A new slow-rotating black hole solution in Chern-Simons axion of Einstein gravity - G.G.L. Nashed (Physics Letters B, 2023)
This research aims to incorporate an axionic field within the context of dynamical Chern-Simons (CS) gravity and investigate the behavior of a slowly rotating black hole (BH) within this theoretical framework. To the best of our knowledge, this is the first instance where such a problem has been tackled within the context of (CS) gravitational theory coupled with the axionic field. The Lagrangian of this theory includes two CS scalar field functions, denoted as ω(ϑ) and U(ϑ), where ϑ represents the CS scalar field. Our investigation involves calculating the equation related to the CS scalar field and demonstrating that deriving a solution necessitates imposing constraints on U and ω, specifically in the form of U′=ω, where U′≡dU(ϑ)dϑ. By utilizing the solution for the CS scalar field in other field equations, we reveal that the enigmatic function U can be expressed explicitly as U=ϑ2p+1, where p represents an integer with unrestricted values. In the instance where p=0, the CS Axion Einstein gravity theory [1] aligns with the study carried out in [2]. Furthermore, our analysis establishes that for positive values of p, the theory is capable of generating a significantly potent CS BH compared to the model derived in [2]. Moreover, our study delves into the geodesics of this BH, deriving its conserved quantities, orbital period, as well as its geodesic precession angle.