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 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.

scholarly journals Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 662 ◽  
Author(s):  
Irina Dymnikova
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Energy Condition ◽  
Phantom Energy ◽  
Weak Energy Condition ◽  
Energy Conditions ◽  
De Sitter ◽  
Dynamical Equations ◽  
De Sitter Vacuum ◽  
Observational Signature

We outline the basic properties of regular black holes, their remnants and self-gravitating solitons G-lumps with the de Sitter and phantom interiors, which can be considered as heavy dark matter (DM) candidates generically related to a dark energy (DE). They are specified by the condition T t t = T r r and described by regular solutions of the Kerr-Shild class. Solutions for spinning objects can be obtained from spherical solutions by the Newman-Janis algorithm. Basic feature of all spinning objects is the existence of the equatorial de Sitter vacuum disk in their deep interiors. Energy conditions distinguish two types of their interiors, preserving or violating the weak energy condition dependently on violation or satisfaction of the energy dominance condition for original spherical solutions. For the 2-nd type the weak energy condition is violated and the interior contains the phantom energy confined by an additional de Sitter vacuum surface. For spinning solitons G-lumps a phantom energy is not screened by horizons and influences their observational signatures, providing a source of information about the scale and properties of a phantom energy. Regular BH remnants and G-lumps can form graviatoms binding electrically charged particles. Their observational signature is the electromagnetic radiation with the frequencies depending on the energy scale of the interior de Sitter vacuum within the range available for observations. A nontrivial observational signature of all DM candidates with de Sitter interiors predicted by analysis of dynamical equations is the induced proton decay in an underground detector like IceCUBE, due to non-conservation of baryon and lepton numbers in their GUT scale false vacuum interiors.

scholarly journals ENERGY CONDITIONS CONSTRAINTS ON A CLASS OF f(R)-GRAVITY

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1315-1321 ◽  
Author(s):  
J. SANTOS ◽  
M. J. REBOUÇAS ◽  
J. S. ALCANIZ
Keyword(s):  
Variational Approach ◽  
Free Parameter ◽  
Functional Form ◽  
Energy Condition ◽  
Gravity Theory ◽  
Weak Energy Condition ◽  
Energy Conditions ◽  
Concrete Application ◽  
The Family ◽  
Locally Homogeneous

We present and discuss the bounds from the energy conditions on a general f(R) functional form in the framework of metric variational approach. As a concrete application of the energy conditions to locally homogeneous and isotropic f(R)-cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the free parameter of the family of [Formula: see text] gravity theory.

A study of some cylindrically symmetric solutions in f(R, G) gravity

2020 ◽  
Vol 98 (4) ◽  
pp. 364-374
Author(s):  
Saeeda Zia ◽  
M. Farasat Shamir
Keyword(s):  
Exact Solutions ◽  
Modified Gravity ◽  
Complete System ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Model Parameters ◽  
Field Equations ◽  
Cylindrically Symmetric ◽  
Modified Theory

In this paper, we present the cylindrically symmetric solutions in a well-known modified theory, namely f(R, G) gravity. After driving the complete system of field equations, six different families of exact solutions using a viable f(R, G) gravity model have been discussed. Moreover, we have investigated the well-known Levi–Civita solution in modified gravity for the model f(R, G) = R2 + αGn for some suitable values of model parameters n and α. Null energy conditions are also calculated for all the obtained solutions. Some regions are observed where the null energy condition is violated, indicating the existence of cylindrical wormholes.

scholarly journals Rotating cylindrical wormholes and energy conditions

2016 ◽  
Vol 31 (02n03) ◽  
pp. 1641022 ◽  
Author(s):  
K. A. Bronnikov ◽  
V. G. Krechet
Keyword(s):  
Scalar Field ◽  
Energy Condition ◽  
Flat Space ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Throat Region ◽  
Cylindrically Symmetric ◽  
Arbitrary Potential

We seek wormholes among rotating cylindrically symmetric configurations in general relativity. Exact wormhole solutions are presented with such sources of gravity as a massless scalar field, a cosmological constant, and a scalar field with an exponential potential. However, none of these solutions are asymptotically flat, which excludes the existence of wormhole entrances as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions using the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space-time at some surfaces [Formula: see text] and [Formula: see text]. It is shown, however, that if the source of gravity in the throat region is a scalar field with an arbitrary potential, then one or both thin shells appearing on [Formula: see text] and [Formula: see text] inevitably violate the null energy condition. Thus, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.

scholarly journals Necessary conditions for having wormholes in f(R) gravity

2016 ◽  
Vol 31 (37) ◽  
pp. 1650203 ◽  
Author(s):  
S. Habib Mazharimousavi ◽  
M. Halilsoy
Keyword(s):  
Necessary Conditions ◽  
Energy Condition ◽  
Weak Energy Condition ◽  
Polynomial Expansion ◽  
Energy Conditions ◽  
Wormhole Solution ◽  
Strong Energy Condition ◽  
Strong Energy ◽  
External Sources

For a generic f(R) which admits a polynomial expansion, we find the near-throat wormhole solution. Necessary conditions for the existence of wormholes in such f(R) theories are derived for both zero and nonzero matter sources. For vanishing external sources, we show that the energy conditions are violated. A particular choice of energy–momentum reveals that the wormhole geometry satisfies the weak energy condition (WEC). For a range of parameters, even the strong energy condition (SEC) is shown to be satisfied.

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.

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