Minimal boson stars in 5 dimensions: classical instability and existence of ergoregions

Abstract

We show that minimal boson stars, i.e. boson stars made out of scalar fields without self-interaction, are always classically unstable in 5 space-time dimensions. This is true for the non-rotating as well as rotating case with two equal angular momenta and in both Einstein and Gauss-Bonnet gravity, respectively, and contrasts with the 4-dimensional case, where classically stable minimal boson stars exist. We also discuss the appearance of ergoregions for rotating boson stars with two equal angular momenta. While rotating black holes typically possess an ergoregion, rotating compact objects without horizons such as boson stars have ergoregions only in a limited range of the parameter space. In this paper, we show for which values of the parameters these ergoregions appear and compare this with the case of standard Einstein gravity. We also point out that the interplay between Gauss-Bonnet gravity and rotation puts constraints on the behaviour of the space-time close to the rotation axis.

Boson stars in higher-derivative gravity

“…As can be seen in Fig 3-6, for low φ 0 (0), both Einstein and sGB theories give same values for all physical parameters. This feature is shared by EGB boson-stars in five dimensions and [2] attribute this behavior to smallness of energy momentum tensor. For scalar fields with low amplitudes, the effective Gauss-Bonnet coupling is not strong enough.…”

“…With coupling of type ξφφ * R, they found that ξ > 4 gives only negative binding energies. Note that we use the similar coupling to Gauss Bonnet term of type Aφφ * G. More importantly, this occurrence of "classically stable" boson-stars in sGB gravity is in stark contrast with EGB boson-stars in 5 dimensions [2] that are always classicallyunstable. However, having negative binding energy does not guarantee the stability against gravitational collapse.…”

Black holes with scalar hair in Einstein–Gauss–Bonnet gravity

“…In principle, all the orders of the Taylor expansion are determined in terms of B 0 , W 0 , Π 1 and H 2 (or alternatively of F 2 obeying (15)). For α > 0, the constraint imposes some limit in α for spinning boson stars of definite angular momentum [12]. In the asymptotic region, the metric has to approach the Minkowski space-time and the scalar field vanishes.…”

“…A general feature seems to be that any solution of this type can be deformed continuously by progressively increasing the Gauss-Bonnet parameter α and ceases to exist at a critical value, say α max . The reasons of this limitation can be found analytically [10], [12] by performing a Taylor expansion of the solutions around the origin. It turns out that Gauss-Bonnet interaction implies some quadratic constraints like (15) between the Taylor coefficients; as a consequence some coefficients might become complex for large values of α and the solution stops to be real.…”

“…The corresponding equations are in general more involved that the Einstein equation and the enhanced non linearity has generically an influence of the solutions. Five-dimensional spinning boson stars in EGB gravity were constructed in [10] with a negative cosmological constant and in [11,12] with Λ = 0. In both cases, it was found that the solutions exist for a limited range of the Gauss-Bonnet coupling constant.…”