2 resultados para Lie Symmetries

em Memorial University Research Repository


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We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

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Although a great deal of research has examined lie-detection among adults, little research has examined the differences between audio and visual mediums for deception among children. In the current study participants were presented (n = 42) with recordings of four children, each describing his/her experience of getting glasses. Two of the accounts were truthful, two were fabricated. Half of the participants were presented with videos, half were presented with audio-recordings. Following the presentation of each recording, participants responded to questions regarding the truthfulness of each child’s account. Results showed that when evaluating truth-tellers, participants’ lie-detection accuracy was significantly greater than chance. Within the video condition, non-parents were shown to report significantly more lie-related cues than parents. Several deception cues were shown to be related to lie-detection accuracy.