Accelerated black holes in (2 + 1) dimensions: quasinormal modes and stability

Abstract We investigate the propagation of a scalar field in a $$(2+1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -dimensional accelerated black hole, recently revisited in Arenas-Henriquez et al. (J High Energy Phys https://doi.org/10.1007/jhep05(2022)063 , 2022). We briefly describe how the conformal configuration renders a trivial scalar perturbation with a rescaling of the field mass. On the contrary, the free scalar field propagation presents an intricate dynamic, whose equation may be reduced through the use of Israel junction conditions and a non-trivial ansatz. In this case, using two different methods we calculate the quasinormal modes of the solution also obtaining unstable field profiles delivered by the linear scalar perturbation to the background geometry. We examine the parameter space of angular eigenvalues of the field and accelerations under which such instabilities occur.