Null Geodesics and Gravitational Lensing in a Nonsingular Spacetime

Shao-Wen Wei,Chun-E Fu,Yu-Xiao Liu

doi:10.1155/2015/454217

Shao-Wen Wei, Chun-E Fu + Show 1 more

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https://doi.org/10.1155/2015/454217

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Abstract

The null geodesics and gravitational lensing in a nonsingular spacetime are investigated. According to the nature of the null geodesics, the spacetime is divided into several cases. In the weak deflection limit, we find the influence of the nonsingularity parameterqon the positions and magnifications of the images is negligible. In the strong deflection limit, the coefficients and observables for the gravitational lensing in a nonsingular black hole background and a weakly nonsingular spacetime are obtained. Comparing these results, we find that, in a weakly nonsingular spacetime, the relativistic images have smaller angular position and relative magnification but larger angular separation than those of a nonsingular black hole. These results might offer a way to probe the spacetime nonsingularity parameter and put a bound on it by the astronomical instruments in the near future.

Highlights

The cosmic censorship hypothesis [1, 2] says that singularities that arise in the solutions of Einstein’s equations are typically hidden within event horizons and cannot be seen from the rest of spacetime
We find that the photon sphere of a nonsingular black hole is always larger than that of a weakly nonsingular spacetime
It is clear that these results reduce to the Schwarzschild black hole spacetime when q = 0

Summary

Introduction

The cosmic censorship hypothesis [1, 2] says that singularities that arise in the solutions of Einstein’s equations are typically hidden within event horizons and cannot be seen from the rest of spacetime. The result showed that gravitational lensing in the strong deflection limit could provide a probe to the noncommutative parameter. According to it, the spacetime is classified into the nonsingular black hole q/2M ∈ (0, Qcr1), the extremal nonsingular black hole q/2M = Qcr, the weakly nonsingular spacetime q/2M ∈ (Qcr, Qcr2), the marginally nonsingular spacetime q/2M = Qcr, and the strongly nonsingular spacetime q/2M ∈ (Qcr2, ∞) Under this classification, we study the lensing features in a nonsingular spacetime in both weak and strong deflection limits.

Null Geodesics and Photon Sphere

Lensing in Nonsingular Spacetime

Summary