# Scalar field quasinormal modes on asymptotically locally flat rotating black holes in three dimensions

## TL;DR

This paper analytically computes the quasinormal modes of a massless scalar field around rotating black holes in three-dimensional New Massive Gravity, revealing unique damping behaviors as angular momentum varies.

## Contribution

It provides the first closed-form solutions for scalar quasinormal frequencies on these asymptotically locally flat rotating black holes.

## Key findings

- Quasinormal frequencies are obtained analytically.
- Imaginary parts tend to minus infinity as angular momentum approaches zero.
- Static black holes in this family do not admit quasinormal modes.

## Abstract

The pure quadratic term of New Massive Gravity in three dimensions admits asymptotically locally flat, rotating black holes. These black holes are characterized by their mass and angular momentum, as well as by a hair of gravitational origin. As in the Myers-Perry solution in dimensions greater than five, there is no upper bound on the angular momentum. We show that, remarkably, the equation for a massless scalar field on this background can be solved in an analytic manner and that the quasinormal frequencies can be found in a closed form. The spectrum is obtained requiring ingoing boundary conditions at the horizon and an asymptotic behavior at spatial infinity that provides a well-defined action principle for the scalar probe. As the angular momentum of the black hole approaches zero, the imaginary part of the quasinormal frequencies tends to minus infinity, migrating to the north pole of the Riemann Sphere and providing infinitely damped modes of high frequency. We show that this is consistent with the fact that the static black hole within this family does not admit quasinormal modes for a massless scalar probe.