Tensor perturbations of Palatinif(R)branes

Abstract

We analyze the tensor perturbations of flat thick domain wall branes in f (R) gravity. Our results indicate that under the transverse and traceless gauge, the metric perturbations decouple from the perturbation of the scalar field. Besides, the perturbed equation reduces to the familiar Klein-Gordon equation for massless spin-2 particles only when the bulk curvature is a constant or when f (R) = R. As an application of our results, we consider the possibility of localizing gravity on some flat thick branes. The stability of these brane solutions is also shortly discussed.

Selective Laser Melting and Remelting of Pure Tungsten

“…Selective laser melting (SLM) is a kind of state-of-the-art processing technology that manufactures components in an incremental layer-by-layer means using the laser to melt, bond, and solidify powder particles on powder bed. [7] It has been widely used in the production of a variety of alloys including titanium alloys, aluminum alloys, and stainless steel, [8][9][10][11][12] providing the possibility for its application in producing tungsten. Tan et al [13] fabricated pure tungsten samples with a relative density of 98.5% using SLM.…”

Tensor perturbations off(T)branes

“…However, the stability of f (T ) brane system is still unknown. In this paper we will focus on this issue and analyse the localization of the graviton zero mode, which is an important issue in brane model since it will ensure the four-dimensional Newtonian potential on the brane [28,[53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]. This paper is organised as follows.…”

Pure geometric thick f(R)-branes: stability and localization of gravity

“…We assume that gravity is not described by general relativity, but by the so-called f (R) theories, where the Lagrangians are proportional to some functions of the scalar curvature R. The f (R) theories were created in the study of cosmology [21][22][23], and they are mainly applied in cosmology nowadays (see [24][25][26][27][28] and references therein). Nevertheless, there are works devoted to embedding branes, either thin [29][30][31][32][33][34], or thick [35][36][37][38][39][40][41][42][43] into various types of f (R) gravities.…”

“…To obtain reliable thick f (R)-brane models, we must either prove that the solutions found in Refs. [35][36][37][38][39][40][41][42][43] are also stable against the vector and the scalar perturbations, or to find some new solutions whose stabilities are easier to prove. In this paper we adopt the second path.…”

“…[35][36][37][38][39][40][41][42][43] are generated by a background scalar field. For f (R)-branes of this type, the tensor perturbation equation has been derived in Ref.…”