Finite-Distance Gravitational Lensing of a Global Monopole in a Schwarzschild-de Sitter Spacetime

Abstract

We investigate the gravitational lensing of a Schwarzschild-de Sitter black hole with a global monopole at finite distances. In this asymptotically nonflat spacetime, the deflection angle of light is decomposed into two parts: the first derives from the orbit differential equation, and the second originates from the metric itself. By absorbing the cosmological constant into the effective impact parameter, we derive an analytical expression for the first part using elliptic integrals. Combined with the second part, we obtain a complete exact solution for the deflection angle in this context. Additionally, considering that the distances from the source to the observer are large, we derive expressions for the light deflection angle in both the weak and strong field limits. In both cases, we find that the deflection is enhanced by the presence of the global monopole, further supporting its potential role as an alternative to elusive dark matter.