Isaac Scientific Publishing

Theoretical Physics

Eikonal Equations for Null Radial Geodesics in the Schwarzschild Metric

Download PDF (2677.4 KB) PP. 41 - 49 Pub. Date: December 31, 2020

DOI: 10.22606/tp.2020.54001

Author(s)

  • Miguel Socolovsky*
    Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510, Ciudad de México, México

Abstract

We study the eikonal function φ corresponding to outgoing and ingoing radial null geodesics (light rays in the short wave length limit) in the Schwarzschild spacetime. Contrary to the behavior of the expansion scalar θ at the singularities (past and future), φ turns out to be finite at r = 0 (except for light travelling along the horizons) and inversely proportional to M, the mass of the black hole, and so proportional to the Hawking temperature.

Keywords

Schwarzschild spacetime, eikonal function, radial light rays

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