A.N. Tawfik1, A.A. Alshehri2

1 Future University in Egypt (FUE), Fifth Settlement (11835 New Cairo, Arab Republic of Egypt)
2 University of Hafr Al Batin (Hafar Al Batin 39524, Kingdom of Saudi Arabia)
1 a.tawfik@fue.edu.eg

To reveal the nature of curvatures and singularitis which are emerged with the proposed quantization imposed on the fundamental tensor, the timelike geodesic congruence of the Reissner-Nordström metric shall be derived, analytically, and analyzed, numerically. The evolution of the geodesic congruence expansion is found nonvanishing everywhere. Furthermore, as the radial distance from the singularity decreases, an extremely large geodesic congruence expansion evolution occurs. The proposed quantization seems to largely enhance and apparently enrich the profile of the geodesic congruence expansion evolution. That the Kretschmann scalar for both versions of the fundamental tensor is found finite everywhere allows for an unambiguous assessment that the curvatures and singularities are likely real and essential (not artifact in some coordinate systems). We conclude that the proposed quantization seems to locally sharpen the curvatures and hence the singularities of the charged, non-rotating, spherically symmetric, and massive Reissner-Nordström black hole. This finding would alter the Schwarzschild radius and even the entire black hole geometry, especially at relativistic quantum scales. We also conclude that the additional curvatures even with their approximate qualitative estimation point to a rich spacetime structure which is apparently overseen in the classical limit.

Tawfik A.N., Alshehri A.A. Reissner-Nordström Black Hole: Curvature and Singularity with Quantized Fundamental Tensor. Nonlinear World. 2024. V. 22. № 3. P. 49–61. DOI: https://doi.org/10.18127/ j20700970-202403-06

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