scholarly journals From the Flamm–Einstein–Rosen bridge to the modern renaissance of traversable wormholes

2016 ◽  
Vol 25 (07) ◽  
pp. 1630017 ◽  
Author(s):  
Francisco S. N. Lobo
Keyword(s):  
Energy Condition ◽  
Einstein Field Equation ◽  
Fundamental Property ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Modified Theories Of Gravity ◽  
Multiply Connected ◽  
Traversable Wormholes ◽  
Normal Matter ◽  
Theories Of Gravity

We consider the possibility of multiply-connected spacetimes, ranging from the Flamm–Einstein–Rosen bridge, geons, and the modern renaissance of traversable wormholes. A fundamental property in wormhole physics is the flaring-out condition of the throat, which through the Einstein field equation entails the violation of the null energy condition (NEC). In the context of modified theories of gravity, it has also been shown that the normal matter can be imposed to satisfy the energy conditions, and it is the higher order curvature terms, interpreted as a gravitational fluid, that sustain these nonstandard wormhole geometries, fundamentally different from their counterparts in general relativity (GR). We explore interesting features of these geometries, in particular, the physical properties and characteristics of these ‘exotic spacetimes’.

scholarly journals A study of traversable wormhole solutions in extended teleparallel theory of gravity with matter coupling

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Allah Ditta ◽  
Ibrar Hussain ◽  
G. Mustafa ◽  
Abdelghani Errehymy ◽  
Mohammed Daoud
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Graphical Analysis ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Modified Theories Of Gravity ◽  
Class 1 ◽  
Theories Of Gravity ◽  
T Tau

AbstractThis study is devoted to explore the physical aspects of wormhole geometry under embedded class-1 spacetime in $$f(T,\tau )$$ f ( T , τ ) gravity, where $$\tau $$ τ denotes the trace of the energy-momentum tensor and T is the torsion. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. To complete this study, we take diagonal and off-diagonal tetrad, and try to build a comparison by considering the validity region of energy conditions in embedded class-1 spacetime. The embedded surface diagram is given to understand the connection between the two different regions of spacetime. The validity regions of all the energy conditions are calculated. A detailed graphical analysis is provided for validity regions of all the energy conditions. The presence of exotic matter is confirmed in both the cases as the null energy condition is violated.

Wormhole solutions via embedding approach in ℛ + βℛ2 gravity with matter coupling

2021 ◽  
Author(s):  
Dan Wang ◽  
G. Mustafa
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Specific Model ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Modified Theories Of Gravity ◽  
Class 1 ◽  
Theory Of Gravity ◽  
Feasible Solutions

In this paper, we examine the embedded wormhole solutions in the modified [Formula: see text] theory of gravity, where [Formula: see text] denotes the trace of the energy–momentum tensor and [Formula: see text] is the Ricci scalar. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. We explore the feasible solutions for the specific model of [Formula: see text] theory of gravity. Energy conditions have been explored using the approach mentioned above. Conclusively, we find that obtained wormhole solutions are acceptable, as the null energy condition is violated in the specific region.

scholarly journals Wormhole geometries in fourth-order conformal Weyl gravity

2016 ◽  
Vol 25 (06) ◽  
pp. 1650064 ◽  
Author(s):  
Gabriele U. Varieschi ◽  
Kellie L. Ault
Keyword(s):  
General Relativity ◽  
Fourth Order ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Conformal Gravity ◽  
Flat Spacetime ◽  
Traversable Wormholes ◽  
Weyl Gravity ◽  
The Subject

We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remains the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic matter might still be needed at the junction between our solutions and flat spacetime, but we demonstrate that the averaged null energy condition (as evaluated along radial null geodesics) is satisfied for a particular set of wormhole geometries. Therefore, if fourth-order conformal Weyl gravity is a correct extension of general relativity, traversable wormholes might become a realistic solution for interstellar travel.

scholarly journals On the existence and stability of traversable wormhole solutions in modified theories of gravity

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Oleksii Sokoliuk ◽  
Alexander Baransky
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Modified Theories Of Gravity ◽  
Energy Tensor ◽  
Field Equations ◽  
Traversable Wormhole ◽  
Existence And Stability ◽  
Theories Of Gravity ◽  
The Stability

AbstractWe study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$ f ( R ) = R + a R 2 , power-law $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$ f ( R ) = f 0 R n , log-corrected $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$ f ( R ) = R + α R 2 + β R 2 ln β R theories, and finally on the exponential hybrid metric-Palatini gravity $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$ f ( R ^ ) = ζ ( 1 + e - R ^ Φ ) . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state $$p_t=\omega \rho $$ p t = ω ρ . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

scholarly journals Traversable wormholes and energy conditions with two different shape functions in f(R) gravity

2019 ◽  
Vol 28 (02) ◽  
pp. 1950039 ◽  
Author(s):  
Nisha Godani ◽  
Gauranga C. Samanta
Keyword(s):  
Energy Density ◽  
Shape Function ◽  
Energy Condition ◽  
State Parameter ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Radial Coordinate ◽  
Shape Functions ◽  
Anisotropic Parameter ◽  
Traversable Wormholes

Traversable wormholes, tunnel-like structures introduced by Morris and Thorne [Am. J. Phys. 56 (1988) 395], have a significant role in connection of two different spacetimes or two different parts of the same spacetime. The characteristics of these wormholes depend upon the redshift and shape functions which are defined in terms of radial coordinate. In literature, several shape functions are defined and wormholes are studied in [Formula: see text] gravity with respect to these shape functions [F. S. N. Lobo and M. A. Oliveira, Phys. Rev. D 80 (2009) 104012; H. Saiedi and B. N. Esfahani, Mod. Phys. Lett. A 26 (2011) 1211; S. Bahamonde, M. Jamil, P. Pavlovic and M. Sossich, Phys. Rev. D 94 (2016) 044041]. In this paper, two shape functions (i) [Formula: see text] and (ii) [Formula: see text], [Formula: see text], are considered. The first shape function is newly defined, however, the second one is collected from the literature [M. Cataldo, L. Liempi and P. Rodríguez, Eur. Phys. J. C 77 (2017) 748]. The wormholes are investigated for each type of shape function in [Formula: see text] gravity with [Formula: see text], where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are real constants. Varying the parameter [Formula: see text] or [Formula: see text], [Formula: see text] model is studied in five subcases for each type of shape function. In each case, the energy density, radial and tangential pressures, energy conditions that include null energy condition, weak energy condition, strong energy condition and dominated energy condition and anisotropic parameter are computed. The energy density is found to be positive and all energy conditions are obtained to be violated which support the existence of wormholes. Also, the equation-of-state parameter is obtained to possess values less than [Formula: see text], that shows the presence of the phantom fluid and leads toward the expansion of the universe.

scholarly journals Quasi-cosmological traversable wormholes in f(R) gravity

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Hanif Golchin ◽  
Mohammad Reza Mehdizadeh
Keyword(s):  
Energy Condition ◽  
Null Energy Condition ◽  
Einstein Gravity ◽  
Gravity Models ◽  
Energy Conditions ◽  
Asymptotically Flat ◽  
Traversable Wormholes ◽  
Whole Space ◽  
Frw Metric ◽  
Standard Energy

Abstract In this paper, we study traversable wormholes in the context of f(R) gravity. Exact solutions of traversable wormholes are found by imposing the nonconstant Ricci scalar. These solutions asymptotically match spherical, flat and hyperbolic FRW metric. By choosing some static f(R) gravity models, we verify the standard energy conditions for the asymptotically spherical, flat and hyperbolic wormhole solutions. Unlike the Einstein gravity, we find that in the context of f(R) modified gravity, the asymptotically spherical, flat and hyperbolic wormhole solutions can respect the null energy condition (NEC) at the wormhole throat and near that. We find that in some static f(R) models, asymptotically flat and hyperbolic wormholes respect the weak energy condition (WEC) through the whole space.

scholarly journals Traversable wormholes in Einsteinian cubic gravity

2019 ◽  
Vol 35 (06) ◽  
pp. 2050017 ◽  
Author(s):  
Mohammad Reza Mehdizadeh ◽  
Amir Hadi Ziaie
Keyword(s):  
Equation Of State ◽  
Gravitational Lensing ◽  
Energy Condition ◽  
Higher Order ◽  
Energy Conditions ◽  
Geodesic Motion ◽  
De Sitter ◽  
Asymptotically Flat ◽  
Traversable Wormholes ◽  
Standard Energy

In this work, we investigate wormhole configurations described by a constant redshift function in Einstein-Cubic gravity ( ECG ). We derive analytical wormhole geometries by assuming a particular equation of state ( EoS ) and investigate the possibility that these solutions satisfy the standard energy conditions. We introduce exact asymptotically flat and anti-de Sitter (AdS) spacetimes that admit traversable wormholes. These solutions are obtained by imposing suitable values for the parameters of the theory so that the resulted geometries satisfy the weak energy condition ( WEC ) in the vicinity of the throat, due to the presence of higher-order curvature terms. Moreover, we find that AdS solutions satisfy the WEC throughout the spacetime. A description of the geodesic motion of time-like and null particles is presented for the obtained wormhole solutions. Also, using gravitational lensing effects, observational features of the wormhole structure are discussed.

scholarly journals Possible formation of wormholes from dark matter in an isothermal galactic halo and void

2019 ◽  
Vol 34 (23) ◽  
pp. 1950188
Author(s):  
Nayan Sarkar ◽  
Susmita Sarkar ◽  
Farook Rahaman ◽  
P. K. F. Kuhfittig ◽  
G. S. Khadekar
Keyword(s):  
Dark Matter ◽  
Galactic Halo ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Galactic Rotation ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Rotation Curves ◽  
Galactic Rotation Curves ◽  
Traversable Wormholes

It is well-known that traversable wormholes are valid solutions of the Einstein field equations, but these structures can only be maintained by violating the null energy condition. In this paper, we have obtained such wormhole solutions in an isothermal galactic halo, as well as in a void. We have shown that the null energy condition is violated, with the help of a suitable redshift function obtained from flat galactic rotation curves.

scholarly journals Traversable wormholes in the bulge of Milky Way galaxy with Global Monopole Charge

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Susmita Sarkar ◽  
Nayan Sarkar ◽  
Farook Rahaman
Keyword(s):  
Milky Way ◽  
Shape Function ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Radial Coordinate ◽  
Global Monopole ◽  
Milky Way Galaxy ◽  
Asymptotically Flat ◽  
Traversable Wormholes ◽  
Crucial Effect

AbstractThe present work looks for the existence of completely new wormhole geometries in the bulge of the Milky Way galaxy (MWG) situated on the dark matter (DM) density profile followed from MacMillan (MNRAS 76:465, 2017) and Boshkayev and Malafarina (MNRAS 484:3325, 2019) concerned with Global Monopole Charge. The obtained shape function is positively increasing against the radial coordinate and it increases faster with the increasing values of Global Monopole Charge. Moreover, the reported shape function satisfies all the essential criterions and hence it constructs wormhole geometry in the bulge of the MWG. Further, the DM candidate around bulge is suitable to harbor wormhole by violating the null energy condition(NEC) corresponding to three different redshift functions. The striking point of our solution is that for zero Global Monopole Charge the wormholes are asymptotically flat corresponding to the first two choices of redshift functions while for positive values of Global Monopole Charge wormhole becomes non asymptotically flat and Global Monopole Charge also has the crucial effect on the violation of NEC. In our solutions, one can note that the total amount of averaged NEC violating matter in the wormhole spacetime depends on the Global Monopole Charge $$\eta $$ η . Furthermore, the respective wormhole solutions are in equilibrium positions.

scholarly journals BEHAVIOR OF TACHYON IN STRING COSMOLOGY BASED ON GAUGED WZW MODEL

2009 ◽  
Vol 24 (04) ◽  
pp. 277-289
Author(s):  
SUNGGEUN LEE ◽  
SOONKEON NAM
Keyword(s):  
Cosmological Model ◽  
Energy Condition ◽  
Flat Space ◽  
Null Energy Condition ◽  
Energy Conditions ◽  
Dilaton Field ◽  
Coset Space ◽  
Tachyon Field ◽  
Strong Energy ◽  
Matter Fields

We investigate a string theoretic cosmological model in the context of the gauged Wess–Zumino–Witten model. Our model is based on a product of non-compact coset space and a spectator flat space; [ SL (2, R)/ U (1)]k × ℝ2. We extend the formerly studied semiclassical consideration with infinite Kac–Moody level k to a finite one. In this case, the tachyon field appears in the effective action, and we solve the Einstein equation to determine the behavior of tachyon as a function of time. We find that tachyon field dominates over dilaton field in early times. In particular, we consider the energy conditions of the matter fields consisting of the dilaton and the tachyon which affect the initial singularity. We find that not only the strong energy but also the null energy condition is violated.

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