Regular Black Holes in Lovelock gravity with a Degenerate AdS Ground State and their shadows (2502.07992v3)

Abstract: In \cite{Estrada:2024uuu}, a relationship between gravitational tension (GT) and energy density, via the Kretschmann scalar (KS), was recently proposed to construct regular black hole (RBH) solutions in Pure Lovelock (PL) gravity. However, in PL gravity it is not viable to include a negative cosmological constant, as this leads to the appearance of a potential curvature singularity \cite{Cai:2006pq}. In this work, by choosing a particular set of coupling constants such that the resulting equations of motion for Lovelock gravity admit an $n$-fold degenerate ground state (LnFDGS) AdS solution, we construct an RBH solution with $\Lambda < 0$, providing an energy density model analogous to (but distinct in its definition of GT) the one previously mentioned. Moreover, since relating the gravitational tension to the KS of the vacuum LnFDGS solution is nontrivial, we provide an alternative definition of both the KS and the GT. Remarkably, we obtain a model where there exists a value $r_$ slightly greater than the extremal radius, $r_ > r_{ext}$, which could be on the order of the Planck length, such that the solutions of the vacuum AdS black hole and our AdS RBH become indistinguishable. However, at short length scales such that $r < r_*$, quantum effects would arise, causing both cases to differ in their geometry (suppressing the central singularity) and their thermodynamic properties. Additionally, since it is not possible to find analytical relationships between the event horizon, the photon sphere radius, and the shadow size in LnFDGS, we propose a method to numerically and graphically obtain the aforementioned relationships and analyze their physical behavior. We also provide a speculative methodology to compare theoretical results from Lovelock gravity with experimental results from the EHT for M87.