Letelier black hole immersed in an electromagnetic universe

Abstract: We investigate a static, spherically symmetric black hole solution surrounded by a cloud of strings and immersed in an electromagnetic universe. By deriving the event horizon from the lapse function, we demonstrate that both the string cloud parameter and the electromagnetic background parameter significantly modify the horizon radius compared to the Schwarzschild case. Consequently, thermodynamic quantities-including the Hawking temperature, Bekenstein-Hawking entropy, and heat capacity-become explicit functions of these additional parameters, with the heat capacity exhibiting divergences that signal phase transitions. We analyze the motion of massive test particles in this spacetime, deriving the effective potential and calculating the innermost stable circular orbit radius, which governs the inner edge of accretion disks and influences orbital stability. Scalar perturbations are examined through the associated effective potential, and quasinormal mode frequencies are computed using the sixth-order WKB approximation; the negative imaginary parts confirm the stability of the black hole under such perturbations. We also study the photon sphere structure, black hole shadow radius, and photon trajectories, showing how the interplay between string clouds and the electromagnetic background shapes the optical properties of this spacetime. Finally, we investigate weak gravitational lensing phenomena by deriving the deflection angle for both massive particles and photons using the Gauss-Bonnet theorem applied to the optical geometry. The results exhibit notable deviations from the Schwarzschild geometry, with the string cloud enhancing the deflection through a $(1-α)^{-1}$ factor while the electromagnetic parameter introduces competing corrections at second order.