed new light on the nature of matter. This theory allows the calculation of the gravitational constant with a precision comparable to the other atomic constants, gives a direct relation between mass and charge of the electron without the need of the ubiquitous “classical electron radius,” and generates a second fine structure constant while also offering the disconcerting possibility of an antigravitational force . In 2013, Ng and Raymond Ooi analysed the gravitational force due to a pulsed Bessel beam and its effect on the probe pulse. They found that the Bessel beam generates gravitational repulsive forces at small distances and attractive forces at large distance. These forces can be coherently controlled in a medium by introducing a slow light effect through electromagnetic induced transparency . In the present work, we have derived a formula for gravitational force acting between the black hole and light particle passing near the radius of
D. Mahto, V. Prakash, U. Prasad, B.K. Singh, and K. M. Singh, “Change in entropy of non-spinning black holes w.r,t. the radius of event horizon in XRBs,” Astrophysics and Space Science, vol. 343, pp. 153–159, 2013.