Greybody factors for a nonminimally coupled scalar field in BTZ black hole background

TL;DR

This paper analytically investigates how a nonminimally coupled scalar field interacts with BTZ black holes, revealing how reflection, absorption, and decay depend on coupling parameters, especially in strong coupling regimes.

Contribution

It provides analytical expressions for greybody factors of a nonminimally coupled scalar in BTZ backgrounds, highlighting the effects of strong coupling and specific parameter regimes.

Findings

Reflection coefficient tends to zero for coupling ξ ≥ 0.25

Greybody factor approaches a finite constant at low energy in zero angular momentum case

The finite constant does not generally match the black hole horizon area

Abstract

In the present work we study the propagation of a probe nonminimally coupled scalar field in BTZ black hole background. We find analytical expressions for the reflection coefficient, the absorption cross-section, and the decay rate in the strong coupling case, where the nonminimal coupling is larger than its conformal value $\xi_{c}= 1/6$. Our main results are summarized in several figures, in which we show how the behavior of the aforementioned quantities depends on the parameters of the theory. Our findings show that i) the reflection coefficient tends to zero only for a nonminimal coupling $\xi \geq 0.25$, and ii) in the zero angular-momentum case the greybody factor in the low energy regime tends to a finite constant that generically does not coincide with the area of the horizon of the black hole. There is, however, a special case in which this holds.