Yunho Kim — Page 2 | Searcharxiv

arXiv2020

Topologically induced black hole charge and its astrophysical manifestations

Quantum corrected effective action for gravity contains massive spin-2 ghost degrees of freedom and admits a topological term which couples longitudinal vector degrees of freedom of the massive spin-2 to Maxwell's electromagnetism. We argue that in the presence of otherwise unobservable gravimagnetic poles this topological term induces an electric charge on a black hole which can be probed through the associated electric and magnetic fields. In particular, we discuss the electromagnetic follow up from the LIGO-sensitive charged black hole binary coalescence due to the synchrotron radiation from the surrounding plasma and the shadow of super-massive charged black holes.

gr-qc↗

arXiv2017

An unconstrained framework for eigenvalue problems

In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = λB{\bf x}$ with two $N\times N$ real symmetric matrices $A, B$ via minimizing a proposed functional whose nonzero critical points ${\bf x}\in\mathbb{R}^N$ solve the eigenvalue problem and whose local minimizers are indeed global minimizers. Inspired by the properties of the proposed functional to be minimized, we provide analysis on convergence of various algorithms either to find critical points or local minimizers. Using the same framework, we will also present an eigenvalue problem for differential operators in the continuous setting. It will be interesting to see that this unconstrained framework is designed to find the smallest eigenvalue through matrix addition and multiplication and that a solution ${\bf x}\in\mathbb{R}^N$ and the matrix $B$ can compute the corresponding eigenvalue $λ$ without using $A$ in the case of $A{\bf x}=λB{\bf x}$. At the end, we will present a few numerical experiments which will confirm our analysis.

math.OC↗