In this paper, a probabilistic methodology for estimating the energy costs in market wind generators associated with prediction errors is proposed. Generators must buy or sell production deviations due to when they bid day-ahead hour-ahead markets. The error modeled through probability density function that represents accuracy of model. Production hourly and their trading are then calculated. Three study cases based on real power installations Spain analyzed. three show can reach as much 10%...

We report numerical evidence of Hawking emission Bogoliubov phonons from a sonic horizon in flowing one-dimensional atomic Bose–Einstein condensate. The presence radiation is revealed peculiar long-range patterns the density–density correlation function gas. Quantitative agreement between our fully microscopic calculations and prediction analog models obtained hydrodynamic limit. New features are predicted robustness signal against finite temperature discussed.

It is known that the Einstein field equations in five dimensions admit more general spherically symmetric black holes on brane than four-dimensional relativity. We propose two families of analytic solutions (with ${g}_{\mathrm{tt}}\ensuremath{\ne}\ensuremath{-}{g}_{\mathrm{rr}}^{\ensuremath{-}1}),$ parametrized by Arnowitt-Deser-Misner mass and post-Newtonian parameter $\ensuremath{\beta},$ which reduce to Schwarzschild for $\ensuremath{\beta}=1.$ Agreement with observations requires...

We have used the analogy between gravitational systems and nonhomogeneous fluid flows to calculate density-density correlation function of an atomic Bose-Einstein condensate in presence acoustic black hole. The emission correlated pairs phonons by Hawking-like process results into a peculiar long-range density correlation. Quantitative estimations effect are provided for realistic experimental configurations.

We show that linear perturbations around the simplest black hole solution of massive bi-gravity theories, bi-Schwarzschild solution, exhibit an unstable mode featuring Gregory-Laflamme instability higher-dimensional strings. The result is obtained for gravity theory which free from Boulware-Deser ghost, as well its extension with two dynamical metrics. These results may indicate static holes in do not exist. For graviton mass order Hubble scale, however, timescale time.

Using the action principle we first review how linear density perturbations (sound waves) in an Eulerian fluid obey a relativistic equation: d'Alembert equation. This analogy between propagation of sound and that massless scalar field Lorentzian metric also applies to non-homogeneous flows. In these cases, waves effectively propagate curved four-dimensional ''acoustic'' whose properties are determined by flow. this analogy, consider regular flows which become supersonic, show acoustic...

We report on what is to our knowledge the first scattering experiment of surface waves an accelerating transcritical flow, which in analogue gravity context described by effective spacetime with a black-hole horizon. This has been probed incident co-current wave, partially scatters into outgoing countercurrent wave each side The measured amplitudes are compatible predictions hydrodynamical theory, where kinematical description terms metric exact.

We study acoustic white holes in a steadily flowing atomic Bose–Einstein condensate. A hole configuration is obtained when the flow velocity goes from super-sonic value upstream region to sub-sonic one downstream region. The scattering of phonon wavepackets on horizon numerically studied terms Gross–Pitaevskii equation mean-field theory: dynamical stability found, as well signature nonlinear back-action incident wavepacket onto horizon. correlation pattern density fluctuations by means...

We present a new class of solutions describing charged black holes in massive (bi)gravity. For generic choice the parameters gravity action, solution is Reissner-Nordström-de Sitter metric written Eddington-Finkelstein coordinates for both metrics. also study special case parameters, which space contains an extra symmetry.

We consider a sonic analog of black hole realized in the one-dimensional flow Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) occurrence horizon, (ii) associated acoustic Hawking radiation, (iii) quantum nature process. The signature behavior persists even at temperatures larger than chemical potential.Received 2 March...

We consider the analytic solutions of massive (bi)gravity which can be written in a simple form using advanced Eddington-Finkelstein coordinates. analyze stability these against radial perturbations. First we recover previously obtained result on instability bidiagonal bi-Schwarzschild solutions. In nonbidiagonal case (which contains, particular, Schwarzschild solution with Minkowski fiducial metric), show that generically there are physical spherically symmetric perturbations, but no unstable modes.

We present a solution for rotating black holes in massive gravity. first give of gravity with one dynamical metric. Both metrics this are expressed the advanced Eddington-Finkelstein--like coordinates: physical metric has original Kerr line element, while fiducial is flat, but written Eddington-Finkelstein form. For bigravity theory we an analogue solution: two have form, but, general, different hole masses. The generalization to include electric charge also given; it Kerr-Newman general...

The behaviors of the modes for a massless minimally coupled scalar field are investigated Unruh state Schwarzschild spacetime and "in" vacuum in which spherically symmetric null shell collapses to form nonrotating black hole. In both cases there two different sets solutions mode equation that make up state. For spacetimes, one set oscillates forever with no damping oscillations other approaches zero at late times. difference between null-shell corresponding vanishes as power law time....

The quantum stress tensor in the Unruh state for a conformal scalar propagating 4D Schwarzschild black hole spacetime is reconstructed its leading behavior at infinity and near horizon by means of an effective action derived functionally integrating trace anomaly.

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of black hole and naked singularity. In the former case, we explore effects various regions relevance for space-time. find lead to growth both event horizon radius ergosphere, reduction angular velocity, compared unperturbed values. Furthermore, they give rise formation curvature singularity at Cauchy show no evidence appearance superradiant instability. case...

The backreaction equations for the linearized quantum fluctuations in an acoustic black hole are given. solution near horizon, obtained within a dimensional reduction, indicates that holes, unlike Schwarzschild ones, get cooler as they radiate phonons. They show remarkable analogies with near-extremal Reissner-Nordstr\"om holes.

In this paper we extend the hydrodynamic results of {A. Fabbri and C. Mayoral, Phys. Rev. D 83, 124016 (2011).} study, analytically, propagation Bogoliubov phonons on top Bose-Einstein condensates with steplike discontinuities in speed sound by taking into account dispersion effects. We focus Hawking signal density-density correlations formation acoustic black-hole-like configurations.

We compute the analogue Hawking radiation for modes which possess a small wave vector perpendicular to horizon. For low frequencies, resulting mass term induces total reflection. This reflection is accompanied by an extra mode mixing occurs in supersonic region, and cancels out infrared divergence of near horizon spectrum. As result, amplitude undulation (0-frequency with macroscopic amplitude) emitted white hole flows now saturates at linear level, unlike what found massless case. In...