We consider the motion of a massive particle in a static, weakly-curved spacetime where the gravitational field is taken to be quantized. We find that Newton's law of free-fall is modified by quantum-gravitational corrections, in addition to the known special-relativistic and post-Newtonian modifications. The quantum-gravitational corrections take the form of stochastic noise in the particle trajectory, where the statistical properties of the noise depend on the quantum state of the gravitational field.
The vulnerability of power theft has hampered the electricity industry for decades. It obstructs social progress by having varying degrees of impact on home, commercial, and industrial customers. Sneak thieves have caught up with contemporary metering systems, putting electricity suppliers in trouble financially. This comparative analysis is the first step in the presentation of principles. Theft of electricity has serious consequences for the power grid's proper operation as well as the economic benefits of power corporations and commercial power service providers. An effective anti-power-theft algorithm is required for tracking power usage statistics in order to detect electricity power theft. In this literature review, we differentiate the Support Vector Machine (SVM) algorithm with other techniques for detecting abnormal usage among consumers (i.e., electricity fraudsters) in time-series data on power consumption. The results show some combinations can reach significantly better values than others, comparing both the balancing techniques for a same machine learning method itself as well as comparing these combinations between themselves.
We find Abelian gauge fields that double copy to a large class of black hole spacetimes with spherical horizon topology known as the Kerr-NUT-(A)dS family. Using a multi-Kerr-Schild prescription, we extend the previously-known double copy structure for arbitrarily rotating general dimension black holes, to include NUT charges and an arbitrary cosmological constant. In all cases, these single copy gauge fields are ‘aligned fields’, because their nonzero components align with the principal tensor which generates the Killing structure of the spacetime. In five dimensions, we additionally derive the same single-copy field strengths via the Weyl double copy procedure.
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