International Journal of Modern Physics D

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use $f(T,\mathcal{𝒯})$ modified gravity, which is characterized by the trace of an energy–momentum tensor as $\mathcal{𝒯}$ and torsion scalar $T$, Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics.

In this paper, we show how the path integral for gravity and matter on a piecewise flat spacetime can be used to define the physical quantum gravity states and the related transition amplitudes. The physical states are given by the path integrals for open manifolds from a certain topological class, while the corresponding transition amplitudes are obtained by gluing two such open manifolds into a closed one and calculating the corresponding path integral. We also solve the problem of how to associate a quantum gravity state to an effective action. This is done by using the path integral for a closed manifold from the transition-amplitude topological class so that the state which corresponds to the effective action can be chosen to be the Hartle–Hawking or the Vilenkin wavefunction for the vacuum manifold component of the transition-amplitude manifold.

General relativity (GR) in its current classical formulation is fundamentally different from quantum mechanics (QM). We argue that the everlasting battle for exploring and understanding the Universe and then privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying these two different benchmarks or at least bringing one closer to another! The latter conservatively describes the consolidating quantum geometric approach, which combines generalization of QM to relativistic energies and gravitational fields and continuous Riemann to discretized Finsler geometry. We found that this type of quantum geometric approach seems to unveil additional quantum-conditioned spacetime curvatures (QCC), sources of gravitation), which obviously could not be disclosed in Einstein’s GR, especially at large scales. This study introduces analytical and numerical analyses of QCC. We conclude that (i) nature and characteristics of QCC are fundamentally distinguishable from the classical GR’s spacetime curvatures, (ii) the QCC are intrinsic, real and essential, i.e. not artifacts that would be removed in a certain coordinate transformation and (iii) the magnitude of QCC are nonnegligible to be underestimated. We also conclude that the spacetime at quantum scales seems to be no longer smooth or continuous so that the proposed quantum geometric approach would be regarded as a novel mathematical framework for the emergence of quantum gravity. Last but not least, a maximal proper force is predicted as a new physical constant, which is responsible for the maximal and gravitational acceleration of a quantum particle that would live in the emerged spacetime curvatures. Thereby, the quantum geometric nature of QCC can be accessed and assessed.

We study the Maxwell field with a general gauge fixing (GF) term in the radiation-dominant (RD) and matter-dominant (MD) stages of expanding Universe, as a continuation to the previous work in the de Sitter space. We derive the exact solutions, perform the covariant canonical quantization and obtain the stress tensor in the Gupta–Bleuler (GB) physical states, which is independent of the GF constant and is also invariant under the quantum residual gauge transformation. The transverse stress tensor is similar in all flat Robertson–Walker spacetimes, and its vacuum part is $\propto k^4$ and becomes zero after the 0th-order adiabatic regularization. The longitudinal-temporal stress tensor, in both the RD and MD stages, is zero due to a cancelation between the longitudinal and temporal parts in the GB states, and so is the particle part of the GF stress tensor. The vacuum GF stress tensor, in the RD stage, contains $k^4,k^2$ divergences and becomes zero by the 2nd-order regularization, however, in the MD stage, contains $k^4,k^2,k^0$ divergences and becomes zero by the 4th-order regularization. So, the order of adequate regularization depends not only upon the type of fields, but also upon the background spacetimes. In summary, in both the RD and MD stages, as in the de Sitter space, the total regularized vacuum stress tensor is zero, independent of the GF constant, only the transverse photon part remains, there is no trace anomaly, and the vanishing GF stress tensor cannot be a candidate for the dark energy.

Understanding the expansion rate history is a primary goal in cosmology. There are various ways to measure the expansion rate at different redshifts and measuring it through the luminosity distance of SNIa is widely used in cosmology. In this work, we split the latest dataset of SNIa (the Pantheon+ sample) into several redshift bins and compute the expansion rate through a non-parametric technique. To do this, we use the Gaussian process to obtain the expansion rate considering data in different redshift bins. For the sake of comparison, we also consider the $\mathrm{\Lambda }$CDM model and find the expansion history through an MCMC analysis. Our results indicate that the degeneracy between free parameters prevents a good constraint using the low redshifts data but this is not the case in the GP scenario. Moreover, we study how high redshift SNIa can affect the current expansion rate and observe that data at $z>0.5$ has almost no impact on the current expansion rate in both approaches.

The conformal scalar propagator as an explicit function of the Schwarzschild black-hole space-time has been established in the preceding three projects. The present project examines the precise relation which that propagator has to the amplitude the Schwarzschild black hole emit a scalar particle in a particular mode of positive energy. It is thereby established that the effect of infinite time-dilation on the event horizon results in both, the thermal radiation in the background of a static exterior space-time geometry and the detraction from thermality if energy-conservation is properly imposed as a constraint on scalar propagation. The derivation of the latter signifies an equivalent approach to the result of Parikh and Wilczek from the semi-classical perspective of the distant observer. From that perspective for that matter, Hawking radiation emerges in both contexts as the exclusive consequence of infinite time-dilation on the event horizon. These results are consistent with Hawking radiation as the exclusive consequence of the causal structure of the Schwarzschild black-hole space-time both, in a static exterior geometry and in such dynamical exterior geometry as energy-conservation signifies. The extension of the thermal case to other spin-fields and black-hole geometries is discussed.