Quantum-Conditions Curvatures as Sources of Quantum Gravity

Abstract

Abstract To reveal the nature of the curvature and singularity that result from the suggested quantum-mechanically imposed revision of the fundamental metric tensor, the timelike geodesic congruence of the black hole metric will be calculated analytically and numerically. We found that the evolution of the geodesic congruence expansion is nonvanishing throughout. Furthermore, when the radial distance decreases, an enormous geodesic congruence expansion evolves. We conclude that the proposed quantization seems to significantly improve the geodesic congruence expansion evolution. The fact that the Kretschmann scalar for both versions of the fundamental metric tensor is finite everywhere allows us to conclude unambiguously that the curvature and singularity are most likely intrinsic, essential, and real. Because these curvatures emerge as a result of the quantized fundamental metric tensor and appear to emerge at quantum scales, they are most likely associated with quantum gravity. We conclude that the proposed quantization appears to reveal quantum gravity in charged, non-rotating, spherically symmetric and massive Reissner-Nordström black holes.