Spherically Symmetric Black Holes and Wormholes in Hybrid Metric-Palatini Gravity

Abstract

The so-called hybrid metric-Palatini theory of gravity.(HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically symmetric vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential V (φ) , and both Riemannian ( R ) and Palatini (R ) Ricci scalars are zero. Such a scalar-tensor theory coincides with general relativity with a phantom conformally coupled scalar field as a source of gravity. Generic asymptotically flat solutions either contain naked central singularities or describe traversable wormholes, and there is a special two-parameter family of globally regular black hole solutions with extremal horizons. In addition, there is a one-parameter family of solutions with an infinite number of extremal horizons between static regions and a spherical radius monotonically changing from region to region. It is argued that the obtained black hole and wormhole solutions are unstable under monopole perturbations. As a by-product, it is shown that a scalar-tensor theory with V (φ) = 0 , in which there is at least one nontrivial (φ = const ) vacuum solution with R ≡ 0 , necessarily reduces to a theory with a conformal scalar field (the latter may be usual or phantom).

Hybrid Metric-Palatini Gravity: Regular Stringlike Configurations

“…In this respect, we can note that HMPG, being a purely geometric source of scalar fields, both canonical and phantom, can provide a natural framework for wormhole construction without other "exotic" sources. Within spherical symmetry, this has already been confirmed [14,15], and a similar consideration in cylindrical symmetry can be one of the subjects of our further studies.…”

“…Let us find out how the above observations are modified if we seek a solitonic solution in the Jordan frame M J . For its description, we can use the same functions ψ, α, β, γ, µ as in M E , obeying the same equations, but the boundary conditions should now be formulated for the metric (14).…”

“…It is of interest that HMPG can be obtained from Palatini R 2 gravity with a Higgs scalar field under the requirement of Weyl invariance [12]. Some papers have been devoted to the possible existence and properties of vacuum static, spherically symmetric black holes and wormholes in HMPD [13][14][15], as well as static cylindrically symmetric configurations that are intended to reproduce the basic properties of cosmic strings [16].…”

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].…”

Wormhole Models and Energy Conditions in f ℛ Gravity with the Hu–Sawicki Model

“…Pavlovic and Sossich [32] have carried out a wormhole study by employing different models of f(R) without considering the exotic matter. Bronnikov [33] has explored the wormhole models in two different theories (scalar tensor theory and f(R) gravity). Saiedi and Nasr Esfahani [34] have discussed the null and weak energy bounds in the background of wormhole f(R) gravity.…”