To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike geodesic congruences for two distinct formulations of the fundamental metric tensor. This analysis is conducted within a nonhomogeneous, anisotropic, and spherically symmetric cosmic background. The results derived from the conventional metric tensor, the building block of Einstein's theory of general relativity, are compared with those obtained from a quantum-mechanically revisited metric tensor. This comparison enables an assessment of the proposed geometric quantization, particularly in terms of whether singularities are regulated or diminished. Utilizing a quantum geometric approach, the numerical analysis incorporating a quantum-mechanically revisited metric tensor applies a mean-field approximation on the integrated quantum operators. In contrast to the results obtained with conventional metric tensor, the quantum-mechanically induced revision of the metric tensor seems to provide a framework for controlling singularities in the new formulation of general relativity. The degree of quantization likely influences the ability to regulate or even potentially remove both singularities. We also conclude that the proposed geometric quantization provides a means to explore the quantum nature of spacetime curvatures, emphasizing that the singularity dilemma arose primarily from the standard semi-classical approximation of Einstein's general relativity.

Egypt

Abdel Nasser Tawfik

Saudi Arabia

Azzah A. Alshehri

Italy

Antonio Pasqua

Expansion evolution of nonhomogeneous metric with quantum-mechanically revisited fundamental metric tensor

The evaluation of the energy-momentum distribution for a new four-dimensional, spherically symmetric, static and charged black hole spacetime geometry with constant nonzero topological Euler density is performed by using the energy-momentum complexes of Einstein and Møller. This black hole solution was recently developed in the context of the coupled Einstein–nonlinear electrodynamics of the Born-Infeld type. The energy is found to depend on the mass <math id="M1"><mrow><mi>M</mi></mrow></math> and the charge <math id="M2"><mrow><mi>q</mi></mrow></math> of the black hole, the cosmological constant <math id="M3"><mrow><mi>Λ</mi></mrow></math>, and the radial coordinate <math id="M4"><mrow><mi>r</mi></mrow></math>, while in both prescriptions all the momenta vanish. Some limiting and particular cases are analyzed and discussed, illustrating the rather extraordinary character of the spacetime geometry considered.

Romania

Irina Radinschi

Greece

Theophanes Grammenos

India

Farook Rahaman

Andromahi Spanou

Marius Mihai Cazacu

Surajit Chattopadhyay

Localization of Energy-Momentum for a Black Hole Spacetime Geometry with Constant Topological Euler Density

The energy-momentum of a new four-dimensional, charged, spherically symmetric, and nonsingular black hole solution constructed in the context of general relativity coupled to a theory of nonlinear electrodynamics is investigated, whereby the nonlinear mass function is inspired by the probability density function of the continuous logistic distribution. The energy and momentum distributions are calculated by use of the Einstein, Landau-Lifshitz, Weinberg, and Møller energy-momentum complexes. In all these prescriptions, it is found that the energy distribution depends on the mass <math id="M1"><mrow><mi>M</mi></mrow></math> and the charge <math id="M2"><mrow><mi>q</mi></mrow></math> of the black hole, an additional parameter <math id="M3"><mrow><mi>β</mi></mrow></math> coming from the gravitational background considered, and the radial coordinate <math id="M4"><mrow><mi>r</mi></mrow></math>. Further, the Landau-Lifshitz and Weinberg prescriptions yield the same result for the energy, while, in all the aforesaid prescriptions, all the momenta vanish. We also focus on the study of the limiting behavior of the energy for different values of the radial coordinate, the parameter <math id="M5"><mrow><mi>β</mi></mrow></math>, and the charge <math id="M6"><mrow><mi>q</mi></mrow></math>. Finally, it is pointed out that, for <math id="M7"><mi>r</mi><mo>→</mo><mi>∞</mi></math> and <math id="M8"><mi>q</mi><mo>=</mo><mn>0</mn></math>, all the energy-momentum complexes yield the same expression for the energy distribution as in the case of the Schwarzschild black hole solution.

Sayeedul Islam

Energy-Momentum for a Charged Nonsingular Black Hole Solution with a Nonlinear Mass Function

Dark energy models are here investigated and studied in the framework of the Chern–Simons modified gravity model. We bring into focus the holographic dark energy model with Granda–Oliveros cut-off, the modified holographic Ricci dark energy model and a model with higher derivatives of the Hubble parameter. The relevant expressions of the scale factor a(t) for a Friedmann–Robertson–Walker Universe are derived and studied, and, in this context, the evolution of the scale factor is shown to be similar to the one displayed by the modified Chaplygin gas in two of the above models.

Brazil

Roldão da Rocha

Holographic dark energy models and higher order generalizations in dynamical Chern–Simons modified gravity

Motivated by the work of Yang et al. (Mod. Phys. Lett. A 26:191, 2011 ), we report on a study of the new holographic dark energy (NHDE) model with energy density given by ρD=3ϕ24ω(μH2+νH˙) in the framework of chameleon Brans–Dicke cosmology. We have studied the correspondence between the quintessence, the DBI-essence, and the tachyon scalar-field models with the NHDE model in the framework of chameleon Brans–Dicke cosmology. Deriving an expression of the Hubble parameter H and, accordingly, ρD in the context of chameleon Brans–Dicke chameleon cosmology, we have reconstructed the potentials and dynamics for these scalar-field models. Furthermore, we have examined the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction of massless conformally invariant fields, and we have seen that the quantum correction could be small when the phantom crossing occurs and the obtained solutions of the phantom crossing could be stable under the quantum correction. It has also been noted that the potential increases as the matter–chameleon coupling gets stronger with the evolution of the universe.

Armenia

Germany

Martiros Khurshudyan

New holographic reconstruction of scalar-field dark-energy models in the framework of chameleon Brans–Dicke cosmology

We consider two-component dark energy models in Lyra manifold. The first component is assumed to be a quintessence field while the second component may be a viscous polytropic gas, a viscous Van der Waals gas, or a viscous modified Chaplygin gas. We also consider the possibility of interaction between components. By using the numerical analysis, we study some cosmological parameters of the models and compare them with observational data.