The paper investigates a Schwarzschild metric that exhibits a signature change across the event horizon, leading to a Lorentzian-Euclidean black hole. The geometry is regularized using the Hadamard *partie fine* technique, ensuring that the metric satisfies the vacuum Einstein equations. The concept of *atemporality* is introduced as the mechanism responsible for the transition from a regime with a real-valued time variable to one featuring an imaginary time, preventing the occurrence of singularities. The regularized Kretschmann invariant is used to discuss the characteristic features of this black hole. The authors show that the metric is a valid distribution-valued solution of the Einstein equations, and the singularity at \( r = 0 \) can be evaded due to the emergence of an imaginary time. The regularization process also allows for the evaluation of the Hawking temperature and entropy, demonstrating that the general formula for black hole entropy is valid for the Lorentzian-Euclidean black hole.The paper investigates a Schwarzschild metric that exhibits a signature change across the event horizon, leading to a Lorentzian-Euclidean black hole. The geometry is regularized using the Hadamard *partie fine* technique, ensuring that the metric satisfies the vacuum Einstein equations. The concept of *atemporality* is introduced as the mechanism responsible for the transition from a regime with a real-valued time variable to one featuring an imaginary time, preventing the occurrence of singularities. The regularized Kretschmann invariant is used to discuss the characteristic features of this black hole. The authors show that the metric is a valid distribution-valued solution of the Einstein equations, and the singularity at \( r = 0 \) can be evaded due to the emergence of an imaginary time. The regularization process also allows for the evaluation of the Hawking temperature and entropy, demonstrating that the general formula for black hole entropy is valid for the Lorentzian-Euclidean black hole.