On event horizon and ergosphere of Kerr–Newman black hole: A prediction application of artificial intelligence

It is a consensus among researchers that the general solution of Einstein’s field equations is the Kerr–Newman solution. It describes the charge, mass and angular momentum of the Kerr–Newman Black Hole (KNBH). The study of this solution is still a topic of research in general relativity and theoretical astrophysics. Therefore, motivated by this fact we offer a benchmark artificial neural networking approximation for the dependency of the ergosphere and event horizon of KNBH on a mass, charge and angular momentum. To be more specific, in the first layer of the neural networking model, the mass, charge and angular momentum of KNBH are considered inputs, while in the last layer, ergosphere and event horizon radius are taken as targets. For the training of the model, 70% (140) of the data are chosen and 15% (30) each is distributed for validation and testing. For training, a Levenberg–Marquardt Algorithm (LMA) is used. To approximate event horizon radius and ergosphere, neural models, namely ANN-I and ANN-II, are developed, respectively. Mean squared error (MSE) and correlation coefficient (R) analysis are conducted to evaluate the performances of neural models. Owing to the training dataset we observed that the ANN-II model achieves a low MSE value (about [Formula: see text]), suggesting excellent accuracy in estimating the ergosphere of the KNBH. R values (9.99992E[Formula: see text]1, 9.99999E[Formula: see text]1) are consistently very close to 1, indicating a high correlation between predicted and actual values of the event horizon and ergosphere of the KNBH. This suggests that the models claim a strong predictive relationship with the real data. The present ANN-based results are thought to be useful in expanding the concept of processing large volumes of intricate data, finding patterns and accurately forecasting astrophysical events.