Special standard static space–times

Dobarro, Fernando; Ünal, Bülent

doi:10.1016/j.na.2004.07.035

Cited by 18 publications

(12 citation statements)

References 25 publications

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“…In [34, p. 228-230] and [16, p. 38-39] the authors proved that if (F, g F ) is compact and f ≡ 0 is a solution of (3.10), then the scalar curvature τ g F is constant (see [24] also). So, by (3.12) and the well known results about the spectrum of the Laplace-Beltrami operator on a compact Riemannian manifold without boundary (see [13]), there results: On the other hand, in [24, Proposition 2.7] the author proved that (see also [26]):…”

Section: Energy Conditions and Implicationsmentioning

confidence: 97%

“…The following formula of the curvature Ricci tensor can be easily obtained from [11,26,27,69]. Proposition 2.3.…”

Section: Preliminariesmentioning

confidence: 99%

“…As a consequence, it is shown that if the complete Riemannian factor F satisfies the nonreturning property and has a pseudoconvex geodesic system and the warping function f : F → (0, ∞) is bounded from above, then the standard static spacetime (a, b) f × F is geodesically connected. In [26], some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.…”

Section: Introductionmentioning

confidence: 99%

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Implications of energy conditions on standard static space–times

Dobarro

Ünal

2009

Nonlinear Analysis: Theory, Methods & Applications

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In the framework of standard static space times, we state a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories. We concentrate our study on questions about the sub-harmonicity of the warping function, the scalar curvature map, conformal hyperbolicity, conjugate points and the time-like diameter of this class of space-times.

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Section: Energy Conditions and Implicationsmentioning

confidence: 97%

“…The following formula of the curvature Ricci tensor can be easily obtained from [11,26,27,69]. Proposition 2.3.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Implications of energy conditions on standard static space–times

Dobarro

Ünal

2009

Nonlinear Analysis: Theory, Methods & Applications

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“…Now, putting Y = W and Y = ∇f in (22) and using the fundamental equation, respectively we obtain Ric(W, W ) = Ric(∇f, W ) = 0.…”

Section: Isotropic Casementioning

confidence: 99%

On a Class of Gradient Almost Ricci Solitons

Güler

2020

Bull. Malays. Math. Sci. Soc.

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In this study, we provide some classifications for half-conformally flat gradient f -almost Ricci solitons, denoted by (M, g, f ), in both Lorentzian and neutral signature. First, we prove that if ||∇f || is a non-zero constant, then (M, g, f ) is locally isometric to a warped product of the form I × ϕ N , where I ⊂ R and N is of constant sectional curvature. On the other hand, if ||∇f || = 0, then it is locally a Walker manifold. Then, we construct an example of 4-dimensional steady gradient f -almost Ricci solitons in neutral signature. At the end, we give more physical applications of gradient Ricci solitons endowed with the standard static spacetime metric.Keywords Ricci soliton · Gradient Ricci soliton · Gradient h-almost Ricci soliton · Half-conformally flat manifold · Walker manifold · Standard static spacetime metric Mathematics Subject Classification (2010) 53C21 · 53C50 · 53C25 IntroductionHamilton introduced the concept of the Ricci flow to prove the Poincare Conjecture in the late of 20th century [1]. Poincare Conjecture was one of the very deep unsolved problem which aims to classify all compact three dimensional manifolds. In the 1900's, Poincare asked if a simply-connected closed three manifold is necessarily the three sphere S 3 . For this purpose, Hamilton introduced the Ricci flow as a partial differential equation ∂g(t) ∂t = −2Ric(g(t)), which evolves the metric in a Riemannian manifold to make it rounder. By

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“…As a consequence, it is shown that if the complete Riemannian factor manifold F satisfies the nonreturning property and has a pseudoconvex geodesic system and if the warping function f : F → (0, ∞) is bounded from above then the standard static space-time (a, b) f × F is geodesically connected. In [13], some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein. In a recent note [29], the authors discussed conditions for static Killing vector fields to be standard and then they obtained an interesting uniqueness result when the so called natural space (in the case of a standard static space-time, this is the Riemannian part) is compact.…”

Section: Introductionmentioning

confidence: 99%

Characterizing killing vector fields of standard static space-times

Dobarro

Ünal

2012

Journal of Geometry and Physics

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Cataloged from PDF version of article.We provide a global characterization of the Killing vector fields of a standard static space-time by a system of partial differential equations. By studying this system, we determine all the Killing vector fields in the same framework when the Riemannian part is compact. Furthermore, we deal with the characterization of Killing vector fields with zero curl on a standard static space-time. © 2011 Elsevier B.V.

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Special standard static space–times

Abstract: Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

Cited by 18 publications

References 25 publications

Implications of energy conditions on standard static space–times

Implications of energy conditions on standard static space–times

On a Class of Gradient Almost Ricci Solitons

Characterizing killing vector fields of standard static space-times

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