Universal time delay in static spherically symmetric spacetimes for null and timelike signals

Abstract

A perturbative method to compute the total travel time of both null and lightlike rays in arbitrary static spherically symmetric spacetimes in the weak field limit is proposed. The resultant total time takes a quasi-series form of the impact parameter. The coefficient of this series at a certain order $n$ is shown to be determined by the asymptotic expansion of the metric functions to the order $n+1$. To the leading order(s), the time delay, as well as the difference between the time delays of two kinds of relativistic signals, is then shown to take a universal form for all SSS spacetimes. This universal form depends on the mass $M$ and a post-Newtonian parameter $\gamma$ of the spacetime. The analytical result is numerically verified using the central black hole of M87 as the gravitational lensing center.

7 pages, 2 figure; added more explanation for some steps; typos corrected

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Cited by in corpus (2)

• Perturbative deflection angle for signal with finite distance and general velocities
• Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow