Ricci flow in general relativity: dynamics of gluon fields on an arbitrary curved background from unified spinor fields

Bellini, Mauricio

doi:10.1088/1402-4896/abef36

Cited by 4 publications

(2 citation statements)

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“…In general, it is believed that λ [s (x α )] has varied along the history of the universe. In this case the right hand of ( 7) must be taken into account in order to make a good relativistic description of the physical system [19,20]. However, as we shall see later in this work, the conceptual meaning of λ [s (x α )] is very much broader than the cosmological meaning.…”

Section: Extension Of General Relativity With An Extended Manifoldmentioning

confidence: 99%

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Spatiotemporal jumps as particular solutions in geodesic trajectories with the Gödel metric on an extended manifold

Bellini

2022

Eur. Phys. J. C

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Using the Gödel metric, we obtain some relevant solutions compatible with spatiotemporal jumps for the geodesic equations, by using an extension of General Relativity with nonzero boundary terms, which are described on an extended manifold generated by the connections $$\delta \Gamma ^{\mu }_{\alpha \beta } = b\,U^{\mu }\,g_{\alpha \beta }$$ δ Γ α β μ = b U μ g α β . These terms are given by a flow of velocities with components $$U^{\nu }$$ U ν : $$3\,b^2\,\nabla _{\nu }U^{\nu }=g^{\alpha \beta }\, \delta R_{\alpha \beta } = \lambda \left[ s\left( x^{\alpha }\right) \right] \,g^{\alpha \beta }\, \delta g_{\alpha \beta }$$ 3 b 2 ∇ ν U ν = g α β δ R α β = λ s x α g α β δ g α β in the varied Einstein–Hilbert action. The solutions are valid for an arbitrary equation of state with ordinary matter: $$\Omega =P/(c^2\,\rho ) = \frac{\left( \frac{\omega }{c}\right) ^2-\lambda (s)}{\left( \frac{\omega }{c}\right) ^{2}+\lambda (s)}$$ Ω = P / ( c 2 ρ ) = ω c 2 - λ ( s ) ω c 2 + λ ( s ) .

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Section: Extension Of General Relativity With An Extended Manifoldmentioning

confidence: 99%

“…In this case the boundary terms can be nonzero for = 0, but the field equations ( 7) are unmodified: ∇ β T αβ = 0. Furthermore, the background equations: ∇ ν U ν = 0, must be modified by introducing the right side term in (19) for massive particles, but not for massless particles.…”

Section: Curvature On the Extended Manifoldmentioning

confidence: 99%