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 article, a large class of static, spherically symmetric Lorentzian wormhole metrics is proposed for a brane world. But the wormholes are not symmetric and asymmetric.
Abstract: The condition R=0, where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of r) of static, spherically symmetric Lorentzian wormhole metrics. The wormholes are globally regular and traversable, can have throats of arbitrary size and can be both symmetric and asymmetric. These metrics may be treated as possible wormhole solutions in a brane world since they satisfy the vacuum Einstein equations on the brane where effective stress-energy is induced by interaction with the bulk gravitational field. Some particular examples are discussed.
229 citations
TL;DR: In this paper, the authors examined the safety conjecture for quantum gravity in four dimensions using the renormalisation group and found evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar.
Abstract: The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using the renormalisation group, we find evidence for an interacting UV fixed point for polynomial actions up to the 34th power in the Ricci scalar. The extrapolation to infinite polynomial order is given, and the self-consistency of the fixed point is established using a bootstrap test. All details of our analysis are provided. We also clarify further aspects such as stability, convergence, the role of boundary conditions, and a partial degeneracy of eigenvalues. Within this setting we find strong support for the conjecture.
229 citations
01 Jan 1993
TL;DR: In this article, Nirenberg posed the question: quelles fonctions K(x) sur S 2 peuvent representer la Courbure de Gauss d'une metrique g sur S n, qui est conformement equivalent a g 0?
Abstract: Soit (S n , g 0 ) la sphere standard de dimension n. L. Nirenberg a pose la question suivante: quelles fonctions K(x) sur S 2 peuvent representer la courbure de Gauss d'une metrique g sur S 2 , qui est conformement equivalent a g 0 ? La meme question se pose en plusieurs dimensions, c'est-a-dire quelles fonctions K (x) sur S n peuvent representer la courbure scalaire d'une metrique g sur S n conformement equivalent a g 0 ?
228 citations
TL;DR: This Letter studies static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms, and discusses some of their thermodynamic properties, and shows that they obey the first law of thermodynamics.
Abstract: Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this Letter we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.
227 citations
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225 citations