We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.
Our work builds temporal deep learning architectures for the classification of time-frequency signal representations on a novel model of simulated radar datasets. We show and compare the success of these models and validate the interest of temporal structures to gain on classification confidence over time.
Micro-Doppler analysis commonly makes use of the log-scaled, real-valued spectrogram, and recent work involving deep learning architectures for classification are no exception. Some works in neighboring fields of research directly exploit the raw temporal signal, but do not handle complex numbers, which are inherent to radar IQ signals. In this paper, we propose a complex-valued, fully temporal neural network which simultaneously exploits the raw signal and the spectrogram by introducing a Fourier-like layer suitable to deep architectures. We show improved results under certain conditions on synthetic radar data compared to a real-valued counterpart.
We will construct explicit examples of four-dimensional neutral signature Walker (but not necessarily degenerate Kundt) spaces for which all of the polynomial scalar curvature invariants vanish. We then investigate the properties of some particular subclasses of Ricci flat spaces. We also briefly describe some four-dimensional neutral signature Einstein spaces for which all of the polynomial scalar curvature invariants are constant.
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