We study exact, analytic, static, spherically symmetric, four-dimensional solutions of minimally coupled Einstein-scalar gravity, sourced by a scalar field whose profile has the form of the sine-Gordon soliton. We present a horizonless, everywhere regular and positive-mass solution-a solitonic star-and a black hole. The scalar potential behaves as a constant near the origin and vanishes at infinity. In particular, the solitonic scalar star interpolates between an anti-de Sitter and an asympototically flat spacetime. The black-hole spacetime is unstable against linear perturbations, while due to numerical issues, we were not able to determine with confidence whether or not the starlike background solution is stable.
Sine-Gordon solitonic scalar stars and black holes
Franzin, Edgardo;Cadoni, Mariano;Tuveri, Matteo
2018-01-01
Abstract
We study exact, analytic, static, spherically symmetric, four-dimensional solutions of minimally coupled Einstein-scalar gravity, sourced by a scalar field whose profile has the form of the sine-Gordon soliton. We present a horizonless, everywhere regular and positive-mass solution-a solitonic star-and a black hole. The scalar potential behaves as a constant near the origin and vanishes at infinity. In particular, the solitonic scalar star interpolates between an anti-de Sitter and an asympototically flat spacetime. The black-hole spacetime is unstable against linear perturbations, while due to numerical issues, we were not able to determine with confidence whether or not the starlike background solution is stable.
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