Abstract
We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field. We find that both the apparent horizon and the local event horizon (measured in luminosity coordinate) monotonically increase with the advanced time as well as the Vaidya mass. At late advanced times, the apparent horizon approaches the event horizon and gradually becomes future outer. Correspondingly, the space-time arrives at stationary black hole states with the relaxation time inversely proportional to the $1/(n-1)$ power of the final black hole mass, where $n$ is the space-time dimension. These results strongly support the solutions describing the formation of black holes with scalar hair. We also obtain new charged dynamical solutions in the non-minimal theory by introducing an Maxwell field which is non-minimally coupled to the scalar. The presence of the electric charge strongly modifies the dynamical evolution of the space-time.
Highlights
JHEP05(2016)[170] the dynamical evolution of the apparent horizon which was studied as a function of the advanced time
We study the global structure of some exact scalar hairy dynamical black holes which were constructed in Einstein gravity either minimally or non-minimally coupled to a scalar field
We find that the apparent horizon grows monotonically with the advanced time and approaches the event horizon at the future infinity
Summary
Where H, h and ρ are all functions of the Eddington-Finkelestein-type coordinates r and u and dΩn−2 is the (n − 2) dimensional space with spherical/torus/hyperbolic symmetries
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