Abstract
We investigate the fragmentation instability of hairy black holes in the theory with a Gauss–Bonnet (GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation.
Highlights
In the cosmological model, the dilatonic Einstein-GaussBonnet (DEGB) theory can provide the possibility of avoiding the initial singularity of the universe [25,26,27]
In the DEGB theory, the nontrivial real dilaton field appears in the black hole solution [31,32,33,34,35,36,37,38,39,40,41,42,43,44] as a scalar hair
The black hole hair is secondary [41] in the DEGB theory, because the scalar hair is determined by the mass of the black hole
Summary
The dilatonic Einstein-GaussBonnet (DEGB) theory can provide the possibility of avoiding the initial singularity of the universe [25,26,27]. That minimum mass there exist upper and lower branch solutions. The upper branch solutions are stable under linear perturbations and approach the Schwarzschild black holes in the large mass limit. The black ring is another type of solutions, which becomes more stable than MP black hole in higher angular momentum [48,49,50,51,52]. 2, we introduce our basic framework and numerical construction of the black holes for the theory where the dilaton field is coupled with the GB term.
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