应用 Gauss-Bonnet 定理研究 Janis-Newman-Winnicour 虫洞的光线引力偏折

Gravitational deflection of light by a Janis-Newman-Winnicour wormhole using the Gauss-Bonnet theorem

摘要:

本文研究弱场极限下 Janise-Newman-Winnicour（JNW）虫洞所致的光线引力偏折. 以谐和规范为基础，我们首先推导了JNW 虫洞在谐和坐标系下的精确度规. 进一步地，采用 Gibbons 和 Werner 所倡导的几何方法，我们将 Gauss-Bonnet 定理应用于该引力场对应的光学度规上，获得了JNW虫洞赤道面内光线的三阶引力偏折角的解析式. 对于史瓦西几何，所得的偏折角与广义相对论中的方法得到的结果是一致的.

Abstract:

In this paper, we study the gravitational deflection of light by a Janise-Newman-Winicour (JNW) wormhole in the weak-field limit. Based on the harmonic gauge, we first derive the exact metric of the JNW wormhole in harmonic coordinates. Moreover, using the geometric method proposed by Gibbons and Werner, we apply the Gauss-Bonnet theorem to the optical metric of this gravity, and obtain the analytical form of the equatorial gravitational deflection angle of light up to the third order induced by the JNW wormhole. For the Schwarzschild geometry, the resulting bending angle is consistent with that of the results obtained by the method in the framework of general relativity.