Gravitational Field of a Global Monopole in a Modified Gravity

Abstract

In this paper we analyze the gravitational field of a global monopole in the context of f (R) gravity. More precisely, we show that the field equations obtained are expressed in terms of F (R) = df (R) dR . Since we are dealing with a spherically symmetric system, we assume that F (R) is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.

Quantum probes of timelike naked singularities in the weak field regime of f (R) global monopole spacetime

“…Employing these conditions in the field equations yields ψ(r) = ψ 0 r and resulting metric function with global monopole is found to be 12) where M is the mass parameter and ψ 0 is a very small parameter ( since ψ 0 r 1) that measures the deviation from the standard general relativity. As stated in [26], for a typical Grand Unified Theory the parameter η is in the order of 10 16 GeV. Hence, 8πGη 2 ≈ 10 −5 .…”

“…Explicit form of f (R) is given in [26] (eq. 42 in [26]). Hence, F (R(r)) = 1 corresponds to the standard general relativity.…”

“…The structure of the solution obtained in [26] and given in eq. (2.12), has remarkable features that deserves to be investigated in detail.…”

The tunneling radiation of a black hole with a f(R) global monopole under generalized uncertainty principle

“…It was shown that the structure of the metric outside a monopole has a solid angle leading all light rays to be deflected at the same angle [8]. In the case of a massive source involving a global monopole in the universe with accelerated expansion, its metric with terms associated with the monopole and f (R) issue are necessary [9,10]. The nonvanishing modified parameter ψ 0 from f (R) theory belonging to the metric components bring a cosmological horizon as a boundary of the universe to the spacetime limited by the f (R) global monopole [9].…”

The fragmentation instability of a black hole with f(R) global monopole under GUP

“…The f (R) gravity generalizes the general relativity and certainly the generalization should appear in the description of the background around the gravitational objects. With the expansion of the analytical function of the Ricci scalar under the weak field approximation, the gravitational field of a global monopole in the modified gravity theory has been explored [9]. It was also found that the presence of the parameter because of the modification of gravity is indispensable in providing stable circular orbits for particles [10].…”