Origin of the Thermal Radiation in a Solid-State Analog of a Black-Hole

An effective black-hole-like horizon occurs, for electromagnetic waves in matter, at a surface of singular electric and magnetic permeabilities. In a physical dispersive medium this horizon disappears for wave numbers with $k>k_c$. Nevertheless, it is shown that Hawking radiation is still emitted if free field modes with $k>k_c$ are in their ground state.Comment: 13 Pages, 3 figures, Revtex with epsf macro

Spinning String and Giant Graviton in Electric/Magnetic Field Deformed AdS3×S3×T4AdS_3 \times S^3 \times T^4

We apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to the 11D M-theory with a stack of M2-branes $\bot$ M2-branes, then, through the mechanism of Kaluza-Klein reduction and a series of the T duality we obtain the corresponding background of a stack of D1-branes $\bot$ D5-branes which, in the near-horizon limit, becomes the magnetic or electric Melvin field deformed $AdS_3 \times S^3 \times T^4$. We find the giant graviton solution in the deformed spacetime and see that the configuration whose angular momentum is within a finite region could has a fixed size and become more stable than the point-like graviton, in contrast to the undeformed giant graviton which only exists when its angular momentum is a specific value and could have arbitrary size. We discuss in detail the properties of how the electric/magnetic Melvin field will affect the size of the giant gravitons. We also adopt an ansatz to find the classical string solutions which are rotating in the deformed $S^3$ with an angular momentum in the rotation plane. The spinning string and giant graviton solutions we obtained show that the external magnetic/electric flux will increase the solution energy. Therefore, from the AdS/CFT point of view, the corrections of the anomalous dimensions of operators in the dual field theory will be positive. Finally, we also see that the spinning string and giant graviton in the near-horizon spacetime of Melvin field deformed D5-branes background have the similar properties as those in the deformed $AdS_3 \times S^3 \times T^4$.Comment: Latex 21 pages, slightly detail calculation

Wind turbine gearbox condition monitoring : experimental validation of a thermal network model

Condition monitoring is an important part of predictive maintenance. Early detection of incipient faults prevents major component failures and allows for the implementation of predictive repair strategies. Gearboxes are responsible for up to one third of all lost wind turbine availability1 , each failure downtime of around 600 hours2 . Deterioration of the drivetrain components will often be reflected in an increase in losses, as a result of increased friction or a reduced efficiency of energy transfer in the cooling mechanism, resulting in elevated temperatures3 . Monitoring temperature changes are useful to understand how the thermal behaviour of a gearbox can change as a result of a fault. In the author’s previous research, a thermal network model of a ”healthy” gearbox was produced. The model was partially validated by prelimary experimental data using an 11kW wind turbine gearbox test rig located at University of Strathclyde. Figure 1 shows the how this research links together. The confidence in the preliminary experiment is limited due to the simplistic nature of the data aquisition (DAQ) equipment. The DAQ system itself plays a significant role, as temperature measurement method influences diagnostic capabilities. A number of studies in literature used experimental methods to use temperature to detect faults4 , in most cases the input variables and measurement uncertainty weren’t quantified. This research focusses on improving the certainty of the experimental data by redeveloping the DAQ system and experiment strategy to improve accuracy. Figure 2 shows all aspects of experiment that have been taken into consideration to ensure validity, reliability and reproducibility. The experiment was carried out on a ”healthy” gearbox, with 8 point sensors and a thermal camera. The rotational speed was fixed and the torque was varied to reflect the wind turbine operation. The results show the way in which heat propagates through the gearbox, and are compared to the thermal model to identify normal operational losses. Faults were then simulated on the test rig with the addition of heat at component locations. The magnitude and location of the applied heat were varied to imitate failure modes. The results show how the additional heat propagates to other parts of the gearbox and indicate the extent to which a fault can be detected. These results can also be used to validate the simulated faults in the thermal model. The outcome of this research can determine if temperature measurements can be used to detect and locate faults, to make condition monitoring more accurate

Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach

We present a method for computing the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency dispersion. The method involves a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations. The modified wave equation is obtained by adding a higher order derivative term suppressed by powers of a fundamental momentum scale $k_0$ to the ordinary wave equation. Depending on the sign of this new term, high frequency modes propagate either superluminally or subluminally. We show that the resulting spectrum of created particles is thermal at the Hawking temperature, and further that the out-state is a thermal state at the Hawking temperature, to leading order in $k_0$, for either modification.Comment: 26 pages, plain latex, 6 figures included using psfi

Trans-Planckian Tail in a Theory with a Cutoff

Trans-planckian frequencies can be mimicked outside a black-hole horizon as a tail of an exponentially large amplitude wave that is mostly hidden behind the horizon. The present proposal requires implementing a final state condition. This condition involves only frequencies below the cutoff scale. It may be interpreted as a condition on the singularity. Despite the introduction of the cutoff, the Hawking radiation is restored for static observers. Freely falling observers see empty space outside the horizon, but are "heated" as they cross the horizon.Comment: 17 pages, RevTe

Large quantum gravity effects: Unexpected limitations of the classical theory

3-dimensional gravity coupled to Maxwell (or Klein-Gordon) fields is exactly soluble under the assumption of axi-symmetry. The solution is used to probe several quantum gravity issues. In particular, it is shown that the quantum fluctuations in the geometry are large unless the number and frequency of photons satisfy the inequality $\N(\hbar G\omega)^2 << 1$. Thus, even when there is a single photon of Planckian frequency, the quantum uncertainties in the metric are significant. Results hold also for a sector of the 4-dimensional theory (consisting of Einstein Rosen gravitational waves).Comment: 8 pages, No figures, ReVTe

Instability of non-supersymmetric smooth geometries

Recently certain non-supersymmetric solutions of type IIb supergravity were constructed [hep-th/0504181], which are everywhere smooth, have no horizons and are thought to describe certain non-BPS microstates of the D1-D5 system. We demonstrate that these solutions are all classically unstable. The instability is a generic feature of horizonless geometries with an ergoregion. We consider the endpoint of this instability and argue that the solutions decay to supersymmetric configurations. We also comment on the implications of the ergoregion instability for Mathur's `fuzzball' proposal.Comment: v2: typos corrected, reference adde

Canonical differential geometry of string backgrounds

String backgrounds and D-branes do not possess the structure of Lorentzian manifolds, but that of manifolds with area metric. Area metric geometry is a true generalization of metric geometry, which in particular may accommodate a B-field. While an area metric does not determine a connection, we identify the appropriate differential geometric structure which is of relevance for the minimal surface equation in such a generalized geometry. In particular the notion of a derivative action of areas on areas emerges naturally. Area metric geometry provides new tools in differential geometry, which promise to play a role in the description of gravitational dynamics on D-branes.Comment: 20 pages, no figures, improved journal versio

When Black Holes Meet Kaluza-Klein Bubbles

We explore the physical consequences of a recently discovered class of exact solutions to five dimensional Kaluza-Klein theory. We find a number of surprising features including: (1) In the presence of a Kaluza-Klein bubble, there are arbitrarily large black holes with topology S^3. (2) In the presence of a black hole or a black string, there are expanding bubbles (with de Sitter geometry) which never reach null infinity. (3) A bubble can hold two black holes of arbitrary size in static equilibrium. In particular, two large black holes can be close together without merging to form a single black hole.Comment: 23 pages, 5 figures, v2: few comments on stability modifie

Hawking radiation without black hole entropy

In this Letter I point out that Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries. Hawking radiation arises for any test field on any Lorentzian geometry containing an event horizon regardless of whether or not the Lorentzian geometry satisfies the dynamical Einstein equations of general relativity. On the other hand, the classical laws of black hole mechanics are intrinsically linked to the Einstein equations of general relativity (or their perturbative extension into either semiclassical quantum gravity or string-inspired scenarios). In particular, the laws of black hole thermodynamics, and the identification of the entropy of a black hole with its area, are inextricably linked with the dynamical equations satisfied by the Lorentzian geometry: entropy is proportional to area (plus corrections) if and only if the dynamical equations are the Einstein equations (plus corrections). It is quite possible to have Hawking radiation occur in physical situations in which the laws of black hole mechanics do not apply, and in situations in which the notion of black hole entropy does not even make any sense. This observation has important implications for any derivation of black hole entropy that seeks to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma