Exploring the Impact of Λ = a · e^π as a Cosmological Constant on Black Hole Solutions in General Relativity and $f(R)$ Gravity

In this paper, we investigate the cosmological constant Λ = a · e^π, where a is an algebraic parameter, and demonstrate its role in $f(R)$ gravity as an indicator of the transcendental form. We analyze the Schwarzschild and Kerr-Newman black holes under this cosmological constant and show that they satisfy the SO × R symmetry. Additionally, we prove that $f(R)$ gravity with this transcendental form also adheres to SO × R symmetry.