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Scalar curvature

About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.


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Journal ArticleDOI
TL;DR: In this paper, the existence of the generalized Misner-sharp energy depends on a constraint condition in the f(R) gravity in a spherically symmetric space-time.
Abstract: We study generalized Misner-Sharp energy in f(R) gravity in a spherically symmetric space-time. We find that unlike the cases of Einstein gravity and Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy depends on a constraint condition in the f(R) gravity. When the constraint condition is satisfied, one can define a generalized Misner-Sharp energy, but it cannot always be written in an explicit quasilocal form. However, such a form can be obtained in a Friedmann-Robertson-Walker universe and for static spherically symmetric solutions with constant scalar curvature. In the Friedmann-Robertson-Walker universe, the generalized Misner-Sharp energy is nothing but the total matter energy inside a sphere with radius r, which acts as the boundary of a finite region under consideration. The case of scalar-tensor gravity is also briefly discussed.

115 citations

Journal ArticleDOI
TL;DR: In this article, the authors study cosmological expansion in F(R) gravity using the trace of the field equations and find that high frequency asymmetric oscillations and a singularity at finite time appear to be present for a wide range of initial conditions.
Abstract: We study cosmological expansion in F(R) gravity using the trace of the field equations. High frequency oscillations in the Ricci scalar, whose amplitude increases as one evolves backward in time, have been predicted in recent works. We show that the approximations used to derive this result very quickly break down in any realistic model due to the non-linear nature of the underlying problem. Using a combination of numerical and semi-analytic techniques, we study a range of models which are otherwise devoid of known pathologies. We find that high frequency asymmetric oscillations and a singularity at finite time appear to be present for a wide range of initial conditions. We show that this singularity can be avoided with a certain range of initial conditions, which we find by evolving the models forwards in time. In addition we show that the oscillations in the Ricci scalar are highly suppressed in the Hubble parameter and scale factor.

115 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined the space of finite topology surfaces in ℝ3 which are complete, properly embedded and have nonzero constant mean curvature, and they proved that the spaceMk of all such surfaces withk ends is locally a real analytic variety.
Abstract: We examine the space of finite topology surfaces in ℝ3 which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the spaceMk of all such surfaces withk ends (where surfaces are identified if they differ by an isometry of ℝ3) is locally a real analytic variety. When the linearization of the quasilinear elliptic equation specifying mean curvature equal to one has noL2-nullspace, we prove thatMk is locally the quotient of a real analytic manifold of dimension 3k−6 by a finite group (i.e. a real analytic orbifold), fork ≥ 3. This finite group is the isotropy subgroup of the surface in the group of Euclidean motions. It is of interest to note that the dimension ofMk is independent of the genus of the underlying punctured Riemann surface to which Σ is conformally equivalent. These results also apply to hypersurfaces of Hn+1 with nonzero constant mean curvature greater than that of a horosphere and whose ends are cylindrically bounded.

115 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of the Newtonian limit in nonlinear gravity models with inverse powers of the Ricci scalar was revisited and two models with f''(R_0)=0 were proposed.
Abstract: I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models with inverse powers of the Ricci scalar. Expansion around a maximally symmetric local background with positive curvature scalar R_0 gives the correct Newtonian limit on length scales << R_0^{-1/2} if the gravitational Lagrangian f(R) satisfies |f(R_0)f''(R_0)|<< 1. I propose two models with f''(R_0)=0.

114 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023268
2022536
2021505
2020448
2019424
2018433