The Noether Symmetry Approach: Foundation and Applications: The Case of Scalar-Tensor Gauss-Bonnet Gravity

被引：6

作者：

Bajardi, Francesco ^{[1
,2
]}

Capozziello, Salvatore ^{[1
,2
,3
]}

Di Salvo, Tiziana ^{[4
]}

Spinnato, Francesca ^{[4
]}

机构：

[1] Scuola Super Meridionale, Largo San Marcellino 10, I-80138 Naples, Italy

[2] Complesso Univ Monte S Angelo, Ist Nazl Fis Nucleare INFN, Sez Napoli, Edificio G,Via Cinthia, I-80126 Naples, Italy

[3] Complesso Univ Monte S Angelo, Univ Napoli Federico II, Dipartimento Fis E Pancini, Edificio G,Via Cinthia, I-80126 Naples, Italy

[4] Univ Palermo, Dipartimento Fis & Chim Emilio Segre, I-90123 Palermo, Italy

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 09期

关键词：

Noether symmetries; modified theories of gravity; exact solutions; NOTHER SYMMETRIES;

D O I：

10.3390/sym15091625

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator xi, related to the spacetime translations. This approach can be used for several applications. In the second part of the work, we consider a gravity theory, including the coupling between a scalar field phi and the Gauss-Bonnet topological term G. In particular, we study a gravitational action containing the function F(G,phi) and select viable models by the existence of symmetries. Finally, we evaluate the selected models in a spatially flat cosmological background and use symmetries to find exact solutions.

引用

页数：15

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