Relativity and Cosmology

    

Geodesic Integration in the Schwarzschild Gravitational Field

Authors: C. A. Laforet

It is demonstrated in the present work that the standard integration of the proper time along a freefalling geodesic in Schwarzschild spacetime does not properly account for the coordinate curvature in the vicinity of the event horizon. It is shown that that the condition given by the metric, namely that the change in proper time of the freefalling observer per change of coordinate time goes to zero at the horizon can be maintained while still allowing for an infinite proper time to the horizon. With the aid of a transformation of the radial Schwarzschild coordinate and analysis of light signals, we find that observers at rest will see the freefalling observer slow exponentially as she approaches the horizon, while the freefaller will see rest observers slow asymptotically as she approaches the horizon.

Comments: 8 Pages.

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Submission history

[v1] 2016-09-16 10:36:16

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