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- Title
Timelike geodesic congruence in the simplest solutions of general relativity with quantum-improved metric tensor.
- Authors
Tawfik, A.; Dabash, T. F.
- Abstract
A recent quantum-geometrical approach for the possible reconciliation of the principles of general relativity and quantum mechanics extends the fundamental tensor to the relativistic (quantum) scales, in which additional geometric structures and curvatures, i.e., additional sources of gravitation, are emerged. This paper introduces some characteristics of the emerged curvatures and their consequences on regulating the space and initial singularities. We analyze the timelike geodesic congruence in the simplest solutions of the Einstein field equations; the homogeneous, isotropic, and spherically symmetric Schwarzschild, de Sitter–Schwarzschild, and Friedmann–Lemaitre–Robertson–Walker (FLRW) metrics. From the expansion of the trajectory congruence that follows the change in the shape of the volume which keeps the same set of geodesics in the bundle along the flow lines which are generated by the velocity fields, we conclude that the analytical and numerical analyses give an unambiguous signature that the space and initial singularities are attenuated or even regulated, especially in the relativistic (quantum) regime. This means that the regulation of the singularity in Einstein's general relativity (GR) would not be possible until quantum-mechanical ingredients are properly imposed on it.
- Subjects
EINSTEIN, Albert, 1879-1955; GENERAL relativity (Physics); EINSTEIN field equations; GEODESICS; NUMERICAL analysis; NONCOMMUTATIVE differential geometry; QUANTUM mechanics
- Publication
International Journal of Modern Physics D: Gravitation, Astrophysics & Cosmology, 2023, Vol 32, Issue 15, p1
- ISSN
0218-2718
- Publication type
Article
- DOI
10.1142/S0218271823500979