Abstract
Since the 1970s, beginning with the work of Vishveshwara, approximation methods
have been developed to compute the quasinormal modes (QNMs) produced by
perturbed black holes. In our attempt to find a new method that can overcome the
shortcomings of the existing approaches, we investigated a novel technique based
on neural networks; namely, physics-informed neural networks (PINNs). Not long
after its recent development, this technique has gained popularity in solving differential
equations that govern many science and engineering problems. We investigated
two variations of PINNs coded in Python; one was built with the DeepXDE
package, while the second (dubbed an eigenvalue solver) was built with the Pytorch
package. The former was implemented in a preliminary work to test the feasibility
of applying PINNs to QNM computations, and the latter was used in the
main part of this dissertation to solve the analytically intractable Schrödinger-like
equations of Schwarzschild black holes perturbed by various test fields. Comparing
our QNM approximations with their counterparts found by Leaver and Konoplya,
we found them to be as accurate as the former’s (arguably the leading technique
in terms of accuracy), at least up to 4 decimal places for the QNMs given
in the literature. In other words, our PINN approximations had percentage deviations
of (δωRe , δωIm ) = (< 0.01%,< 0.01%), at best. However, regarding efficiency,
our PINNs fall behind the computation times of the extant methods; therefore, they
currently provide no advantages in terms of overall performance for solving wellstudied
perturbation scenarios.