The optical geometry definition of the total deflection angle of a light ray in curved spacetime
Jun 23, 2020Citations per year
Abstract: (IOP)
Assuming a static and spherically symmetric spacetime, we propose a novel concept of the total deflection angle of a light ray in terms of the optical geometry which is the Riemannian geometry experienced by the light ray. The total deflection angle is defined by the difference between the sum of internal angles of two triangles; one of the triangles lies on curved spacetime distorted by a gravitating body and the other on its background. The triangle required to define the total deflection angle can be realized by setting three laser-beam baselines as in planned space missions such as LATOR, ASTROD-GW, and LISA. Accordingly, the new total deflection angle is, in principle, measurable by gauging the internal angles of the triangles. The new definition of the total deflection angle can provide a geometrically and intuitively clear interpretation. Two formulas are proposed to calculate the total deflection angle on the basis of the Gauss-Bonnet theorem. It is shown that in the case of the Schwarzschild spacetime, the expression for the total deflection angle αSch reduces to Epstein-Shapiro's formula when the source of a light ray and the observer are located in an asymptotically flat region. Additionally, in the case of the Schwarzschild-de Sitter spacetime, the expression for the total deflection angle αSdS comprises the Schwarzschild-like parts and coupling terms of the central mass m and the cosmological constant Λ in the form of O(Λ m) instead of O(Λ/m). Furthermore, αSdS does not include the terms characterized only by the cosmological constant Λ.Note:
- 25 pages, 5 figures. Accepted for publication in Journal of Cosmology and Astroparticle Physics
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