---
abstract: 'It is shown that the quasi-normal modes arise, in a natural way, when considering the oscillations in unbounded regions by imposing the radiation condition at spatial infinity with a complex wave vector $k$. Hence quasi-normal modes are not peculiarities of gravitation problems only (black holes and relativistic stars). It is proposed to consider the space form of the quasi-normal modes with allowance for their time dependence. As a result, the problem of their unbounded increase when $r\to \infty$ is not encountered more. The properties of quasi-normal modes of a compact dielectric sphere are discussed in detail. It is argued that the spatial form of these modes (especially so-called surface modes) should be taken into account, for example, when estimating the potential health hazards due to the use of portable telephones.'
author:
- 'V. V. Nesterenko'
- 'A. Feoli'
- 'G. Lambiase'
- 'G. Scarpetta'
title: |
    Quasi-normal modes of a dielectric sphere\
    and some their implications
---

Introduction
============

Quasi-normal modes (qnm) are widely used now in black hole physics and in relativistic theory of stellar structure (see, for example, Refs. [@Nollert; @FN; @KS]). The corresponding eigenfrequencies are complex numbers, however it is not due to the dissipative 