arXiv:gr-qc/0703143v1 29 Mar 2007
A
Theoretical
Construction
of
Thin
Shell
Wormhole
from
Tidal
Charged
_______
hole
F.Rahaman*†, M.Kalam‡ , K A Rahman* and S.Chakraborti*
Abstract
Recently, Dadhich et al [ Phys.Lett.B 487, 1 (2000)] have discovered a _______
hole solution localized on a three brane in five dimensional gravity in the Randall-
Sundrum scenario. In this article, we develop a new class of thin shell wormhole
by surgically grafting above two _______ hole spacetimes. Various aspects of this thin
wormhole are also analyzed.
Introduction:
Inrecentyears, several scientists around theworldhavegiventheirattentiontothebrane
worldgravity. Withintheframework ofbraneworld, onecanexplain oneof thehierarchy
problems in the current standard models of high energy physics [1]. Also, brane world
framework may give clue how to solve the greatest challenging problem in theoretical
physics namelytheunificationof allfundamentalforcesinnature[2]. Actually,thestring
theory was the inspiration behind the idea of brane world scenario. The brane world
idea is that the matter fields are located on a three dimensional subspace, called brane
embedded in 1 + 3 + d dimensions in which the gravity can propagate in the d-extra
dimensions. Here, the d-extra dimensions need not all be small or even compact. Most of
the recent studies consider a simple version of the brane world scenario where all matters
( except gravity ) are confined to a 3-brane embedded in a five dimensional spacetime
(bulk)while gravity can propagate in the bulk.
0
Pacs Nos : 04.20 Gz,04.50 + h, 04.20 Jb
Key words: Thin shell wormhole, Brane worlds, Stability
*Dept.of Mathematics, Jadavpur University, Kolkata-700 032, India:
E-Mail:farook rahaman@yahoo.com
†
Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi -110025
‡Dept. ofPhys. ,NetajiNagarCollegeforWomen,RegentEstate,Kolkata-700092,India.
1
As a consequence, thegravityonthebrane canbedescribedbythe modified4-dimensional
Einstein equations which contains(i) S
µ
, which is quardratic in the stress energy tensor
of matter confined on the brane (ii) the trace less tensor E
µ
, originating from the 5D
Weyl tensor and describing tidal effects on the brane from the bulk geometry. Recently,
Dadhich et al[3] havepresented aspherically symmetric solution whichdescribes a_______
hole localized on a three brane in five dimensional gravity in the brane world scenario.
This_______hole( without electric charge) istermed astidal charged_______hole. Inthis
case tidal charge is arising via gravitational effects from the fifth dimension.
Motivated by Morris and Thorne’s work [4], the study of traversable wormhole have
been a focus of interest in recent years. These are the solutions of Einstein’s equations
that have two regions connected by a throat. To get a wormhole solution, one has to
tolerate the violation of null energy condition. In other words, the presence of exotic
matter ( i.e. the matter which violates the null energy condition ) is unavoidable to
get a wormhole solution. As it is difficult to deal with exotic matter, it is useful to
minimize the usage of exotic matter. In recent past, Visser [5] has proposed a way,
which is known as ’Cut and Paste’ technique, of minimizing the usage of exotic matter to
construct a wormhole in which the exotic matter is concentrated at the wormhole throat.
In ’Cut and Paste’ technique, the wormholes are theoretically constructed by cutting
and pasting two manifolds to obtain geodesically complete new manifold with a throat
placed in the joining shell. Using Darmois-Israel [6] formalism, one can determine the
surfacestresses oftheexoticmatter( locatedinthinshellplaced atthejoining surface
). Recently, several physicists are interested to develop thin shell wormholes. Visser
and Poisson have analyzed the stability of thin shell wormhole constructed by joining
thetwoSchwarzschildgeometries[7]. The stability oftransparent spherical symmetric
thin-shellwormholeswasexaminedbyIshak andLake[8] .EiroaandRomero[9] have
studied the linear stability of charged thin shell wormholes constructed by joining the
two Reissner-Nordstr¨om spacetimes under spherically symmetric perturbations. Lobo
andCrawford[10] have extendedthelinear stability analysistothethin shell wormholes
withCosmologicalConstant. Eiroa andSimeone[11]have studied cylindrically symmetric
thin shell wormholegeometries associated togauge cosmic strings. Also, the same authors
have constructed a charged thin shell wormhole in dilaton gravity and they have shown
that the reduction of the total amount of exotic matter is dependent on the Dilaton-
Maxwell couplingparameter[12]. The fivedimensionalthinshell wormholesinEinstein-
Maxwell theory with a Gauss Bonnet term has been studied by Thibeault et al [13].
They have made a linearized stability analysis under radial perturbations. Recently,
the present authors have studied thin shell wormholes in higher dimensional Einstein-
Maxwell theory which is constructed by Cutting and Pasting two metrics corresponding
to ahigherdimensionalReissner-Nordstr¨om_______hole[14]. Also,the same authorshave
constructed thin shell wormholeinheterotic string theory[15]. Inthis article, we study
thin shell wormhole in Brane worlds. We develop the model by cutting and pasting two
metrics corresponding to atidal charged_______hole. According toDadhich et al[3] tidal
force arising via gravitational effects from the fifth dimension i.e. it is arising from the
projection onto the brane of free gravitational field effects in the bulk.
2
The tidal charge ’q’ of Dadhich et al’s brane world _______ hole contains the information
of the extra dimension and does affect on the geodesics as well as on the gravitational
potential. So, it is of great interest to investigate how the tidal force affects on the thin
shell wormhole. Various aspects of these thin shell wormhole, namely, temporal evolution
of the throat, stability, total amount of exotic matter will be discussed. We have shown
the tidal charge affects significantly on stability of this thin shell wormhole. It is also
shown that the total amount of exotic matter is reduced by increasing of the tidal charge.
The layout of the paper as follows :
In section 2, the reader is reminded about tidal charged _______ hole obtained by Dadhich
et al. In section 3, thin shell wormhole has been constructed by means of the Cut and
Pastetechniques. Insection4,thetimeevolutionof theradiusof thethroatisconsidered
whereas linearized stability analysis is studied in section 5. Section 6 is devoted to a brief
summary and discussion including the calculation of the total amount of exotic matter
needed.
2.
Brane
world
_______
holes
:
The gravitational field equations induced on the brane is described by modified Einstein
equations from 5-dimensional gravity with the aid of Gauss-Codazzi equations to the
effective4-dimensional field containing thenewtermscarryingbulk effectsontothebrane
as[1-2]
Gµ =
gµ + k
2
4
Tµ + k
4
5
Sµ -Eµ (1)
Here is the 4D cosmological constant expressed in terms of the 5D , 5 and brane
tension .:
1
2
4
5
1k6
.
(5 +
.);
=
8pG = k54
k
2
4
=
6
where k4 isthe4Dgravitational constant andGistheNewton’s constant ofgravity. Tµ
is the usual energy momentum tensor of matter on the brane and the local bulk effects
on the matter, Sµ consists of squares of Tµ (itisalocalhigher energycorrectionterm).
Eµ consists of theprojection of thebulkWeyl tensor onto thebrane(itis nonlocalfrom
thebranepoint of view). By construction, Eµ
is trace less, Eµµ =0 and on the brane, in
the vacuum case, it satisfies conservation equation .µEµ
= 0. Inspite of the absence of
matter, Eµ
may not be zero.
3
Considering the static spherically symmetric spacetime,
dr2
ds2 = f(r)dt2 --r 2d
22
, (2)
f(r)
and using thevacuumbrane field equation( with setequal tozero)
G = -E ,
µµ
Dadhich et al[3],have obtained a new_______hole solution as
2mq dr2
ds2 =(1- +)dt2 --r 2d
22
, (3)
22mq
rr(1- r + r2
)
These _______ holes are characterized by two parameters : their mass and dimension less
tidal charge, q. The tidal charge parameter q comes from the projection on the brane
of free gravitational field effects in the bulk. Here the tidal charge q can take both
positive andnegative values. When the tidal charge takespositive values, then the metric
(3) is analogous to Reissner-Nordstr¨om _______ hole solution. For q<m2, it describes
tidal charge _______ hole with two horizons at rh = m ± m2 -q, which are below the
Schwarzschild radius. Now for q< 0, the above tidal charge _______ hole has only one
horizon at rh = m + m2+ |q |, above the Schwarzschild radius. The gravitational field
of this _______ hole is increased due the presence of the tidal charge.
3.
Cut
and
Paste
Tactics:
Dadhich et al [3] have given exact localized _______ hole solution in which the brane is
located at . =0( . is the fifth coordinate ). This _______ hole formed from collapsed
matter confined on brane. The induced four dimensional metric on the brane is given
in equation(3). We work with( 3+1) dimensionalbrane, whichis containedin a(
4+1) dimensionalbulk and consider the4-dimensionalhorizon structure ofthebrane
world_______holebecauselikeDadhich et al[3], we are notinterestedtotakethe effect of
the brane world _______ hole on the bulk geometry. And for that we do not consider the
bulk metric. Thus, to construct thin shell wormhole in brane world, we cut two copies of
region from the tidal charged _______ hole geometry described by
± =(x |r = a), where
a = rh (position ofevent horizon). In this study, we assume the case, where tidal charge
is negative i.e. horizon of this _______ hole is greater than the Schwarzschild horizon. Now
taking the two copies of the remaining regions, M± =(x |r = a), wepaste the twopieces
together at the hypersurface = ± =(x |r = a). This surgical grafting produces a
geodesically complete manifold M = M+ M- with a matter shell at the surface r = a ,
where the throat of the wormhole is located. Thus a single manifold M is obtained which
connects two asymptotically flat regions at their boundaries and the throat is placed
at( hereis a synchronoustimelikehypersurface). SinceMis apiece wisetidal
charged _______ hole spacetime, the stress energy tensor is either every where zero or obeys
all energy conditions except at the throat itself.
4
At , one expects that the stress energy tensor to be proportional to a delta function.
FollowingDarmois-Israelformalism, we shalldeterminethe surface stresses atthejunction
boundary. The intrinsic coordinates in are taken as .i =(t,.,f)with t is the proper
time on the shell.
To understand the dynamics of the wormhole, we assume the radius of the throat be a
function of the proper time a = a(t). The parametric equation for is defined by
: F(r,t)= r -a(t) (4)
The extrinsic curvature associated with the two sides of the shell are
± .2X .X .X
K±
ij = -n [ +.. ]| (5)
..i..j ..i ..j
±
where n are the unit normals to ,
.F .F .F
2
n ± = ±|g |-1
(6)
.X .X .X
with nµnµ =1.
The intrinsic metric on is given by
ds2 = -dt2 + a(t)2d
2
2 (7)
FromLanczos equation, one can obtainthe surface stress energytensorSj
i = diag(-s,-v,-v)
(wheres is the surface energy density and v, , the surface tensions) as
12mQ
s = - 1-- +.a2 (8)
2
2pa aa
11- m +.a2 + aa¨
-v = -v = -v =
.
a (9)
4pa 2m - Q 2
1- +.a
2
aa
where over dot means the derivative with respect to t and q = -Q,Q> 0.
Negative surface energy density in(8) impliesthe existence of exotic matter atthe shell.
The negative signs of the tensions mean that they are indeed pressures.
5
4.
Time
evolution
of
radius
of
the
throat:
The static equations are obtained with .a =0 and a¨=0inequations(8) and(9):
12mQ
s0 = - 1-- (10)
2
2pa aa11- m
v0 = - .
a (11)
4pa 2m - Q
1-
2
aa
[suffix0indicatesthe static situation]
Now, one can writethe equations(10) and(11)intheform
v0 = w(a)s0 (12)
where
11- m
w(a)= a (13)
2 2m - Q
(1- aa)
2
FollowingEiroa et al andCBejarano et al[12], we assume that the equation of statedoes
not depend on the derivative of a(t) i.e. it is the same form as in the static one. Now
putting s, vinplaceof s0 , v0 from(8) and(9)in(12),wegetthefollowing expression as
Q mQ
a¨(a -2m - )-a.2( +)=0 (14)
2
a aa
This implies,
1- 2mQ
-
a() a2
() 1
a.(t)= a.(t0)[ ]2
(15)
1- 2mQ
-
a(0
) a2
(0
)
Here, t0 is arbitrary fixed time.
Thus we get,
.
a() Q
da ]-1
2
Q = a.(t0)(t -t0)[1- 2m -
1
a(0
)
a(0
) - 2
a2
(0
)
[1- 2m ]
a()
a2()
This gives,
a.(t0)(t -t0)
[a 2(t)-2ma(t)-Q]
12
+m ln[2(a 2(t)-2ma(t)-Q)
12
+2a(t)-2m]= (16)
(1- 2mQ )
1
2
a(0
)a2
(0
)
The above implicit expression gives the time evolution of the radius of the throat.
6
The velocity and acceleration of the throat are
1- 2mQ
-
a() a2
() 1
2
a.(t)= a.(t0)[ ] (17)
1- 2mQ
-
a(0
) a2
(0
)
and
mQ
+
a2
() a3
()
a¨(t)= a.2(t0)[ ] (18)
1- 2mQ
-
a(0
) a2
(0
)
From the above two expressions, one can easily see that the sign of the velocity is given
by the sign of the initial velocity and the acceleration is always positive. It is immaterial
whether theinitial velocityispositive or negative, the throat expandsforever. This would
imply that the equilibrium position is always unstable. However, if the initial velocity
is zero, the velocity and acceleration of the throat would be zero i.e. throat be in static
equilibrium position. Now, we shall study the stability of the configuration under small
perturbations aroundstatic solution situated at a0 (initialvelocity will be assumed to be
zero).
5.
Linearized
Stability
Analysis:
Rearranging equation(8), we obtainthethin shell’s equation of motion
a.2 + V(a)=0 (19)
Here the potential is defined as
2mQ
V(a)=1- --4p2 a 2s2(a) (20)
2
aa
Linearizing around a static solution situated at a0, one can expand V(a) around a0 to
yield
1 '' (a0)(a -a0)3]
V = V(a0)+V ' (a0)(a -a0)+
Va0)2 +0[(a -(21)
2
where prime denotes derivative with respect to a.
Since we are linearizing around a static solution at a = a0, we have V(a0) =0and
'' (a0)
V ' (a0)=0. ThestableequilibriumconfigurationscorrespondtotheconditionV> 0.
Now wedefine aparameter ß, which is interpreted as the speed of sound, by the relation
[7]
.p
ß2(s)= | (22)
.s
Here,
'' (a)
4m 6Q
V = - 3 - 4 -8p2s2 -32p2ass ' -8p2 a 2(s ' )2 -8p2 a 2ss '' (23)
aa
7
Sincethe negativetensionis equivalenttopressure, wetake -v = -v = -v = p. From
equations(8) and(9), one can write energy conservation equation as
a.
s.+2 (p+ s)=0 (24)
a
or
d
(4psa2)+pd
(4pa2)=0 (25)
dtdt
From equation(24)( by using(22)), we obtain,
s ''
+
2
s ' (1+ß2)-
2(p+ s)=0 (26)
2
aa
Now, the second derivative of the potential is taken the following form as
2(a0 -m)3 + m(m2 + Q)
'' (a0)2
V = - 4[a0[2 ]+2(a0 -3ma0 -2Q)ß0
2)] (27)
a0 a0 -2ma0 -Q
'' (a0)
The wormhole solution is stable if V> 0 i.e. if
(a0 -m)3 + m(m2 + Q)
(a0
2 -3ma0 -2Q)ß0
2 < -a0[)] (28)
2(a0
2 -2ma0 -Q
The right hand side of this inequality is negative because, a0 >m(1+ 1+ m
Q )= rh.
2
The left hand side flips sign at a0 = 3
2m[1+ 1+ 9
8
m
Q = r+ >rh. Therefore, if one treats
2
a0, m andQ are specifiedquantities, thenthe stability ofthe configuration requires the
following restrictions on the parameter ß0.
(a0
-m)3
+m(m+Q)
ß0
2 < -a0[
2
]if, a0 >r+
2(a2
-2ma0
-Q)(a2
-3ma0
-2Q)
00
(a0
-m)3
+m(m+Q)
ß0
2 > -a0[ 2
22
]if, rh <a0 <r+
2(a0
-2ma0
-Q)(a0
-3ma0
-2Q)
This means there exists some part of the parameter space where the throat location is
stable. For a lot of useful information, we show the stability regions graphically. For
normal situation i.e. in case of real matter, ß0 represents the velocity of sound and it
lies within the interval, ß0
2 o (0,1]. However, in the presence of exotic matter ( as it
happens to be in the throat), ß0 is not velocity of sound. So for, exotic matter this range
may be relaxed. One can see ref.[7] for an extensive discussion on the respective physical
interpretation of ß0 in the presence of exotic matter.
8
–1
–0.8
–0.6
–0.4
–0.2
z
3.5 4 4.5 5 5.5 6x
–1
–0.8
–0.6
–0.4
–0.2
z
3.5 4 4.5 5 5.5 6x
Figure 1: Here we plot z = ß2 Vs. x = a0
for a0 >r+ ( Q = .1) . The stability
|(a=a0
) mm
region is situated below the curve.
2
3
4
5
6
z
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9x
for rh < a0 < r+ (Q
m
m
Figure 2: Here we plot z = ß2 Vs. x = a0
= .1). The stability
|(a=a0
)
region is situated above the curve.
9
6.
Summary
and
Discussions:
In this article, we have studied thin shell wormhole in brane world scenario by surgically
graftingtwotidalcharged_______holespacetimes. Thoughthetidalchargeparameter ’q’of
this_______hole cantakebothpositive and negative values,butinthis study, we consider
the case for q< 0[ For q> 0, the solution is analogous to the Reissner-Nordstr¨om _______
hole solution]. In this case, the_______holehas only onehorizon, whichlies outside the
Schwarzschild horizon. We have considered an equation of state that relates the tension
with the surface energy density of the exotic matter at the throat. We have obtained the
time evolution of the radius of throat. One could see that whether the initial velocity is
positive or negative, the throat expands indefinitely. But, when initial velocity is zero,
then the radius of the throat remains constant i.e. the throat be in a static equilibrium
position. Wehave analyzedthedynamical stability ofthethin shell, consideringlinearized
radialperturbations around static solution. To analyzethis, wedefine aparameterß2 =
p '
'
as aparametrization of the stability of equilibrium. Wehave obtained a restriction on ß2
to get stable equilibrium of the thin wormhole( see eq.(28)).
The total amount of exotic matterfor the thin wormhole canbequantified by theintegral
( In this case, radial pressure, pr = 0 and we have .< 0,. + pr < 0 i.e. both energy
conditions are violated. The transverse pressure is pt = p = p = -v and one can see
from(10) and(11) that the sign of . + pt is not fixed but depends on the value of the
parameters)
.
v
=[.+ pr] -gd3 x .
Following Eiroa andSimone[11] , weintroduce a new radial coordinate R = ±(r -a)in
M( ± for M± respectively) sothat
.
R.
v
2 8
= [.+ pr] -gdRd.df
00 -8
Since the shell does not exert radial pressure and the energy density is located on a thin
shell surface, so that . = d(R)s0, then we have
R.
v
= 2[. -g]|r=a0
d.df =4pa02
s(a0)
00
2m - Q
Thus one gets,
= -2a0 1- a0
a2
.
0
One could see that the tidal charge and mass of the _______ hole affect the total amount of
exotic matter needed. The variation of the total amount of exotic matter with respect to
tidal charge and mass of the _______ hole is shown in the figure 3.
10
mQ
Figure 3: Here we plot z = Vs. x = and y = a.
2
a0
a0
0
11
Now we are interested to the fact that under what conditions the total amount of exotic
matter could be reduced. If mass of the _______ hole remains fixed , then the total amount
of exotic matter is reduced by increasing the tidal charge. Thus tidal charge contains the
information of extra dimension plays significant role to reducing total amount of exotic
matter needed.
Also if tidal charge of the _______ hole is kept fixed, then the total amount of exotic matter
is reduced by increasing the mass of the _______ hole. Thus one can see that less exotic
matter is needed when tidal charge and mass of the _______ hole are increased. These are
depicted in figure 4 and 5.
–1.8
–1.6
–1.4
–1.2
–1
–0.8
–0.6
–0.4
–0.2
0
z
0.2 0.4 0.6 0.8 1y
Q 1
for m
Figure 4: Here we plot
z =
Vs. y
=
=.
10
20
a0
a0
a
–1.6
–1.4
–1.2
–1
–0.8
–0.6
–0.4
–0.2
0
z
0.2 0.4 0.6 0.8 1x
mQ
Figure 5: Here we plot
z =
for
=
.35
V
=
s. x
.
20
a0
a0
a
Further,from the above expression, one can see that
approaches to zero when wormhole
radiustendstotheeventhorizon(i.e. when a0 . rh ). So one canget vanishing amount
of exotic matter by taking a0 near rh. Thus, one can note that the total amount of exotic
matter needed to support traversable wormhole canbe madeinfinitesimal smallby taking
wormhole radius near the event horizon of the tidal charged _______ hole. This is depicted
in the figure-6.
12
–35
–30
–25
–20
–15
–10
–5
0
Omega
2 4 6 8 10 12 14 16 18 20
a_0
–35
–30
–25
–20
–15
–10
–5
0
Omega
2 4 6 8 10 12 14 16 18 20
a_0
Figure 6: We choose m =2 and Q= .5. The variation of total amount of exotic matter
on the shell with respect to a0 is shown in the figure.
Acknowledgments
F.R. is thankful to Jadavpur University and DST , Government of India for providing
financial support. MKhasbeenpartially supportedbyUGC,Government ofIndiaunder
MRP scheme. Wearethankful toCentreforTheoreticalPhysics,JamiaMilliaIslamiafor
worm hospitality, where a part of the work has been carried out. Finally, we are grateful
to the referees for pointing out the errors and their constructive suggestions.
References
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[4] M.Morris andK.Thorne ,AmericanJ.Phys.56,39(1988)
[5] MVisser,Nucl.Phys.B328,203( 1989)
[6] WIsrael,NuovoCimento44B ,1(1966) ;erratum -ibid.48B,463(1967)
[7] EPoisson andMVisser,Phys.Rev.D52,7318(1995)[arXiv:gr-qc/9506083]
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13
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Cecilia Bejarano, Ernesto F. Eiroa, Claudio Simeone, Phys.Rev.D75:027501,2007.
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[14] F.Rahaman , M.Kalam and S.Chakraborty, gr-qc/0607061
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14
Worm Holes - ______ Holes
In physics, a wormhole, also known as an Einstein-Rosen bridge (and less commonly as an Einstein-Rosen-Podolsky bridge or Einstein-Podolsky-Rosen bridge), is a hypothetical topological feature of spacetime that is essentially a "shortcut" through space and time.
A wormhole has at least two mouths which are connected to a single throat. Matter can 'travel' from one mouth to the other by passing through the throat.The name "wormhole" comes from the following analogy used to explain the phenomenon: imagine that the universe is the skin of an apple, and a worm is traveling over its surface. The distance from one side of the apple to the other is equal to half the apple's circumference if the worm stays on the apple's surface, but if it instead burrows a wormhole directly through the apple the distance it has to travel is considerably less.
Intra-universe wormholes connect one location of a universe to another location of the same universe. A wormhole should be able to connect distant locations in the universe by bending spacetime, allowing travel between them that is faster than it would take light to make the journey through normal space. See the image above.
Inter-universe wormholes connect one universe with another. This gives rise to the speculation that such wormholes could be used to travel from one parallel universe to another. A wormhole which connects (usually closed) universes is often called a Schwarzschild wormhole.
Another application of a wormhole might be time travel. In that case it is a shortcut from one point in space and time to another. In string theory a wormhole has been envisioned to connect two D-branes, where the mouths are attached to the branes and are connected by a flux tube. Finally, wormholes are believed to be a part of spacetime foam.
There are two main types of wormholes: Lorentzian wormholes and Euclidean wormholes. Lorentzian wormholes are mainly studied in semiclassical gravity and Euclidean wormholes are studied in particle physics. Traversable wormholes are a special kind of Lorentzian wormholes which would allow a human to travel from one side of the wormhole to the other.
Serguei V. Krasnikov tossed the term spacetime shortcut as a more general term for (traversable) wormholes and propulsion systems like the Alcubierre drive and the Krasnikov tube to indicate hyperfast interstellar travel.
It is unknown whether (Lorentzian) wormholes are possible or not within the framework of general relativity. Most known solutions of general relativity which allow for wormholes require the existence of exotic matter, a theoretical substance which has negative energy density. However, it has not been mathematically proven that this is an absolute requirement for wormholes, nor has it been established that exotic matter cannot exist. Recently Amos Ori envisioned a wormhole which allowed time travel, did not require any exotic matter, and satisfied the weak, dominant, and strong energy conditions. Since there is no established theory of quantum gravity, it is impossible to say with any certainty whether wormholes are possible or not within that theoretical framework.
It is unknown whether (Lorentzian) wormholes are possible or not within the framework of general relativity. Most known solutions of general relativity which allow for wormholes require the existence of exotic matter, a theoretical substance which has negative energy density. However, it has not been mathematically proven that this is an absolute requirement for wormholes, nor has it been established that exotic matter cannot exist. Recently Amos Ori envisioned a wormhole which allowed time travel, did not require any exotic matter, and satisfied the weak, dominant, and strong energy conditions. Since there is no established theory of quantum gravity, it is impossible to say with any certainty whether wormholes are possible or not within that theoretical framework.
Lorentzian traversable wormholes would allow travel from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another universe. Because wormholes not only connect spatial locations they would also allow time travel.
Often there is confusion about the idea that wormholes allow superluminal (faster-than-light) space travel. In fact there is no real superluminal travel involved. Assume that the wormhole connects two remote locations. While traveling through a wormhole subluminal (slower-than-light) speeds can be used. The time in which the distance was traveled would appear faster than it would take light to make the journey through normal space.
A wormhole could potentially allow time travel. This could be accomplished by accelerating one end of the wormhole relative to the other, and then sometime later bringing it back; relativistic time dilation would result in less time having passed for the accelerated wormhole mouth compared to the stationary one, meaning that anything which entered the stationary wormhole mouth would exit the accelerated one at a point in time prior to its entry.
The path through such a wormhole is called a closed timelike curve, and a wormhole with this property is sometimes referred to as a "timehole."It is thought that it may not be possible to convert a wormhole into a time machine in this manner, however; some mathematical models indicate that a feedback loop of virtual particles would circulate through the timehole with ever-increasing intensity, destroying it before any information could be passed through it.
This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. There is also the Roman ring, which is a very stable configuration of more than one wormhole.
This ring allows a closed time loop with stable wormholes. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps, and will likely require a theory of quantum gravity to resolve.Many physicists, including Stephen Hawking, believe that due to the problems a wormhole would theoretically create, including allowing time travel, that something fundamental in the laws of physics would prohibit them.
However, this remains speculation, and the notion that nature would censor inconvenient objects has already failed in the case of the cosmic censorship principle.
Wormholes known as Schwarzschild wormholes are theoretical bridges between areas of space that are thought to be found in the center of a black hole and ______ hole, joining two universes. They exist in solutions to Einstein's equations, and are thought to be extremely unstable, and would instantly fall apart once created. Some speculation exists that quasars are actually ______ holes instead of supermassive black holes.
It is impossible for a traveller to go through this type of wormhole because they can only go through a horizon in one direction. If the traveler is formed of non-exotic matter once they reach the center of the Schwarzschild wormhole then, they can't leave the other side, and they can't leave through where they came since the side they came in though was a black hole, meaning nothing can escape it once inside the Schwarzschild radius.
Wormholes are also a feature of science fiction.
They are a centerpiece of Carl Sagan's novel Contact, for which Kip Thorne advised Sagan on the possibilities of wormholes.
Wormholes are also the principal means of space travel in the Stargate movie and the spin-off television series, Stargate SG-1 and Stargate Atlantis. The central plot device of the programs is a transportation network consisting of the ring-shaped devices known as Stargates, which generate wormholes that allow one-way matter transmission between gates when the correct spatial coordinates are "dialed".
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______ Holes
______ Holes are the theoretical exact opposite of black holes, and their existence is implied by a negative square root solution to the Schwarzchild metric. The Schwarzchild metric is based on General Relativity, which is time symmetric. This means that the most technical definition of ______ hole is simply a black hole running backwards in time. It is a location in space time that, instead of being impossible to escape, is impossible to reach.
Under the definition given by the solution to this equation they repel everything, including massive particles as well as photons, nothing can enter them. We have never discovered a ______ hole, and given these properties we believe that they would be rather difficult to miss. Furthermore, an object that acts in this manner directly violates the second law of thermodynamics which states that heat naturally flows from a region of high temperature to a region of low temperature.
The contradiction this causes is that any object with heat should eventually dissipate it's heat energy to its surroundings, and a ______ hole by definition never runs out of heat or mass, thus standing in violation of every other major law of physics we have in order to hold true to the second law of thermodynamics.
This, however, only applies to our universe. The same equations that suggest the existence of ______ holes also seem to imply that they exist in a universe parallel to our own, and would exist connected to a black hole by way of a worm hole in order to complete the Schwarzchild geometry suggested by the equation which predicted the existence of black holes. This worm hole joining 2 separate universes is known as the Einstein-Rosen bridge and is one of the most fascinating concepts in theoretical physics.
While the concept of this connection is extremely exciting we know very little about it, as we have no ______ holes to observe and black holes are extremely hard to detect given their light absorbing nature. Given our current understanding of black holes and ______ holes we are not even sure of such a connection could exist, or if it did, where it would take us. Current knowledge does not even give enough information to suggest if such a link would even be to somewhere else in our own universe.
Unfortunately, current theory does not even allow for the ultimate destination of a worm hole to be much of a worry because it is believed that passing through a worm hole is impossible. Instant death would be a near certainty given any imaginable method of protection, and no matter the circumstances return would be impossible given everything we know about black holes and the way they would interact with ______ holes.
The only method where death would not be a near certainty is if a worm hole could somehow be stabilized for longer than the brief amount of time under which they are naturally believed to remain stable. This is an impossibility given our current understanding of science and would obviously be grander in scope than anything ever attempted by mankind in the history of Earth.
It is theoretically possible, although highly improbable that a worm hole could somehow be stabilized to allow safe passage through it. The only theoretical way this could be done that I was able to find involves using 'exotic matter', or matter unlike any we know, highly exotic matter. In order to stabilize the worm hole the throat of the singularity would have to be threaded with this matter which would be spherical in nature. The properties this matter would have to have would be negative mass, and yet still be capable of exerting a positive surface pressure.
It must have these two properties for very specific reasons, the negative mass ensures the the throat of the worm hole lies outside the protected region and the positive surface pressure is the property that prevents the throat of the worm hole for collapsing. These properties of matter are not arbitrary or purely theoretical, we have determined this is the type of space-time geometry most likely needed to produce a stable worm hole. Einstein's equations then specify what the energy-momentum content of matter must be in an area to produce the needed geometry. From as general a standpoint as a matter such as this can be, these are the properties normally suggested to be needed to stabilize a worm hole. As a side note, the notion of negative mass matter is certainly rather disturbing, however because of vacuum fluctuations near a black hole it is not considered to be an impossibility.
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In astrophysics, a ______ hole is a postulated celestial body that spews out matter, in other words an anti-black hole, or the time reversal of a black hole.
______ holes have long been speculated about in Science Fiction. They have been postulated as a means of transport between points of spacetime and even different universes. Due to a black hole's suggested funnel-like nature, matter travelling through a black hole and exiting through a ______ hole would be crushed to an immensely dense but small size, this would go against transportation because it is very unlikely that a ______ hole would have the ability to recompose the matter to its original state prior to entering the black hole. The existence of ______ holes is hypothetical, as they appear to violate the second law of thermodynamics.
Other speculations include the hypothesis that quasars are actually ______ holes instead of supermassive ______ holes.
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