Scalar Field Probes of Power-Law Space-Time Singularities

We analyse the effective potential of the scalar wave equation near generic space-time singularities of power-law type (Szekeres-Iyer metrics) and show that the effective potential exhibits a universal and scale invariant leading x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that the metrics satisfy the strict Dominant Energy Condition (DEC). This result parallels that obtained in hep-th/0403252 for probes consisting of families of massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The detailed properties of the scalar wave operator depend sensitively on the numerical coefficient of the x^{-2}-term, and as one application we show that timelike singularities satisfying the DEC are quantum mechanically singular in the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We also comment on some related issues like the near-singularity behaviour of the scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde

Grid Awareness Under Normal Conditions and Cyber-Threats

The situational grid awareness is becoming increasingly important for power system operations due to smaller operational margins, wide range of uncertainties entailed by renewables and highly critical infrastructure failures due to potential cyber-attacks. In this chapter, we look at some of the state-of-the-art technologies to monitor events in a power system under normal operating condition, followed by detection algorithms for regular business risk events, such as faults and equipment failures, and finally, we look into methods for quantifying vulnerability of under the rare and men-orchestrated cyber-attacks. First, we outline an architecture of a central piece of today’s grid awareness system, Wide Area Monitoring, Protection and Control technology. Next, we review an event detection method used to identify and record faults and failures in the grid. Finally, we present a method for vulnerability assessment of grids under cyber-attacks