A general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime

Saw, Vee-Liem; Chew, Lock Yue

doi:10.1007/s10714-012-1435-3

Cited by 8 publications

(45 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A safe geodesic for the lower-dimensional catenary wormhole was shown to be the one where u = π, corresponding to the outermost extreme of the wormhole [1]. The same turns out to be true for the (3+1)-d counterpart, as we will now show.…”

Section: B a Safe Geodesic Through The Catenary Wormholesupporting

confidence: 69%

“…We have described the method of constructing curved traversable wormholes in (3+1)-d spacetime, building on the previous lower-dimensional study in [1]. The static zero tidal force Teo's rotating wormhole [27].…”

Section: Discussionmentioning

confidence: 99%

“…Comparisons can be made with the (2+1)-d version which is discussed in [1]. In that lower-dimensional analysis for the general metric including spatial cross-terms, all terms in the Einstein tensor vanish in the absence of tidal force except for the G 00 = 1 2 R term.…”

Section: The Physics Of the Zero Tidal Force (3+1)-d Wormholes (mentioning

confidence: 99%

“…The difference between using a straight line and a plane curve is that the g vv term for the former depends only on v (the parameter for points along the given straight line) due to the spherical symmetry, in constrast to the dependence on u and v for the latter (the parameters for the "loop" around the given curve as well as for the points along the given curve) due to the lack of spherical symmetry. Moreover for space curves, the metric for the (3+1)-d helical wormhole with the two non-zero spatial cross-terms [1] indicates even further deviation from the spherical symmetry.…”

Section: The Physics Of the Zero Tidal Force (3+1)-d Wormholes (mentioning

confidence: 99%

See 3 more Smart Citations

Curved traversable wormholes in (3+1)-dimensional spacetime

Saw

Chew

2014

Gen Relativ Gravit

Self Cite

View full text Add to dashboard Cite

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms.The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics -involving pressures and shear forces of the mass-energy fluid supporting the former -is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.

show abstract

Section: B a Safe Geodesic Through The Catenary Wormholesupporting

confidence: 69%

Section: Discussionmentioning

confidence: 99%

Section: The Physics Of the Zero Tidal Force (3+1)-d Wormholes (mentioning

confidence: 99%

Section: The Physics Of the Zero Tidal Force (3+1)-d Wormholes (mentioning

confidence: 99%

See 2 more Smart Citations

Curved traversable wormholes in (3+1)-dimensional spacetime

Saw

Chew

2014

Gen Relativ Gravit

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar to black holes, wormholes in 2 + 1 dimensions [1][2][3][4][5][6][7][8][9][10][11] also have a certain degree of simplicity compared to their 3 + 1-dimensional counterparts [12]. The absence of gravitational degrees in 2 + 1 dimensions enforces us to introduce appropriate sources to keep the wormhole alive against collapse.…”

Section: Introductionmentioning

confidence: 99%

Hypocycloidal throat for $$2+1$$ 2 + 1 -dimensional thin-shell wormholes

Mazharimousavi

Halilsoy

2015

Eur. Phys. J. C

View full text Add to dashboard Cite

Recently we have shown that for 2 + 1-dimensional thin-shell wormholes a non-circular throat may lead to a physical wormhole in the sense that the energy conditions are satisfied. By the same token, herein we consider an angular dependent throat geometry embedded in a 2 + 1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided by a hypocycloid. That is, two flat 2 + 1 dimensions are glued together along a hypocycloid. The energy required in each hypocycloid increases with the frequency of the roller circle inside the large one.

show abstract

Helicalised fractals

Saw

Chew

2015

Chaos, Solitons & Fractals

Self Cite

View full text Add to dashboard Cite

We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line and circle, showing that it takes the form of the self-similar dimension for a self-similar fractal, with lower bound of 1. Upper bounds to the Hausdorff dimension as functions of $\omega$ have been determined for the linear helical fractal, curved helical fractal and circular fractal, based on the no-self-intersection constraint. For large number of windings $\omega\rightarrow\infty$, the upper bounds all have the limit of 2. This would suggest that carrying out a topological analysis on the structure of chromosomes by modelling it as a two-dimensional surface may be beneficial towards further understanding on the dynamics of DNA packaging.Comment: 25 pages, 10 figures. v3: Detailed derivation of the Hausdorff dimension included. Accepted by Chaos, Solitons & Fractal

show abstract

A general method for constructing curved traversable wormholes in (2+1)-dimensional spacetime

Cited by 8 publications

References 32 publications

Curved traversable wormholes in (3+1)-dimensional spacetime

Curved traversable wormholes in (3+1)-dimensional spacetime

Hypocycloidal throat for $$2+1$$ 2 + 1 -dimensional thin-shell wormholes

Helicalised fractals

Contact Info

Product

Resources

About