Whenever an experiment can be described classically, quantum physics must predict the same outcome. Intuitively, there is nothing quantum about an accelerating observer travelling through vacuum. It is, therefore, not surprising that many people are puzzled by the Unruh effect, which predicts that the observer encounters photons in a thermal state. This paper uses a recently introduced local photon approach to show that the quantised electromagnetic field in a non-inertial reference frame can be modelled without violating the principles of general relativity while both observers share a common vacuum. The only difference between a resting and an accelerating observer is that they each experience different worldline densities which implies different zero point energy densities in each reference frame.

In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.

We consider the integral and derivative operators of tempered fractional calculus, and examine their analytic properties. We discover connections with the classical Riemann-Liouville fractional calculus and demonstrate how the operators may be used to obtain special functions such as hypergeometric and Appell's functions. We also prove an analogue of Taylor's theorem and some integral inequalities to enrich the mathematical theory of tempered fractional calculus.

We study the greybody factors, quasinormal modes, and shadow of the higher dimensional de-Sitter (dS)/ anti de-Sitter (AdS) black hole spacetimes derived from the Einstein-bumblebee gravity theory within the Lorentz symmetry breaking (LSB) framework. We specifically apply the semi-analytical WKB method and the time domain approach to study the scalar and Dirac perturbations of the black hole. In-depth researches are done on the effects of the LSB and dimensionality on the bosonic/fermionic greybody factors, quasinormal modes, and shadow of the higher dimensional bumblebee black hole. The results obtained are discussed, tabulated, and illustrated graphically.

Byzantine fault-tolerant (BFT) systems are able to maintain the availability and integrity of IoT systems, in presence of failure of individual components, random data corruption or malicious attacks. Fault-tolerant systems in general are essential in assuring continuity of service for mission critical applications. However, their implementation may be challenging and expensive. In this study, IoT Systems with Byzantine Fault-Tolerance are considered. Analytical models and solutions are presented as well as a detailed analysis for the evaluation of the availability. Byzantine Fault Tolerance is particularly important for blockchain mechanisms, and in turn for IoT, since it can provide a secure, reliable and decentralized infrastructure for IoT devices to communicate and transact with each other. The proposed model is based on continuous-time Markov chains, and it analyses the availability of Byzantine Fault-Tolerant systems. While the availability model is based on a continuous-time Markov chain where the breakdown and repair times follow exponential distributions, the number of the Byzantine nodes in the network studied follows various distributions. The numerical results presented report availability as a function of the number of participants and the relative number of honest actors in the system. It can be concluded from the model that there is a non-linear relationship between the number of servers and network availability; i.e. the availability is inversely proportional to the number of nodes in the system. This relationship is further strengthened as the ratio of break-down rate over repair rate increases.

We give a pedagogical introduction to black holes (BHs) greybody factors (GFs) and quasinormal modes (QNMs) and share the recent developments on those subjects. In this study, our primary focus will be on the bosonic and fermionic GFs and QNMs of various BH and brane geometries and reveal the fingerprints of the invisibles with the radiation spectra to be obtained by the WKB approximation and bounding the Bogoliubov coefficients (together with the Miller-Good transformation) methods. (*Due to the notification of arXiv "The Abstract field cannot be longer than 1,920 characters", the appeared Abstract is shortened. For the full Abstract, please download the Article.)

To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics [Bennett et al., Eur. J. Phys. 37, 014001 (2016)]. To identify the relevant Hilbert space, we notice that mechanical particles can occupy any position x while moving at any velocity v. Afterwards, we promote the classical states (x,v) to pairwise orthogonal quantum states |x,v> and demand that these evolve according to Newton's equations of motion. The resulting quantum theory is mass-independent, when Newton's equations of motion are mass-independent, as one would expect. The basic formulation of quantum mechanics emerges from quantum mechanics in configuration space as a semi-classical approximation when a fixed mass is imposed and several other adjustments are made.

We investigate the dynamics of test particles, perturbations, and greybody factors within the framework of a Bardeen-like AdS black hole (BH) with a phantom global monopole. This study explores the interactions between nonlinear electrodynamics, the energy scale of symmetry breaking, and space-time topology. We analyze the geodesic motion of null and time-like particles, deriving effective potentials that describe their trajectories. Utilizing the Regge-Wheeler potential, we calculate the quasinormal modes (QNMs) for scalar, vector, and tensor perturbations, applying the sixth-order WKB approximation. Our findings highlight how the Bardeen-like parameter ($\mathrm{b}$) and the energy scale of symmetry breaking, characterized by the parameter ($\eta$), influence the QNM spectra, with potential implications for gravitational wave observations. We also examine greybody factors, focusing on the transmission and reflection coefficients for scalar and axial fields, and employ semi-analytic techniques to derive precise bounds. Furthermore, we assess the thermodynamic stability of the BH, emphasizing the role of these parameters in phase transitions and stability criteria.

The research of superradiant instability in the realm of quantum gravity is a well-known topic, with many physicists and astronomers studying the potential impact it can have on gravitational waves, the structure of the universe, and spacetime itself. In this work, we investigate the superradiant (in)stability of a rotating black hole obtained from the nonlinear Maxwell $f(R)$ gravity theory. In this study, the evaluation of stability/instability is going to be based on non-existence and existence of magnetic field, when the magnetic field constant becomes $c_{4}=0$ and $c_{4}\neq 0$, respectively. The analyzes of greybody factor (GF) and quasinormal modes (QNMs) are investigated in the stationary black hole spacetime both in the absence and presence of the magnetic field parameter. To this end, we first consider the Klein-Gordon equation for the complex scalar field in the geometry of that rotating black hole. In the sequel, the obtained radial equation is reduced to a one-dimensional Schrödinger-like wave equation with an effective potential energy. The effects of the nonlinear Maxwell $f(R)$ gravity theory parameters ($q$, $c$, and $c_{4}$) on the effective potential, GFs, and QNMs are thoroughly investigated. The obtained results show that even though the factors $q$, $c$, and $c_{4}$ all affect the effective potential, this phenomena, surprisingly, is not valid for the GFs and QNMs. With the proper graphics and tables, all outputs are depicted, tabulated, and interpreted.

In this paper, we study the symmetric rendezvous search problem on the line with n > 2 robots that are unaware of their locations and the initial distances between them. In the symmetric version of this problem, the robots execute the same strategy. The multi-robot symmetric rendezvous algorithm, MSR presented in this paper is an extension our symmetric rendezvous algorithm, SR presented in [23]. We study both the synchronous and asynchronous cases of the problem. The asynchronous version of MSR algorithm is called MASR algorithm. We consider that robots start executing MASR at different times. We perform the theoretical analysis of MSR and MASR, and show that their competitive ratios are $O(n^{0.67})$ and $O(n^{1.5})$, respectively. Finally, we confirm our theoretical results through simulations.