Fig 2 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Numerical solution for (20) and Flaring-out condition validation/violation for positive α parameter in quadratic gravity
Source publication
We 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}}+...
Context in source publication
Context 1
... numerically solved Eqs. (20) and (21) on the Figure. 2. The flaring-out condition was solved for only positive values of α, because, as it turned out, with α < 0 we have that flaring-out condition is violated generally. Thus, in quadratic MOG for positive values of MOG parameter, we have physically acceptable shape function, that satisfies EFE's. Finally, for almost all positive alpha ...
Similar publications
We consider symmetric teleparallel gravity (STEGR), in which gravitational Lagrangian is given by the arbitrary function of non-metricity scalar $Q$ to study static and spherically symmetric charged traversable wormhole solutions with non-commutative background geometry. The matter source at the wormhole throat is acknowledged to be anisotropic, an...
Citations
... The idea of the stability of wormholes is discussed in the literature. Sokoliuk et al investigated the existence and stability of traversable wormhole solutions in modified theories of gravity in [38]. In [39] the stability of thin shell wormhole in f(R) theory of gravity is studied by A Eid. Thin-shell wormholes in Einstein and Einstein-Gauss-Bonnet theories of gravity was investigated by Kokubu et al in [40], and the authors have shown that the effect of the Gauss-Bonnet term on stability depends on the space-time symmetry. ...
The static spherically symmetric wormhole solution for a non-isotropic perfect
fluid energy-momentum tensor within the context of teleparallel-Rastall
gravity is investigated. First, by imposing static and non-static conformal
symmetry on the static spherically symmetric space-time metric, we investigated
the null energy condition at the throat of traversable wormholes and
showed that the null energy condition in the throat and its neighborhood is
violated. Secondly, with the aim of minimize the usage of exotic matter, we
found regions where the energy conditions are valid at the junction surface.
We found that in the static case of conformal symmetry solution, the null
energy condition (NEC), weak energy condition (WEC), and Strong energy
condition (SEC) are valid for different λ0 parameters. Moreover, we obtained
that for the non-static symmetric solution of conformal symmetry, the NEC
and WEC are satisfied for different sets of (k, ˜ λ0) parameters. Finally, we
have explored the stable regions by the parameter η2 ( square speed of sound)
for different sets of (k, ˜ λ0) parameters.
... The stability of compact objects, such as stellar structures, can be also examined through the Tolman-Oppenheimer-Volkov (TOV) equation, initially introduced in the context of neutron stars [39,40]. Hence, the stability conditions for wormholes could be investigated by employing an equilibrium condition obtained from the TOV equation [41][42][43][44]. Combining the Morris-Thorne metric ansatz (2.2) with the conservation law of stress-energy tensor ∇ µ T µν = 0, we obtain the following TOV equation in a 2 + 1 dimensional spacetime: ...
This work presents new three-dimensional traversable wormhole solutions sourced by the Casimir density and pressures related to the quantum vacuum fluctuations in Yang-Mills (Y-M) theory. We begin by analyzing the noninteracting Y-M Casimir wormholes, initially considering an arbitrary state parameter ω and determine a simple constant wormhole shape function. Next, we introduce a new methodology for deforming the state parameter to find well-behaved redshift functions. The wormhole can be interpreted as a legitimate Casimir wormhole with an expected average state parameter of ω = 2. Then, we investigate the wormhole curvature properties, energy conditions, and stability. Furthermore, we discover a novel family of traversable wormhole solutions sourced by the quantum vacuum fluctuations of interacting Yang-Mills fields with a more complex shape function. Deforming the effective state parameter similarly, we obtain well-behaved redshift functions and traversable wormhole solutions. Finally, we examine the energy conditions and stability of solutions in the interacting scenario and compare to the noninteracting case.
... Casimir Energy is currently the only possible substitute for exotic matter, that could be obtained in the laboratory. Firstly, we could present energy conditions, that we will use in this paper [42]: ...
... where L M is the Lagrangian of the matter fields. Then, by varying the Einstein-Hilbert action we could obtain (modified) EFE [42]: ...
... Now, we think that it will be appropriate to compare our results for ZTF Casimir wormhole with the usual Morris-Thorne wormholes within the same f (R) theories of gravity considered. Morris-Thorne wormholes were investigated in details within the both quadratic and power-law gravities in the work [42]. In the quadratic gravity, it was shown that NEC, SEC for radial and tangential pressures were respected only for α ≥ 0 and only in the case, when α is relatively small (which coincides well with the Casimir wormholes, that was investigated in the present study). ...
For the spherically symmetric static traversable wormholes, supported by the Casimir energy in $f(\mathcal{R})=\mathcal{R}+\alpha \mathcal{R}^2$ Quadratic, $f(\mathcal{R})=f_0 \mathcal{R}^n$ power-law Modified Gravity (MOG) theories we investigate energy conditions and dynamical stability of the wormhole solutions. Especially, we study Zero Tidal Forces (ZTF) Casimir WH's with anisotropic fluid located at the throat. By using the Casimir energy density and modified Einstein Field Equations (EFE's) we derived suitable shape functions for each modified gravity of our consideration. The stability of Casimir traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman-Oppenheimer-Voklov (MTOV) equation. Besides, we have numerically solved MTOV and derived hydrodynamical, anisotropic and extra forces, that is present due to the non-conserved stress-energy tensor. Moreover, other fundamental quantities, such as Volume Integral Quantifier and total gravitational energy were derived.
... Casimir Energy is currently the only possible substitute for exotic matter, that could be obtained in the laboratory. Firstly, we could present energy conditions, that we will use in this paper [42]: ...
... where L M is the Lagrangian of the matter fields. Then, by varying the Einstein-Hilbert action we could obtain (modified) EFE [42]: ...
... Now, we think that it will be appropriate to compare our results for ZTF Casimir wormhole with the usual Morris-Thorne wormholes within the same f (R) theories of gravity considered. Morris-Thorne wormholes were investigated in details within the both quadratic and power-law gravities in the work [42]. In the quadratic gravity, it was shown that NEC, SEC for radial and tangential pressures were respected only for α ≥ 0 and only in the case, when α is relatively small (which coincides well with the Casimir wormholes, that was investigated in the present study). ...
For the spherically symmetric static traversable wormholes, supported by the Casimir energy in f (R) = R + αR 2 Quadratic, f (R) = f 0 R n power-law Modified Gravity (MOG) theories we investigate energy conditions and dynamical stability of the wormhole solutions. Especially, we study Zero Tidal Forces (ZTF) Casimir WH's with anisotropic fluid located at the throat. By using the Casimir energy density and modified Einstein Field Equations (EFE's) we derived suitable shape functions for each modified gravity of our consideration. The stability of Casimir traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman-Oppenheimer-Voklov (MTOV) equation. Besides, we have numerically solved MTOV and derived hydrodynamical, anisotropic and extra forces, that is present due to the non-conserved stress-energy tensor. Moreover, other fundamental quantities, such as Volume Integral Quantifier and total gravitational energy were derived.
... Casimir Energy is currently the only possible substitute for exotic matter, that could be obtained in the laboratory. Firstly, we could present energy conditions, that we will use in this paper [42]: ...
... where L M is the Lagrangian of the matter fields. Then, by varying the Einstein-Hilbert action we could obtain (modified) EFE [42]: ...
... Now, we think that it will be appropriate to compare our results for ZTF Casimir wormhole with the usual Morris-Thorne wormholes within the same f (R) theories of gravity considered. Morris-Thorne wormholes were investigated in details within the both quadratic and power-law gravities in the work [42]. In the quadratic gravity, it was shown that NEC, SEC for radial and tangential pressures were respected only for α ≥ 0 and only in the case, when α is relatively small (which coincides well with the Casimir wormholes, that was investigated in the present study). ...
Wormholes are considered to be hypothetical tunnels connecting two distant regions of the universe or two different universes. In general relativity (GR), the formation of traversable WH requires the consideration of exotic matter that violates energy conditions (ECs). If the wormhole geometry can be described in modified gravitational theories without introducing exotic matter, it will be significant for studying these theories. In the paper, we analyze some physical properties of static traversable WH within the framework of f(R, T) modified gravitational theory. Firstly, we explore the validity of the null, weak, dominant and strong energy conditions for wormhole matter for the considered f(R,T)=R+αR2+λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R,T)=R+\alpha R^2+\lambda T$$\end{document} model. Research shows that it is possible to obtain traversable WH geometry without bring in exotic matter that violates the null energy condition (NEC) in the f(R, T) theory. The violation of the dominant energy condition (DEC) in this model may be related to quantum fluctuations or indicates the existence of special matter that violates this EC within the wormhole. Moreover, it is found that in the f(R,T)=R+αR2+λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(R,T)=R+\alpha R^2+\lambda T$$\end{document} model, relative to the GR, the introduction of the geometric term αR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha R^2$$\end{document} has no remarkable impact on the wormhole matter components and their properties, while the appearance of the matter-geometry coupling term λT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda T$$\end{document} can resolve the question that WH matter violates the null, weak and strong energy condition in GR. Additionally, we investigate dependency of the valid NEC on model parameters and quantify the matter components within the wormhole using the “volume integral quantifier”. Lastly, based on the modified Tolman–Oppenheimer–Volkov equation, we find that the traversable WH in this theory is stable. On the other hand, we use the classical reconstruction technique to derive wormhole solution in f(R, T) theory and discuss the corresponding ECs of matter. It is found that all four ECs (NEC, WEC, SEC and DEC) of matter in the traversable wormholes are valid in this reconstructed f(R, T) model, i.e we provide a wormhole solution without introducing the exotic matter and special matter in f(R, T) theory.
Nowadays, alternative gravity is a crucial tool for addressing some enduring observational problems, such as the dark universe. Additionally, they can be used to advance the results of general relativity in astrophysics. Wormholes, or imagined passageways through spacetime, have the potential to revolutionize interstellar transport and cosmic interconnection. In the present work, the existence and characteristics of wormhole solutions in the context of the non‐linear function of gravity are investigated. A typical characteristic of maintaining wormholes is the presence of exotic stuff that defines the energy conditions (ECs). The authors looked at the ECs that must be met and analyzed how the function affects the energy‐momentum requirements for maintaining the wormholes open. For a comprehensive understanding of wormhole geometries, we also studied the embedding diagram and volume integral quantifier.
In this manuscript, we find the exact solutions of asymptotically flat wormhole (WH) geometry in the
background of symmetric $f(Q)$ gravity (vanishing curvature and torsion) where the non-metricity term
$Q$ is accountable for fundamental interaction. In this scenario, we choose two different $f(Q)$
gravity models (logarithmic and exponential) along with the special choice of shape function
$b(r)=\frac{r}{\exp(\gamma(r-r_{0}))}$, and redshift function $\phi(r)=\frac{r_{0}}{2r}$. Here,
$\gamma$ affects the radius of curvature of WH. Under this scenario, we analyze the viability of
the shape function and energy constraints of the WH solutions for each model. For both models,
we determine the validity regions of energy conditions under some parameter spaces of the model
parameters. The allowed parameter spaces for logarithmic and exponential models are illustrated
in Tables I and II, respectively. The validity region for the null energy condition represents that
WH geometry in chosen $f(Q)$ gravity models is supported by ordinary matter while exotic matter
elsewhere. Furthermore, we represent the WH construction by embedding diagrams and
shows that the derived WH solutions are stable for the allowed range of model parameters. Finally,
it is concluded that such particular modified gravity can give us a more realistic and stable
WH geometry.
The present study analyses the wormhole solution both in the dRGT- f ( R , T ) massive gravity and Einstein massive gravity. In both the models, the anisotropic pressure solution in ultrastatic wormhole geometry gives rise to the shape function that involves massive gravity parameters $$ \gamma $$ γ and $$ \Lambda $$ Λ . However, the terms consisting of $$ \gamma $$ γ and $$ \Lambda $$ Λ acts in such a way that the spacetime loses asymptotic flatness. Similar to the black hole solution in massive gravity, this inconsistency arises due to the repulsive effect of gravity which can be represented by the photon deflection angle that goes negative after a certain radial distance. It is investigated that the repulsive effect induced in the massive gravitons push the spacetime geometry so strongly that the asymptotic flatness is effected. On the other hand, in this model, one can have a wormhole with ordinary matter at the throat that satisfies all the energy conditions while the negative energy density is sourced by massive gravitons. Finally, using the TOV equation, it is found that the model is stable under the hydrostatic equilibrium condition.
