56,57] under peculiar assumptions on the metric potentials. In a similar fashion, accelerating 4-D cosmologies, induced by generalized 5-Df(R) gravity, have also been studied considering a curvature–matter coupling [58]. Furthermore, a vacuum fourth-order Kaluza–Klein...
Because θ is a spatial angle, it is customary in geodesy to describe it by two components, the meridian ξ and the prime vertical η components. The former is the projection of θ onto the local meridian plane, and the latter is the projection onto the local prime vertical plane (plane ...
4.3). It is customary to impose energy conditions of two types on the components of the energy–momentum tensor. The weak energy condition will hold if ρ ≥ 0, ρ + pm ≥ 0 (m = 1, 2, 3). “These inequalities are very reasonable requirements and are satisfied by...
we will summarize different approaches to this question, and how they connect with our search for a theory of quantum gravity. We will see that almost all such approaches lead us to find that the
It is customary to impose energy conditions of two types on the components of the energy–momentum tensor. The weak energy condition will hold if ρ ≥ 0, ρ + pm ≥ 0 (m = 1, 2, 3). "These ine- qualities are very reasonable requirements and are satisfied by all...
Instead, in 𝑑=4−𝜖d=4−ϵ, it is customary to measure 𝜆λ in units of 𝜇μ in order to still have a dimensionless coupling. This is achieved through the replacement 𝜆→𝜇𝜖𝜆λ→μϵλ, as shown in the main text. The counterterm in the new units becomes 𝐴...
In the following, however, we shall restrict the treatment to the customary case in which the background metric tensor solution of the Einstein field equations is purely dependent only on the 4-position rµ, namely is of the form g = g (r) , (4) which identifies a stationary metric ...