Abstract
We discuss static, cylindrically symmetric vacuum solutions of hybrid metric-Palatini gravity (HMPG), a recently proposed theory that has been shown to successfully pass the local observational tests and produce a certain progress in cosmology. We use HMPG in its well-known scalar-tensor representation. The latter coincides with general relativity containing, as a source of gravity, a conformally coupled scalar field ϕ and a self-interaction potential V(ϕ). The ϕ field can be canonical or phantom, and, accordingly, the theory splits into canonical and phantom sectors. We seek solitonic (stringlike) vacuum solutions of HMPG, that is, completely regular solutions with Minkowski metric far from the symmetry axis, with a possible angular deficit. A transition of the theory to the Einstein conformal frame is used as a tool, and many of the results apply to the general Bergmann-Wagoner-Nordtvedt class of scalar-tensor theories as well as f(R) theories of gravity. One of these results is a one-to-one correspondence between stringlike solutions in the Einstein and Jordan frames if the conformal factor that connects them is everywhere regular. An algorithm for the construction of stringlike solutions in HMPG and scalar-tensor theories is suggested, and some examples of such solutions are obtained and discussed.
Highlights
General relativity (GR) is well known to be quite successful in describing local observational effects in the Solar system, in stellar astrophysics and, quite probably, in black hole physics
It faces serious problems at larger scales: on the galactic scale, it does not give a satisfactory explanation of the rotation curves without introducing the so-called Dark Matter (DM) of still unknown nature, and it cannot account for the observed accelerated expansion of the Universe without introducing the so-called Dark Energy (DE), which is an unknown kind of matter with large negative pressure
As in [16], we will employ the scalar-tensor theory (STT) representation of hybrid metric-Palatini gravity (HMPG), but, unlike these authors, we essentially use the well-known conformal mapping leading to the Einstein frame, which formally coincides with GR with a minimally coupled scalar field as the source of gravity
Summary
General relativity (GR) is well known to be quite successful in describing local observational effects in the Solar system, in stellar astrophysics and, quite probably, in black hole physics. HMPG, which combines the metric and Palatini approaches to the description of gravity and extends the formulation of f ( R) theories, has a number of achievements described in the reviews [7,8,9] It agrees with the classical tests in the Solar system [10], fairly well solves the DM problem concerning the dynamics of galaxies and galaxy clusters; it has been shown to be able to describe an accelerating Universe without invoking a cosmological constant [11]. As in [16], we will employ the scalar-tensor theory (STT) representation of HMPG, but, unlike these authors, we essentially use the well-known conformal mapping leading to the Einstein frame, which formally coincides with GR with a minimally coupled scalar field as the source of gravity The latter problem has been studied in [22], and a number of results and observations that were obtained there turn out to be useful for studying the present problem.
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