Recent results show that when non-linear electrodynamics is considered the no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which are valid for the cases of neutral black holes and charged black holes in the Maxwell electrodynamics, can be circumvented [1,2]. What is even more, in the present work, we find new non-unique, numerical solutions describing charged black holes coupled to non-linear electrodynamics in a special class of scalar-tensor theories. One of the phases has a trivial scalar field and coincides with the corresponding solution in General Relativity. The other phases that we find are characterized by the value of the scalar field charge. The causal structure and some aspects of the stability of the solutions have also been studied. For the scalar-tensor theories considered, the black holes have a single, non-degenerate horizon, i.e., their causal structure resembles that of the Schwarzschild black hole. The thermodynamic analysis of the stability of the solutions indicates that a phase transition may occur.
The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The noscalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.
We examine the possibility of travelling wave solutions within the nonlinear Euler-Heisenberg electrodynamics. Since this theory resembles in its form the electrodynamics in matter, it is a priori not clear if there exist travelling wave solutions with a new dispersion relation for ω(k) or if the Euler-Heisenberg theory stringently imposes ω = k for any arbitrary ansatz E(ξ) and B(ξ) with ξ ≡ k · r − ωt. We show that the latter scheme applies for the Euler-Heisenberg theory, but point out the possibility of new solutions with ω = k if we go beyond the Euler-Heisenberg theory, allowing strong fields. In case of the Euler-Heisenberg theory the quantum mechanical effect of the travelling wave solutions remains in corrections to the energy density and the Poynting vector.
We study equilibrium configurations of boson stars in the framework of a
class scalar-tensor theories of gravity with massive gravitational scalar
(dilaton). In particular we investigate the influence of the mass of the
dilaton on the boson star structure. We find that the masses of the boson stars
in presence of dilaton are close to those in general relativity and they are
sensitive to the ratio of the boson mass to the dilaton mass within a typical
few percent. It turns out also that the boson star structure is mainly
sensitive to the mass term of the dilaton potential rather to the exact form of
the potential.Comment: 9 pages, latex, 9 figures, one figure dropped, new comments added,
new references added, typos correcte
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