Conformal cylindrically symmetric spacetimes in modified gravity

2015 ◽  
Vol 30 (37) ◽  
pp. 1550202 ◽  
Author(s):  
Murat Metehan Türkog̃lu ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Casimir Force ◽  
Conformal Symmetry ◽  
Vacuum State ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Symmetric Spacetimes ◽  
Cylindrically Symmetric Spacetime ◽  
Symmetric Spacetime

We investigate cylindrically symmetric spacetimes in the context of [Formula: see text] gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle–Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special [Formula: see text] function convenient to [Formula: see text]-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different [Formula: see text] models. Finally, geometrical and physical results of the solutions are discussed.

scholarly journals Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
Zi-Chao Lin ◽  
Ke Yang ◽  
Shao-Wen Wei ◽  
Yong-Qiang Wang ◽  
Yu-Xiao Liu
Keyword(s):  
The Novel ◽  
Field Equations ◽  
Four Dimensions ◽  
Link Type ◽  
Cylindrically Symmetric ◽  
Local Gravity ◽  
Cylindrically Symmetric Spacetime ◽  
Bonnet Term ◽  
Symmetric Spacetime

AbstractRecently, a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory was presented to bypass the Lovelock’s theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $$\alpha \rightarrow \alpha /(D-4)$$ α → α / ( D - 4 ) and to take the limit $$D\rightarrow 4$$ D → 4 . However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem (http://arxiv.org/abs/2003.11552, http://arxiv.org/abs/2003.12771, http://arxiv.org/abs/2004.08362, http://arxiv.org/abs/2004.09472, http://arxiv.org/abs/2004.10716). The resultant regularized four-dimensional EGB theory has the same on-shell action as the original theory. Thus it is expected that the novel four-dimensional EGB theory is equivalent to its regularized version. However, the equivalence of these two theories is symmetry-dependent. In this paper, we test the equivalence in a cylindrically symmetric spacetime. The well-defined field equations of the two theories are obtained, with which our follow-up analysis shows that they are equivalent in such spacetime. Cylindrical cosmic strings are then considered as specific examples of the metric. Three sets of solutions are obtained and the corresponding string mass densities are evaluated. The results reveal how the Gauss–Bonnet term in four dimensions contributes to the string geometry in the new theory.

Conformal and traversable wormholes with monopole and perfect fluid in f(R)-gravity

2016 ◽  
Vol 25 (02) ◽  
pp. 1650017 ◽  
Author(s):  
Dog̃ukan Taṣer ◽  
Melis Ulu Dog̃ru
Keyword(s):  
Perfect Fluid ◽  
Modified Gravity ◽  
Conformal Symmetry ◽  
Phantom Energy ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Field Equations ◽  
Traversable Wormholes ◽  
Symmetry Properties ◽  
Symmetric Spacetime

We investigate spherically symmetric spacetime filled with global monopole and perfect fluid in [Formula: see text]-gravity. We consider field equations of [Formula: see text]-gravity in order to understand the global monopole and the perfect fluid curve to the spacetime. It has taken advantages of conformal symmetry properties of the spacetime to solve these equations. The obtained solutions are improved in case of phantom energy. It is shown that obtained [Formula: see text] function is consistent with well-known models of the modified gravity. Also, it is examined whether the obtained solutions support a traversable wormhole geometry. Obtained results of the solutions have been concluded.

scholarly journals KINKS, ENERGY CONDITIONS AND CLOSED TIMELIKE CURVES

2000 ◽  
Vol 09 (05) ◽  
pp. 531-541 ◽  
Author(s):  
PEDRO F. GONZÁLEZ-DÍAZ
Keyword(s):  
Energy Condition ◽  
Weak Energy Condition ◽  
Energy Conditions ◽  
Closed Timelike Curves ◽  
Causality Violation ◽  
Incoherent Radiation ◽  
Cylindrically Symmetric ◽  
Cylindrically Symmetric Spacetime ◽  
Geodesically Complete ◽  
Symmetric Spacetime

A link between the possibility of extending a geodesically incomplete kinked spacetime to a spacetime which is geodesically complete and the energy conditions is discussed for the case of a cylindrically-symmetric spacetime kink. It is concluded that neither the strong nor the weak energy condition can be satisfied in the four-dimensional example, though the latter condition may survive on the transversal sections of such a spacetime. It is also shown that the matter which propagates quantum-mechanically in a kinked spacetime can always be trapped by closed timelike curves, but signaling connections between that matter and any possible observer can only be made of totally incoherent radiation, so preventing observation of causality violation.

scholarly journals The Kasner brane

2015 ◽  
Vol 30 (34) ◽  
pp. 1550185
Author(s):  
Mark D. Roberts
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Vacuum Solution ◽  
Energy Conditions ◽  
Field Equations ◽  
Einstein Tensor ◽  
Five Dimensions

Solutions are found to field equations constructed from the Pauli, Bach and Gauss–Bonnet quadratic tensors to the Kasner and Kasner brane spacetimes in up to five dimensions. A double Kasner space is shown to have a vacuum solution. Brane solutions in which the bulk components of the Einstein tensor vanish are also looked at and for four-branes a solution similar to radiation Robertson–Walker spacetime is found. Matter trapping of a test scalar field and a test perfect fluid are investigated using energy conditions.

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

Higher-dimensional gravitational collapse of perfect fluid spherically symmetric spacetime in f(R, T) gravity

2018 ◽  
Vol 33 (12) ◽  
pp. 1850065 ◽  
Author(s):  
Suhail Khan ◽  
Muhammad Shoaib Khan ◽  
Amjad Ali
Keyword(s):  
Perfect Fluid ◽  
Outer Region ◽  
Energy Tensor ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Higher Dimensional ◽  
Stress Energy ◽  
Inner Region ◽  
Symmetric Spacetime ◽  
Spherically Symmetric Spacetime

In this paper, our aim is to study (n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f(R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static (n + 2)-dimensional metric in the inner region and Schwarzschild (n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f(R, T) gravity, we choose the stress–energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f(R0, T0) slows down the collapsing process.

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