Modern Physics Letters A

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, $〈x^{\mu }〉$, becomes uncertain. There exists a specific range of coordinates where the accessibility to $〈{(x^{\mu })}^2〉$ is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value $〈x^{\mu }〉$. This expectation value is dependent on $〈{(x^{\mu })}^2〉$, which is itself limited by a minimum measurable length $\mathrm{\Delta }{x}_{min}^2$. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between $\mathrm{\Delta }{x}_{min}$ and $\sqrt{-{〈g〉}^{\mu \nu }}$ is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between $\mathrm{\Delta }{x}_{min}$ and the Planck length ${\ell }_p$ is established with a proportionality factor of $\sqrt{-{〈g〉}^{\mu \nu }}\sqrt{{\beta }_2}$, where ${\beta }_2$ denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction $\psi (x,t)$, leading to an unrealistic $\mathrm{\Delta }p$. It is also noted that the lower limit of $〈{(p^{\mu })}^2〉$ is directly proportional to the fundamental tensor.

In this paper, we involve the galactic halo observational data to test the weak field General Relativity involving the cosmological constant. By using the data for 15 hydrogen (Hi) VLA super spirals and the Tully–Fisher relation, we obtain constraints for each galaxy. The results are consistent with previous results for spiral galaxies, as well as with the scaling relations for the halos, thus confirming the efficiency of the use of dark halo data and Tully–Fisher relation, including the baryonic Tully–Fisher index (BTFR), for testing modified gravity models.

The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.

We study the recent gravitational analogue of the Aharonov–Bohm effect for a classical system, namely a complex scalar field. We use this example to demonstrate that the Aharonov–Bohm effect in principle has nothing to do with quantum-mechanics. We then discuss how this classical field description can be connected to the standard one particle quantum description of the Aharonov–Bohm effect.

The Quantum Key Distribution (QKD) network approach has emerged as a promising solution and has garnered significant interest across various domains. QKD networks can be broadly categorized into two main types: those based on measurement-device-dependent (MDD) protocols and those based on measurement-device-independent (MDI) protocols. A novel network scheme is proposed combining these two protocols to guarantee end-to-end secure communication. It comprises two interconnected networks — the first uses a measurement-device-dependent protocol to connect routers with nearby nodes, while the second employs a measurement-device-independent protocol to interconnect the routers. In the first network, the process begins with Alice (Router) generating two types of weak quantum signals — the first has intensity, frequency and polarization or phase randomly varied, while the second with different delay times. Alice randomly transmits either signal states carrying information or decoy states with varying properties to the receivers (Bobs) over the quantum channels. She also sends a synchronization signal along with the quantum signals. At the receiver end, the synchronization pulse timestamps the incoming quantum signals. Each Bob then randomly shifts the frequencies of the received signals and measures their phase/polarization of the first signal and measures the delay times of the second signal. The secret key is derived by combining the frequency, the delay time and the phase/polarization information of the quantum signals, resulting in longer key lengths. Encoding information across multiple degrees of freedom enables extended key generation for secure communication. However, between the routers, MDI-QKD protocols are used to securely share the keys. This hybrid approach aims to ensure secure end-to-end communication across the network.

In a dilaton gravity model, we revisit the calculation of the temperature of an evaporating black hole that is initially formed by a shock wave, taking into account the quantum backreaction. Based on the holographic principle, along with the assumption of a boundary equation of motion, we show that the black hole energy is maintained for a while during the early stage of evaporation. Gradually, it decreases as time goes on and eventually vanishes. Thus, the Stefan–Boltzmann law tells us that the black hole temperature, defined by the emission rate of the black hole energy, starts from zero temperature and reaches a maximum value at a critical time, and finally vanishes. It is also shown that the maximum temperature of the evaporating black hole never exceeds the Hawking temperature of the eternal AdS₂ black hole. We discuss physical implications of the initial zero temperature of the evaporating black hole.

In this paper, we calculate the vacuum energy as a functional from the phion propagator in 4D model of complex scalar field (phion) which interacts with a real matrix scalar field (chion). The condition of stationarity of this functional gives us the equation for phion propagator. At some critical value of the coupling, the propagator changes its asymptotic behavior in the deep-Euclidean region of momenta. This behavior corresponds to some critical phenomenon. The study of the convexity of the energy functional shows that the solution obtained actually corresponds to the theory. We also discuss the stabilization of the ground state in the strong-coupling region by effective self-action of phions.

In this study, we work on understanding the behavior of relativistic fermions within the framework of a (2+1)-dimensional gravitational wave environment. Our main objective is to uncover an analytical solution for the massless Dirac equation in this particular scenario. Initially, we derive a set of coupled equations that describe the quantum dynamics of the system under consideration. Subsequently, we embark on finding an analytical solution for the resulting wave equation governing Weyl fermions by utilizing the generators associated with the $s{\ell }_2$ algebra. This approach enables us to determine the relativistic frequency modes of the system. We then delve into examining how the parameters of the gravitational wave spacetime influence the real oscillation modes of Weyl fermions. Our findings highlight the sensitivity of Weyl fermions to the specific gravitational wave spacetime background being considered.

In this paper, we construct a Schwarzschild metric in the fractal dimension based on fractal calculus, and we study the deflection of light near the sun. It was observed that the new fractal spherically symmetric spacetime metric may describe supermassive black holes, which have been detected through various astronomical observations such as SDSS. We have discussed the deflection of light by the gravitational field of the sun. It was observed that the total deflection of light is affected by the fractal dimension. To estimate the numerical value of the fractal dimension, we have used the 2004analysis of almost 2 million VLBI observations of 541 radio sources made by 87 VLBI sites, which estimates the factor $\gamma$ based on PNN formalism. It was observed that the fractal dimension is roughly less than unity. However, our analysis showed that large bending gravity gives fractal dimensions lower than unity to some extent. We also gave a naïve idea about the emission thermal Unruh process in fractal dimension. It was observed that both the temperature and the entropy of black holes are affected by the fractal dimension, and that for low numerical values, the entropy of the black hole is enhanced.

A theoretical comparison has been made for some calcium isotopes (${}_{20}$Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some ${}_{20}$Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ($Q_{0\mathrm{\text{Th}}})$ and theoretical deformation parameters (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0\mathrm{\text{Th}}}$ and the (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0\mathrm{\text{Th}}}$ and theoretical deformation parameter (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$, using the fpbm, the fpd6 and the kb3 interactions were the best.