New Results for Quasi Normal Modes of Gravitational Waves

Abstract

We briefly consider the data of collaboration LIGO/VIRGO for gravitational waves (GW) and the recent observations of Event Horizon Telescope (EHT), and we discuss difficulties for finding the right theory of gravity and the nature of the observed Extremely Compact Objects (ECOs). The only undisputable way to establish existence of event horizon of ECOs, is the extraction of Quasi Normal Modes (QNMs) from the ringing phase of the sources of GW. We present our method for calculation of QNMs of GW in the Schwarzschild metric with different boundary conditions. It is based on exact solutions of the Regge-Wheeler and Zerilli equations in terms of the confluent Heun functions. We present also new numerical results of high precision ($ \geq 16$ digits) for QNM frequencies. We indicate the difficulties for comparison of theoretical results for QNMs with the observations.