Constructing Regular Lovelock Black Holes with degenerate vacuum and $\Lambda < 0$, using the gravitational tension. Shadow analysis

In \cite{Estrada:2024uuu}, a link between gravitational tension (GT) and energy density via the Kretschmann scalar (KS) was proposed to construct regular black holes (RBHs) in Pure Lovelock (PL) gravity. However, including a negative cosmological constant in PL gravity leads to a curvature singularity \cite{Cai:2006pq}. Here, we choose the coupling constants such that the Lovelock equations admit an $n$-fold degenerate AdS vacuum (LnFDGS), allowing us to construct an RBH with $\Lambda < 0$, where the energy density is analogous to the previously mentioned model. To achieve this, we propose alternative definitions for both the KS and GT. We find that, for mass parameter values greater than the extremal value $M_{\text{min}}$, our RBH solution becomes indistinguishable from the AdS vacuum black hole from inside the event horizon out to infinity. At small scales, quantum effects modify the geometry and thermodynamics, removing the singularity. Furthermore, due to the lack of analytical relationships between the event horizon, photon sphere, and shadow in LnFDGS, we propose a numerical method to represent these quantities.