Cylindrically symmetric and plane-symmetric solutions in $f(R)$ theory via Noether symmetries

Abstract

The $f(R)$ theory is considered for static cylindrically symmetric and plane-symmetric spacetimes. In order to find solutions to the field equations of these models, the Noether symmetry method is used. First, we examine the GR case for cylindrically symmetrical space-time with the $w=-1$ dark energy state. Then, with the assumption of $f(R)=f_0{R}^n$, cases with matter and non-matter are examined and general solutions are determined for both space-times. Thus, it is shown that inclusive new solutions are obtained, considering the Noether symmetric conditions. In addition, the GR limit for each cases are examined.

9 pages, no figures, version accepted for publication in the European Physical Journal C. arXiv admin note: text overlap with arXiv:2109.08938

References in corpus (18)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Dark Energy and Gravity
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Dark Energy and Dark Gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• Plane symmetric thin-shell wormholes: solutions and stability
• Cylindrical solutions in metric f(R) gravity
• Time-dependent matter instability and star singularity in $F(R)$ gravity
• Thermodynamics in $F(R)$ gravity with phantom crossing
• Noether symmetry in $f(R)$ cosmology
• Cylindrical Solutions in Modified f(T) Gravity
• Cylindrical Thin-shell Wormholes in $f(R)$ gravity
• Cylindrically Symmetric Solutions in $f(R,T)$ Gravity
• Dynamics of Charged Plane Symmetric Gravitational Collapse
• (Compactified) black branes in four dimensional f(R)-gravity
• Three-dimensional black holes via Noether symmetries

Cited by in corpus (1)

• Static plane symmetric solutions in $f(Q)$ gravity