Cosmic strings in $$f\left( R,L_m\right) $$ f R , L m gravity

Abstract

We consider Kasner-type static, cylindrically symmetric interior string solutions in the f (R, L m ) theory of modified gravity. The physical properties of the string are described by an anisotropic energy-momentum tensor satisfying the condition T t t = T z z ; that is, the energy density of the string along the z-axis is equal to minus the string tension. As a first step in our study we obtain the gravitational field equations in the f (R, L m ) theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor components have a power law dependence on the radial coordinate r . String solutions in two particular modified gravity models are investigated in detail. The first is the so-called "exponential" modified gravity, in which the gravitational action is proportional to the exponential of the sum of the Ricci scalar and matter Lagrangian, and the second is the "self-consistent model", obtained by explicitly determining the gravitational action from the field equations under the assumption of a power law dependent matter Lagrangian. In each case, the thermodynamic parameters of the string, as well as the precise form of the matter Lagrangian, are explicitly obtained.

Locally rotationally symmetric Bianchi type I cosmology in f(R, T) gravity

“…Houndjo [53] reconstructed f (R, T ) gravity by taking f (R, T ) = f 1 (R) + f 2 (T ) and it was shown that f (R, T ) gravity allowed for a transition of matter from a dominated phase to an acceleration phase. Harko and Lake [54] investigated cylindrically symmetric interior string like solutions in f (R, L m ) theory of gravity. In a recent paper [55], we explored the exact solutions of a cylindrically symmetric spacetime in f (R, T ) gravity and recovered two solutions, which corresponded to an exterior metric of cosmic string and a non-null electromagnetic field.…”

Cosmic string in gravity’s rainbow

“…It also becomes important when some types of the topological effects are needed suddenly by assigning an independent metric. In the context of modified theories of gravity, cosmic strings are investigated in f (R) gravity [58,60], teleparallel theories [61][62][63], brane worlds [64], Kaluza-Klein models [65], Lovelock Lagrangians [66], Gauss-Bonnet [67][68][69], Born-Infeld [70,71], bimetric theories [72], non-relativistic models of gravity [73], scalar-tensor theories [74][75][76][77][78][79], Brans-Dicke theory [80][81][82][83][84][85], dilation gravity [86,87], non-minimally coupled models of gravity [88], Mimetic gravity [89] and, recently, in the Bose-Einstein condensate strings [90]. However, the cosmic string is still unexplored in gravity's rainbow setting.…”

Bose-Einstein condensate strings

“…Hence, in order to determine the asymptotic form of the metric, the solutions presented in this paper must be matched onto the exterior cylindrically symmetric vacuum metric. In the case of cylindrical symmetry, and by assuming that the exterior gravitational field is described by standard general relativity, this metric is the Kasner metric [49][50][51][52]61,62],…”