Search Results (18)

The entropy of a Schwarzschild black hole is commonly derived using thermodynamic relations whose physical interpretation is not always transparent, in particular with respect to the localization of temperature and entropy. In this paper, we present a derivation of the Bekenstein–Hawking entropy based exclusively on the principles of phenomenological thermodynamics, formulated entirely in regions where spacetime is effectively flat. The analysis considers a reversible evaporation process in which the black hole is surrounded by a tunable thermal radiation bath whose temperature is kept arbitrarily close to the Hawking temperature. In this limit, entropy production can be made negligible. By integrating the entropy flux through a distant reference surface over the evaporation process, the standard entropy formula is obtained without invoking assumptions about the localization of the black hole entropy or about microscopic degrees of freedom. The derivation is mathematically simple but conceptually instructive. The approach is intended to be accessible to readers familiar with classical thermodynamics and general relativity at an advanced undergraduate or graduate level. Full article

We develop a general framework for quantum field theory in curved spacetime based on Local Minkowski Coordinates (LMC), which incorporates curvature effects into local Feynman diagrammatics. Gravitational influence enters through a curvature-dependent normalization function $B\left(x\right)$, derived from covariant current conservation, and a gravitational phase $S\left(x\right)$, obtained via the WKB approximation. These quantities enter through local phase accumulation and observer-dependent normalization of external states, without modifying globally conserved fluxes. As a first application, we analyze the local redshift normalization and phase structure of quantum amplitudes in the vicinity of a Schwarzschild black hole. Within their range of validity, the curvature-dependent factors $B\left(x\right)$ and $S\left(x\right)$ reproduce the expected gravitational redshift of field amplitudes in general relativity. When amplitudes are propagated to asymptotic infinity and evaluated in a standard global quantum state (such as the Unruh state), the resulting flux is consistent with the standard Hawking result. The framework refines the local WKB structure and clarifies the separation between local normalization effects and globally conserved fluxes. Full article

We develop an informational extension of spacetime thermodynamics in which local entropy production is coupled to spacetime curvature within an effective covariant framework. Spacetime is modeled as a continuum limit of finite-capacity information registers, giving rise to a coarse-grained entropy field whose gradients define an informational flux. Within a nonminimally coupled scalar–tensor formulation, the resulting field equations imply that the local divergence of this flux is sourced by the Ricci scalar, establishing a direct relation between curvature and entropy production. The corresponding integral form links cumulative entropy generation to the integrated spacetime curvature over a causal region. In stationary limits, the framework reproduces the Bekenstein–Hawking entropy of horizons, while in homogeneous expanding cosmologies it yields monotonic entropy growth consistent with the observed arrow of time. The construction remains compatible with unitarity at the microscopic level and with holographic entropy bounds in the stationary limit. Numerical solutions in flat FLRW backgrounds are used as consistency checks of the coupled evolution equations and confirm the expected curvature–entropy behavior across cosmological epochs. Overall, the results provide a thermodynamically consistent interpretation of curvature as a geometric source of irreversible information flow, without modifying the underlying gravitational field equations. Full article

We developed a self-consistent double-null description of an evaporating white-hole spacetime by embedding the outgoing Vaidya solution in a coordinate system that remains regular across the future horizon. Starting from the radiation-coordinate form, we specialize in retarded time so that a monotonically decreasing mass function $M\left(u\right)$ encodes outgoing positive-energy flux. Expressing the metric in null coordinates $(u,v)$, Einstein’s equations for a single-directional null-dust stress–energy tensor, $T_{uu}=\rho \left(u\right)$, then reduce to one first-order PDE for the areal radius: ${\mathsf{\partial }}_{v}r=B\left(u\right)\left(1-2M\left(u\right)/r\right)$. Its integral, $r+2M\left(u\right)ln|r-2M(u\left)\right|=v-C\left(u\right)$, defines an implicit foliation of outgoing null cones. The metric coefficient follows algebraically as $f(u,v)=1-2M\left(u\right)/r$. Residual gauge freedom in $B\left(u\right)$ and $C\left(u\right)$ is fixed so that u matches the Bondi retarded time at null infinity, while v remains analytic at the apparent horizon, generalizing the Kruskal prescription to dynamical mass loss. In the limit $M\left(u\right)\to M$, the construction reduces to the familiar Eddington–Finkelstein and Kruskal forms. Our solution, therefore, provides a compact analytic framework for studying white-hole evaporation, Hawking-like energy fluxes, and back-reaction in spherically symmetric settings without encountering coordinate singularities. Full article

A mass-conserved formulation for the Ffowcs-Williams–Hawkings (FW–H) integral is proposed to suppress contributions of spurious mass flux to the far-field sound at very low Mach numbers. The far-field condition and compact-source region assumptions are employed. By using higher-order derivatives of Green’s function, an expansion of the integrand in the monopole term is performed. This expansion transforms the mass-flux like monopole term into a series including different orders of velocity moment. At very low Mach numbers, the zero-order term is exactly the contribution from the spurious mass flux. The proposed mass-conserved formulation is confirmed by using an unsteady dipole, a two-dimensional (2D) incompressible convecting vortex, a circular-cylinder flow, and a co-rotating vortex pair. Additional spurious mass flux is added to the unsteady dipole, 2D incompressible convecting vortex, and flows over a circular cylinder; and the spurious mass flux of the co-rotating vortex pair comes from the residual of an incompressible-flow simulation. The far-field sound is found to be sensitive to spurious mass flux in the unsteady dipole and 2D incompressible convecting vortex cases. Then, the computation of the monopole-term expansion with the flow over a circular cylinder is presented. Fast convergence performance was observed, suggesting that the expansion requires little extra computational resources. Finally, FW–H boundary dependence is observed in the co-rotating vortex-pair case and eliminated by using the proposed mass-conserved formulation. Full article

This study proposes a control architecture based on iterative stochastic algorithms to control the doubly-fed induction machine (DFIM), often used in wind systems. We briefly present the modeling of this machine. We describe in more detail the control architecture based on indirect vector control by flux orientation (IFOC). This control architecture is optimized with the application of iterative stochastic algorithms applied to the speed controller. The optimization algorithms used were Particle Swarm Optimization (PSO), Harris Hawk Optimization (HHO) and Salp Swarm Algorithm (SSA). A comparative study under Matlab/Simulink between the different results obtained clearly shows the effectiveness of our approach. Full article

The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation of the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting rotor BVI noise using a high-resolution numerical method based on the Reynolds-averaged Navier–Stokes and the Ffowcs Williams–Hawkings equations. The seventh-order improved WENO-Z scheme is utilized to minimize the inherent numerical dissipation of the reconstruction method in the monotone upstream-centered scheme for conservation laws (MUSCL), thereby improving the rotor wake resolution and the BVI noise-prediction accuracy. The three-layer dummy cell method is used to ensure that the flux at the boundary maintains seventh-order accuracy. The effectiveness of the flow solver and the acoustic solver is validated using the Helishape-7A rotor and the UH-1H rotor, respectively. The flow field and BVI noise characteristics of the OLS rotor obtained from the fifth- and seventh-order WENO-Z schemes are compared with that of the third-order MUSCL for coarse and fine background grids. The wake resolution, noise-prediction accuracy, and computational cost of the three schemes are compared. The results show that the high-order WENO scheme provides higher accuracy for flow field simulation and BVI noise prediction than the MUSCL, but the computational cost of the WENO scheme increases substantially as the grid resolution increases. However, the WENO scheme can predict BVI using a coarser grid than the MUSCL. The computational cost of the WENO scheme is relatively low under the same flow field simulation resolution. Full article

We propose quantum simulations of 1 + 1D radial sections of different black hole spacetimes (Schwarzschild, Reissner–Nordstrøm, Kerr and Kerr–Newman), by means of a dc-SQUID array embedded on an open transmission line. This was achieved by reproducing the spatiotemporal dependence of 1 + 1D sections of the spacetime metric with the propagation speed of the electromagnetic field in the simulator, which can be modulated by an external magnetic flux. We show that the generation of event horizons—and therefore Hawking radiation—in the simulator could be achieved for non-rotating black holes, although we discuss limitations related to fluctuations of the quantum phase. In the case of rotating black holes, it seems that the simulation of ergospheres is beyond reach. Full article

We derive a correspondence between the Hawking radiation spectra emitted from general classes of Taub-NUT black holes with that induced by the relativistic motion of an accelerated Dirichlet boundary condition (i.e., a perfectly reflecting mirror) in (1+1)-dimensional flat spacetime. We demonstrate that the particle and energy spectra is thermal at late times and that particle production is suppressed by the NUT parameter. We also compute the radiation spectrum in the rotating, electrically charged (Kerr–Newman) Taub-NUT scenario, and the extremal case, showing, explicitly, how these parameters affect the outgoing particle and energy fluxes. Full article

The sound field properties of non-cavitating marine propellers are investigated using a hybrid method, in which the FWH (Ffowcs William-Hawkings) analogy is coupled with the BEM (Boundary Element Method) approach. The investigations include both the uniform and non-uniform inflow conditions. For both conditions, the dominant sound source terms and the decay rate of the noise with regard to the distance to propeller centre are investigated. The influence of the permeable surface dimensions in the permeable FWH approach on the hydroacoustic result is also investigated. To carry out the investigations, the formulation to calculate acoustic pressure generated by the propeller wake sheet is proposed for the first time. The issues associated to coupling permeable FWH approach and BEM are also discussed, including the fictitious volume flux problem and the consideration of the ship wake field. It was found that the influence of the permeable surface dimension is little for the 1st BPF (Blade Passage Frequency), but cannot be ignored for the 3rd BPF. In the uniform inflow situation the thickness terms are found to be dominant, while in the non-uniform inflow situation the loading terms are dominant. Full article

The purpose of this study is to investigate radiation from asymptotic zero acceleration motion where a horizon is formed and subsequently detected by an outside witness. A perfectly reflecting moving mirror is used to model such a system and compute the energy and spectrum. The trajectory is asymptotically inertial (zero proper acceleration)—ensuring negative energy flux (NEF), yet approaches light-speed with a null ray horizon at a finite advanced time. We compute the spectrum and energy analytically. Full article

It is shown that in Einstein’s theory and in the theory of gravity with Logunov constraints, there is a field-theoretical model of dark energy that is consistent with the observational data indicating that the Hubble value increases over time. In the developed model of dark energy, the isotropic energy dominant condition is violated. It solves the problem of the cosmological singularity and the singularity of “black holes”. The compact configuration of the scalar field can generate a flux of particles by the pairs of particles production mechanism from the vacuum by a field of barrier and in the process of transformation of thermal energy (Hawking radiation) and acceleration energy into radiation. The scalars can play the role of the so-called “black holes” with no singularity inside themselves. Full article

Turbulence parameters in the lower troposphere (up to ~4.5 km) are estimated from measurements of high-resolution and fast-response cold-wire temperature and Pitot tube velocity from sensors onboard DataHawk Unmanned Aerial Vehicles (UAVs) operated at the Shigaraki Middle and Upper atmosphere (MU) Observatory during two ShUREX (Shigaraki UAV Radar Experiment) campaigns in 2016 and 2017. The practical processing methods used for estimating turbulence kinetic energy dissipation rate $\epsilon$ and temperature structure function parameter $C_T^2$ from one-dimensional wind and temperature frequency spectra are first described in detail. Both are based on the identification of inertial (−5/3) subranges in respective spectra. Using a formulation relating $\epsilon$ and $C_T^2$ valid for Kolmogorov turbulence in steady state, the flux Richardson number $R_f$ and the mixing efficiency ${\chi }_m$ are then estimated. The statistical analysis confirms the variability of $R_f$ and ${\chi }_m$ around $~0.13-0.14$ and $~0.16-0.17$ , respectively, values close to the canonical values found from some earlier experimental and theoretical studies of both the atmosphere and the oceans. The relevance of the interpretation of the inertial subranges in terms of Kolmogorov turbulence is confirmed by assessing the consistency of additional parameters, the Ozmidov length scale $L_O$ , the buoyancy Reynolds number $R{e}_b$ , and the gradient Richardson number Ri. Finally, a case study is presented showing altitude differences between the peaks of $N^2$ , $C_T^2$ and $\epsilon$ , suggesting turbulent stirring at the margin of a stable temperature gradient sheet. The possible contribution of this sheet and layer structure on clear air radar backscattering mechanisms is examined. Full article

In earlier work concerning the sparsity of the Hawking flux, we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focusing specifically on Schwarzschild black holes, we have re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a pedagogically useful semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, being based on a variant of the “transfer matrix” formalism, are closely related to so-called “product integrals”, leading to quite straightforward and direct numerical evaluation, while side-stepping any need for numerically solving the relevant ordinary differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable “global models” for these greybody factors in the intermediate frequency regime, where most of the Hawking flux is actually concentrated. Working in a more general context, these path-ordered-exponential techniques are also likely to be of interest for generic barrier-penetration problems. Full article

In this study, cavitation flow around a hydrofoil and its radiated hydro-acoustic fields were numerically investigated, with an emphasis on the effects of viscous flux vectors. The full three-dimensional unsteady compressible Reynolds-averaged Navier–Stokes equations were numerically solved. The mass transfer model was adopted to model phase changes between liquid water and vapor. To resolve the numerical instability problem arising from the rapid changes in local density and speed of sound of the mixture, the preconditioning and dual-time stepping methods were employed. The filter-based turbulent model was applied to resolve the unstable cavitation flow field more accurately. In splitting the viscous terms, three approaches for dealing with viscous flux vectors were considered: the so-called viscous lagging, full viscous, and thin-layer models. Radiated hydro-acoustic waves were predicted by applying the Ffowcs Williams and Hawkings equations. The effects of the viscous flux vectors on the predicted flow fields and its radiated noise were then examined by comparing the hydro-dynamic forces, velocity distribution, volume fraction, far-field sound directivities, and sound spectrum of the three approaches. The results revealed that the thin-layer model can provide predictions as accurate as the full viscous model, but required less computational time. Full article