Abstract
We study massive scalar field perturbation on Kerr black holes in dynamical Chern–Simons gravity by performing a (2+1)-dimensional simulation. Object pictures of the wave dynamics in time domain are obtained. The tachyonic instability is found to always occur for any nonzero black hole spin and any scalar field mass as long as the coupling constant exceeds a critical value. The presence of the mass term suppresses or even quench the instability. The quantitative dependence of the onset of the tachyonic instability on the coupling constant, the scalar field mass and the black hole spin is given numerically.
Highlights
Past years have witnessed the great achievements in astronomical observations, especially the first-ever detection of gravitational wave (GW) [1,2,3]
To alleviate the tension, a variety of modified gravity theories (MOGs) have been proposed among which some were found viable by employing the current available observational constraints, such as scalar–tensor theory, dynamical Chern–Simons gravity, scalar-Einstein–Gauss–Bonnet theory and Lorentz-violating gravity [5]
With the presence of such coupling and in Kerr background, it is found that the massless scalar field will acquire an effective mass square which becomes negative in the vicinity of black hole horizon, resulting in the tachyonic instability and leading to the so-called spontaneous scalarization [32,33,34]
Summary
Past years have witnessed the great achievements in astronomical observations, especially the first-ever detection of gravitational wave (GW) [1,2,3]. The minority existing work on the tachyonic instability in dSCG [32,33,34] are all focused on the case when the scalar field is massless. At linearized level, only the mass term can alter the onset of the tachyonic instability and the induced spontaneous scalarization. In the present paper, we would like to extend the study of the tachyonic instability of Kerr black hole in dCSG to the case when the scalar field is massive. We will see later that the inclusion of mass term will alter the object picture of the wave dynamics and the onset of the tachyonic instability considerably. 2, we give a brief introduction of the dCSG theory and write out the scalar field perturbation equation.
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