  In this article, we consider a Renormalization Group flow of the
Thermofield-Double state in a UV-complete description of Holography, by
introducing a relevant deformation to the ${\cal N}=4$ super Yang-Mills theory
at strong coupling. This RG-flow is known to have a non-trivial, interacting
${\cal N}=1$ fixed point at the IR. Geometrically, an RG-flow of the TFD-state
naturally continues radially and inside the black hole event horizon and yields
a Kasner-structure near singularity, as has been observed in recent works. We
show that for a generic value of the deformation, the putative IR fixed point
remains inside the black hole. By fine-tuning this deformation, the "fixed
point" can be brought arbitrarily close to the event horizon, while always
remaining inside. Physically, this distinguishes between the vanishing
temperature limit of the RG-flows with the one at exactly zero temperature. We
further discuss its general implications in the context of Holography. We also
discuss how correlations between the two-copies of the TFD-state depend on this
explicit RG-flow.
