Abstract
From the Schwarzschild metric we obtain the higher-order terms for the deflection of light around a massive object using the Lindstedt-Poincare method to solve the equation of motion of a photon around the stellar object. The asymptotic series obtained by this method was obtained up to order 20 in the expansion parameter, and was found to better approximate the numerical solution with higher order terms—a property that can’t be taken for granted for any asymptotic series. Additionally, we obtain diagonal Pade approximants from the perturbation expansion, and we show how these are a better fit for the numerical data than the original formal Taylor series. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around massive objects.
Highlights
The General Theory of Relativity (GTR) is probably one of the most elegant theories ever performed
We obtain diagonal Padé approximants from the perturbation expansion, and we show how these are a better fit for the numerical data than the original formal Taylor series
One of the most relevant predictions of General Relativity is the gravitational deflection of light
Summary
The General Theory of Relativity (GTR) is probably one of the most elegant theories ever performed. In Equation (3) R represents a region of space-time, LF is the Lagrangian density due to the fields of matter and energy and g is the determinant of the metric tensor. One of the most relevant predictions of General Relativity is the gravitational deflection of light. It was demonstrated during the solar eclipse of 1919 by two british expeditions [10]. We make use of Pade approximants on our asymptotic series for the deflection angle to both increase its region of validity, and to improve as we shall see, matches the qualitative behavior of the deflection angle We use these approximants in ray-tracing algorithms to model the bending of light around the massive object. We think that this paper can be very useful for undergraduate students to learn the use of perturbative techniques for solving problems within the framework of the General Theory of Relativity, and in other fields of Physics
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