Periodic orbits and gravitational wave radiation in short hair black hole spacetimes for an extreme mass ratio system

TL;DR

This paper investigates how the parameters of a short hair black hole influence particle orbits and gravitational wave signals, offering potential observational methods to distinguish such black holes from classical ones and test the no-hair theorem.

Contribution

It provides a detailed analysis of the effects of hair parameters on orbits and gravitational waves in extreme mass ratio systems, revealing observable differences from Schwarzschild black holes.

Findings

Increased hair parameter $Q_m$ decreases orbit radius and angular momentum.

Higher $Q_m$ and lower $k$ amplify gravitational wave signals.

Short hair black holes can be distinguished from classical black holes through gravitational wave observations.

Abstract

For a short hair black hole(BH) which circumvents the "no-short-hair" theorem, it manifests intense hair behavior in the vicinity of the event horizon, accompanied by remarkable quantum effects. These effects may carry important information about the internal structure and dynamical evolution of BHs, thereby providing a new perspective on the problem of black hole information loss. Therefore, in this paper, we analyze the influence of the hair parameter $Q_m$ and the structural parameter $k$ of the short hair BH in an extreme mass ratio(EMR) system on the periodic orbits of particles and gravitational wave radiation. The results show that as $Q_m$ increases, the radius and angular momentum of the bound orbit decrease, and the $E-L$ space shifts to the left. An increase in $k$ weakens this trend. When $k$ takes a larger value, the short hair BH and the Schwarzschild BH tend to be degenerate. Compared with the Schwarzschild BH, the bound orbit energy and angular momentum of the short hair black hole are reduced. Under the conditions of higher $Q_m$ and lower $k$, the gravitational wave period is suppressed and the signal amplitude is significantly increased. These results provide new observational means for distinguishing short hair BH from classical BH and offer new insights for verifying the no-hair theorem and understanding the physical behavior near the event horizon.