Hybrid Metric-Palatini Gravity: Regular Stringlike Configurations

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.

Thick brane structures in generalized hybrid metric-Palatini gravity

“…It is interesting to note that this theory, which in the linear approach takes the form R + f (R), one retains the positive results through the Einstein-Hilbert term R and the addi-tional gravitational corrections are given by the metric-affine f (R) component, where the Palatini curvature scalar R is constructed in terms of an independent connection. A wide variety of applications of this hybrid metric-Palatini theory has been explored, namely, in considering that dark matter is a geometric effect of modified gravity [25,26], in exploring the Cauchy problem [27] and the Noether symmetries [28], black hole, wormhole and stellar solutions [29][30][31][32][33][34], the Einstein static Universe [35], string-like configurations [36,37], and thick branes [38], among others [39].…”

Weak-field regime of the generalized hybrid metric-Palatini gravity

“…This implies the existence of a long-range scalar field, which is able to modify the cosmological [26,27] and galactic dynamics [28,29], but leaves the Solar System unaffected [30]. A plethora of applications exist in the literature, such as in cosmology [31][32][33][34][35][36] and extra-dimensions [37,38], stringlike configurations [39,40], black holes and wormholes [41][42][43][44][45], stellar configurations [46], tests of binary pulsars [47], observational constraints [48], among other applications (we refer the reader to [23,24] for more details). However, one may consider further generalizations of the linear hybrid metric-Palatini theory, by taking into account an fðR; RÞ extension [49,50].…”

Spherically Symmetric Space-Times in Generalized Hybrid Metric-Palatini Gravity

“…At the cosmological level, it has been shown to create models of accelerated expansion without invoking a cosmological constant [7]; for more detailed descriptions see the reviews [8,9] and also [10] for a study of Noether symmetries in HMPG, and [11] for a discussion of a relationship between HMPG and R 2 gravity. Spherically symmetric static solutions of HMPG, describing, in particular, black holes and wormholes, were studied in [12][13][14], and static cylindrical stringlike objects in [15,16].…”