Cálculos newtoniano e relativístico da deflexão da luz e a contribuição da constante cosmológica

Abstract

The deflection of light by the sun was first studied by Cavendish in (1784) and later revised by Soldner in (1801). The newtonian physics was the base to these calculations. Currently, the deflection of light can be measured with accuracy indicating the double of the value predicted by the newtonian calculus. The correct result of the deflection of light is obtained by the application of the General Theory of Relativity GR, which gives the conceptual bases for the discussion of the given phenomenon. However, current authors argue that the newtonian calculus yields the result observed for this phenomenon. In the first part of this work we show by different methods that this statement is incorrect. The newtonian result is, in fact, half of the results yielded by observations. In particular, we show that in the non-relativistic limit the GR yields the newtonian result obtained by Cavendish and Soldner. In the second part of this paper we study local effects of the cosmological constant. This problem leads naturally to the Kottler (Schwarzschild - de Sitter) geometry. In this context, we analyze the effect of the cosmological constant on the deflection of light in the GR as well as in the newtonian theory. Lastly, we discuss some results obtained from current literature on the subject, which indicates that the calculus of the deflection of light based on the Kottler geometry must be modified to take into account effects of the expansion of the universe.