Abstract Recent research has revealed that curvatures that are primarily orthogonal to the conventional semiclassical type may emerge when a geometric quantization ansatz is employed in Einsteinian general relativity. The timelike geodesic congruence in Reissner–Nordström metric, which has been both analytically derived and numerically examined, is used to investigate whether these phenomena are not artifacts of specific coordinate systems. It has been observed that the geodesic congruence expansion remains consistently non-vanishing, especially at small radial distance r . As r decreases, a significantly exponential evolution is found. The finiteness of the Kretschmann scalar for both conventional and quantized metric enables a definitive evaluation, suggesting that the conventional as well as the quantum curvatures are likely real, essential, and intrinsic (not artifacts of certain coordinate systems). Furthermore, we conclude that the proposed quantization approach seems to enhance the local focusing of the quantum curvatures in the charged, massive, non-rotating, and spherically symmetric Reissner–Nordström black hole. We also find that the quantum curvatures, despite their approximate qualitative estimation, indicate a complex spacetime structure that appears to be overlooked due to the semiclassical approximation utilized in conventional general relativity.
Tawfik et al. (Mon,) studied this question.