The paper investigates a Schwarzschild metric with a signature change across the event horizon, termed a Lorentzian-Euclidean black hole. The metric is regularized using the Hadamard partie finie technique, which allows it to satisfy vacuum Einstein equations. The concept of atemporality is introduced as the mechanism responsible for the transition from a real-time regime to an imaginary-time regime, preventing the formation of a singularity. The regularized Kretschmann invariant shows that the metric is free of distributional singularities, and the velocity of infalling radial trajectories vanishes on the event horizon, becoming imaginary upon crossing it. This avoids the singularity at r = 0, unlike the standard Lorentzian-signature case. The metric is analyzed in Schwarzschild and Gullstrand-Painlevé coordinates, with the latter facilitating regularization. The regularized Riemann tensor, Ricci tensor, and Weyl tensor show no distributional components, and the Einstein tensor vanishes everywhere. The analysis confirms that the Lorentzian-Euclidean black hole has no surface layer or impulsive wave at the change surface. The Hawking temperature and entropy are calculated, showing consistency with standard results. The model avoids the singularity at r = 0 by allowing an imaginary time inside the black hole, which is linked to the concept of atemporality. The regularized metric is a valid solution of Einstein equations, with no distributional stress-energy tensor associated with the change surface. The study also discusses the implications of degenerate metrics and the behavior of radial geodesics, showing that infalling particles take infinite proper time to reach the event horizon, avoiding the singularity. The results highlight the role of atemporality in preventing the formation of a singularity in this black hole model.The paper investigates a Schwarzschild metric with a signature change across the event horizon, termed a Lorentzian-Euclidean black hole. The metric is regularized using the Hadamard partie finie technique, which allows it to satisfy vacuum Einstein equations. The concept of atemporality is introduced as the mechanism responsible for the transition from a real-time regime to an imaginary-time regime, preventing the formation of a singularity. The regularized Kretschmann invariant shows that the metric is free of distributional singularities, and the velocity of infalling radial trajectories vanishes on the event horizon, becoming imaginary upon crossing it. This avoids the singularity at r = 0, unlike the standard Lorentzian-signature case. The metric is analyzed in Schwarzschild and Gullstrand-Painlevé coordinates, with the latter facilitating regularization. The regularized Riemann tensor, Ricci tensor, and Weyl tensor show no distributional components, and the Einstein tensor vanishes everywhere. The analysis confirms that the Lorentzian-Euclidean black hole has no surface layer or impulsive wave at the change surface. The Hawking temperature and entropy are calculated, showing consistency with standard results. The model avoids the singularity at r = 0 by allowing an imaginary time inside the black hole, which is linked to the concept of atemporality. The regularized metric is a valid solution of Einstein equations, with no distributional stress-energy tensor associated with the change surface. The study also discusses the implications of degenerate metrics and the behavior of radial geodesics, showing that infalling particles take infinite proper time to reach the event horizon, avoiding the singularity. The results highlight the role of atemporality in preventing the formation of a singularity in this black hole model.