Topic
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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TL;DR: In this paper, a modified action functional with a non-minimum coupling between the scalar curvature and the matter Lagrangian is considered, and its consequences on stellar equilibrium are discussed.
Abstract: We consider a modified action functional with a nonminimum coupling between the scalar curvature and the matter Lagrangian, and study its consequences on stellar equilibrium. Particular attention is paid to the validity of the Newtonian regime, and on the boundary and exterior matching conditions, as well as on the redefinition of the metric components. Comparison with solar observables is achieved through numerical analysis, and constraints on the nonminimum coupling are discussed.
114 citations
TL;DR: In this article, the authors studied the quantum sphere as a quantum Riemannian manifold in the quantum frame bundle approach and exhibited its 2-dimensional cotangent bundle as a direct sum Ω 0,1⊕Ω 1,0 in a double complex.
Abstract: We study the quantum sphere Open image in new window as a quantum Riemannian manifold in the quantum frame bundle approach We exhibit its 2-dimensional cotangent bundle as a direct sum Ω0,1⊕Ω1,0 in a double complex We find the natural metric, volume form, Hodge * operator, Laplace and Maxwell operators and projective module structure We show that the q-monopole as spin connection induces a natural Levi-Civita type connection and find its Ricci curvature and q-Dirac operator Open image in new window We find the possibility of an antisymmetric volume form quantum correction to the Ricci curvature and Lichnerowicz-type formulae for Open image in new window We also remark on the geometric q-Borel-Weil-Bott construction
113 citations
113 citations
TL;DR: In this paper, the authors studied the thermodynamics of a charged AdS black hole in the special f(R) correction with the constant Ricci scalar curvature and showed that the ratio ρc occurring at the critical point increases monotonically with the derivative term f'(R0), and that the critical exponents are the same as those of the liquid-gas phase transition in the van der Waals model.
Abstract: We study the thermodynamics of a charged AdS black hole in the special f(R) correction with the constant Ricci scalar curvature. Our results show that the f(R) correction influences the Gibbs free energy and the phase transition of system. The ratio ρc occurring at the critical point increases monotonically with the derivative term f'(R0). We also disclose that the critical exponents are the same as those of the liquid-gas phase transition in the van der Waals model, which does not depend on the f(R) correction considered here.
113 citations
TL;DR: In this article, a variational formulation of the pull-back metric realization problem is presented, and necessary and sufficient conditions for existence of a W 2,2 isometric immersion of a given 2 d metric into.
Abstract: Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its Γ -convergence under the proper scaling. As a corollary, we obtain new necessary and sufficient conditions for existence of a W 2,2 isometric immersion of a given 2 d metric into .
113 citations