In this talk, we consider electromagnetic waves in presence of a metallic inclusion with corners, assuming that the dielectric permittivity has a very small imaginary part, that will be neglected, and a negative real part. Due to the sign-change of the dielectric permittivity, very unusual singular phenomena take place at corners. In particular, for some configurations, a part of the energy may be trapped by the corners: this is the so-called blackhole effect [1]. In this presentation, we first give a mathematical analysis of this blackhole phenomenon, based on a detailed description of the corner’s singularities, in the 2D case. This phenomenon leads to numerical instabilities of finite element simulations. The solution that we have found and validated is to introduce a complex scaling at the corners. Finally, we compute the plasmonic eigenvalues of a 2D subwavelength particle with a corner [2]. While a smooth particle has a discrete sequence of eigenvalues, blackhole waves at the corner lead to the presence of an essential spectrum filling an interval. Numerical results show that the complex scaling deforms this essential spectrum, so as to unveil both embedded eigenvalues and complex plasmonic resonances. The latter are analogous to well-known complex scattering resonances, with the local behaviour at the corner playing the role of the behaviour at infinity. [1] A-S Bonnet-BenDhia et al, J. Comput. Phys., vol. 322, pp. 224-247, 2016 [2] A-S Bonnet-BenDhia et al, https://hal.archives-ouvertes.fr/hal-02923259