Rotating Boson Stars in Einstein-Gauss-Bonnet gravity Yves Brihaye † 1 , J¨ urgen Riedel ‡ 2 † Physique-Math´ ematique, Universit´ e de Mons, 7000 Mons, Belgium ‡ Institut f¨ ur Physik, Universit¨ at Oldenburg, 26111 Oldenburg, Germany February 2, 2014 Abstract A self-interacting SU(2)-doublet of complex scalar fields, minimally coupled to Einstein-Gauss-Bonnet gravity is considered in five space-time dimensions. The classical equations admit two families of solitons corresponding to spinning and non-spinning bosons stars. The generic solutions are constructed numerically and agree with exact results that are available in special limits of the parameters. The pattern of the boson stars is shown to be qualitatively affected by the Gauss-Bonnet coupling constant. PACS Numbers: 04.70.-s, 04.50.Gh, 11.25.Tq 1 Introduction Boson stars and Q-balls have been known for a long time. They are non-topological solitons [1, 2] characterized by a conserved Noether charge associated with a U(1) symmetry of the Lagrangian. One of the first constructions of non-topological solitons was achieved in [3], within a field theory describing a self-interacting complex scalar field. Q-balls are classical solutions; they are stationary with an explicite time-dependent phase with frequency ω. The conserved Noether charge Q is then related to the global phase invariance of the theory and is directly proportional to the frequency; Q can further be interpreted as the particle number. In [4], it was shown that a non-normalizable Φ 6 -potential is necessary to support soliton solutions. Using such a potential, several Q-ball solutions in 3 + 1 dimensions have been studied in details in [4, 5, 6]. The interest for these type of classical solutions was enhanced in particular after it was shown [7, 8] that supersymmetric extensions of the Standard Model (SM) also possess Q-ball solutions. In [9] an effective potential involving these effects was suggested and the properties of the corresponding Q-balls have been investigated [10]. Many astrophysical implications have been discussed, see [11] for a non exhaustive list. Recently several authors addressed the existence and the construction of globally regular solutions in scalar field theories coupled (minimally or not) to gravity in more than four dimensions [12],[13],[14]. Several features of the four-dimensional boson stars hold also in higher dimensions. For example the spectrum of the solutions as functions of the frequency ω present several branches existing on specific intervals of this parameter. Also, sequences of radially excited solutions exist. Perhaps, one of the most promising way to discover new features of these solitons is to emphasize their spinning properties. Classical solutions living in d-dimensions can have (d − 1)/2 independent angular momenta. It is therefore natural to emphasize the construction of rotating boson stars and Q-balls. The first construction of rotating boson stars in five dimensional is reported in [15]. In this paper it is shown that rotating solitons in d=5 can be accommodated if two complex scalar fields are present, assuming the two angular momenta to be equal, the classical equations leads to a system of ordinary differential equations. 1 email: yves.brihaye@umons.ac.be 2 email: jriedel@thescienceinstitute.com 1