Can an observer really catch up with light

Details Can an observer really catch up with light Can an observer really catch up with light

2002-11-03

arxiv.org/abs/gr-qc/0211010v1

Class.Quant.Grav. 20 (2003) 3927-3932

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, no figures, submited to Physical Review D

Scientific paper

10.1088/0264-9381/20/18/306

Given a null geodesic $\gamma_0(\lambda)$ with a point $r$ in $(p,q)$ conjugate to $p$ along $\gamma_0(\lambda)$, there will be a variation of $\gamma_0(\lambda)$ which will give a time-like curve from $p$ to $q$. This is a well-known theory proved in the famous book\cite{2}. In the paper we prove that the time-like curves coming from the above-mentioned variation have a proper acceleration which approaches infinity as the time-like curve approaches the null geodesic. This means no observer can be infinitesimally near the light and begin at the same point with the light and finally catch the light. Only separated from the light path finitely, does the observer can begin at the same point with the light and finally catch the light.

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