Thin-shell wormholes from the regular Haywardregular black hole Seminar

8/13/2019 Thin-shell wormholes from the regular Haywardregular black hole Seminar

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Aotrnkubtano Mfywfrk rcgudfr edfbi mndc Rtfedc tmao smcdd wnrjmndc Rnjc jnkcds nh cxntab jfttcr suppnrtaog tmc [RWM Bnob

[mao-smcdd wnrjmndcs hrnj tmc rcgudfr Mfywfrk

rcgudfr edfbi mndc

J.Mfdadsny, R.M.Jfzmfrajnusfva, F.Nvguo

Cfstcro Jckatcrrfocfo Soavcrsaty, Onrtm Byprus

Kcbcjecr 6=, 5062

J.Mfdadsny, R.M.Jfzmfrajnusfva, F.Nvguo CJS

[mao-Rmcdd Mfywfrk EM
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Nvcrvacw

6 AotrnkubtanoFestrfbt

5 Mfywfrk rcgudfr edfbi mndcJfgoctab jnonpndc f snurbc hnr tmc Mfywfrk edfbi mndc

2 Rtfedc tmao smcdd wnrjmndc

; Rnjc jnkcds nh cxntab jfttcr suppnrtaog tmc [RWMDaocfr gfs (DG)Bmfpdygao gfs (BG)

Gcocrfdazck Bmfpdygao gfs (GBG)Jnkastck Gcocrfdazck Bmfpdygao gfs (JGBG)Dngfratmjab gfs (DG)

3 Bnobdusano


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Festrfbt

Ao tmc strst pfrt nh tmc pfpcr wc rcbnosakcr tmc Mfywfrkrcgudfr edfbi mndc ao ;-kajcosanofd spmcrabfd syjjctrab stftabspfbctajc watm tmc snurbc nh onodaocfr jfgoctab stcdk.

Ao tmc scbnok pfrt nh tmc pfpcr wc cstfedasm f spmcrabfdtmao-smcdd watm aosakc tmc Mfywfrk edfbi mndc fok nutsakcsajpdy Rbmwfrzsmadk spfbctajc.

[mc Rurhfbc strcss frc kctcrjaock usaog tmc Kfrjnas-Asrfcd

hnrjfdasj ft tmc wnrjmndc tmrnft.Wc fofdyzc tmc stfeadaty nh tmc tmao-smcdd bnosakcraog daocfrgfs(DG), bmfpdygao gfs(BG), pmfotnj-cocrgy nr gcocrfdasckBmfpdyggao gfs (GBG), jnkastck gcocrfdazck bmfpdygaogfs(JGBG) fok dngfratmjab gfs(DG) cquftano nh stftcs hnrtmc cxntab jfttcr ft tmc tmrnft.

Ao tmc dfst pfrt nh tmc pfpcr wc cstfedasm f tmao-smcdd wnrjmndcao tmc Mfywfrk rcgudfr edfbi mndc spfbctajc fok smnw tmcstfeadaty rcganos nh pntcotafds.


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YMfywfrk, 611;Z, kcstock fs tmc enuokfry nh f spfbc-tajc rcgano aowmabm aoatafddy kavcrgcot dagmt rfys cvcotufddy bnovcrgc. [masenuokfry bfo ec dnbftck ey aovcstagftaog tmc ecmfvanur nh dagmt

bnocs ao tmc rcgano.

Hagurc< F trfppaog mnrazno hndaftck ey jfrgaofd surhfbcs as smnwo mcrc.Aosakc trfppck rcganos nutwfrkdy karcbtck dagmt sagofdsjnjcotfradyhfdd



R R R B
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aowfrks.



A k a M k d ed i m d R ed ma m dd m d R k d h a a m [RWM B
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[mc jctrab huobtano nh tmas edfbi mndc h (r) :

6 5jr5r2+5jd5

ft dfrgc recmfvcs fs Rbmwfrzsbmadk spfbctajc

dajr h(r) 6

5jr

+ N

6r;

(;)

ft sjfdd recmfvcs fs kc-Rattcr edfbi mndc

dajr0 h(r) 6 r5

d5 + N r3 . (3)[mc burvfturc aovfrafot sbfdfrs frc fdd stoatc ft r: 0 . [mcMfywfrk edfbi mndc fkjats cvcot mnrazno wmabm as tmc dfrgcst rcfdrnnt nh tmc hnddnwaog cquftano

r2 5jr5 + 5jd5 : 0. (8)Rcttaog r:j fok d:j (x) ecbnjcs

2

55 + 55 : 0 (7)



A t k ta M k d ed i m d Rt ed tma m dd m d R k d h ta tt ta tm [RWM B
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wmabm fkjats on mnrazno (rcgudfr pfrtabdc sndutano) hnr 5 ? 6857 ,noc mnrazno (rcgudfr cxtrcjfd edfbi mndc) hnr 5 : 6857 fok twnmnraznos (rcgudfr edfbi mndc watm twn mnraznos) hnr 5 4 6857 .

[mcrchnrc tmc ajpnrtfot as tmc rftano nh dj

watm bratabfd rftan ft dj

brat.

: ;2

2eut ont d fok j aokavakufddy. [mas suggcsts tn sct

j: 6 ao tmc scqucd watmnut dnsc nh gcocrfdaty a.c.,h(r) : 6 5r5

r2+5d5. Hnr d5 4 6857 tmc cvcot mnrazno ( tmc pnaot nh on

rcturo) as gavco ey

rm :6

2

2

+ ;

2

+ 5

(=)

ao wmabm : = 57d5 + 2

57d5 (2d5 5). Hnr tmc bfsc nhcxtrcjfd edfbi mndc a.c. d5 : 6857 tmc saogdc mnrazno fbbrucs ftrm :

;2 . Hnr tmc bfsc d

5

6857 tmc stfokfrk Mfwiaog tcjpcrfturcft



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tmc cvcot mnrazno as gavco ey

[M: h (rm)

;

: 6

;2

5 5

rm (1)

wmabm bdcfrdy hnr d5 : 6857 vfoasmcs fok hnr d5 4 6857 as pnsatavc (Noc

just ontc tmft rm ;2 ). Bnosakcraog tmc stfokfrk kcstoatano hnr tmccotrnpy nh tmc edfbi mndc R:F; ao wmabmF : ;r5m noc stoks tmcmcft bfpfbaty nh tmc edfbi mndc wmabm as kcstock fs

Bd:

[M

R

[M

d

(60)

wmabm as kctcrjaock fs

Bd : ;r2m

25 5

rm

(66)

wmabm as bdcfrdy ono-ocgftavc. Dfttcr smnws tmfttmcrjnkyofjabfddy tmc edfbi mndc as stfedc.



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Jfgoctab jnonpndc f snurbc hnr tmc Mfywfrk edfbi mndc

Dcts bnosakcr tmc hnddnwaog fbtano

A:

6

68 k;x

g(U

D(H)) (65)

ao wmabm U as tmc Uabba sbfdfr fok

D (H) : 8

d5 6 + H

2/;

5 (62)

as tmc onodaocfr jfgoctab stcdk Dfgrfogafo kcosaty watmH :HH

tmc Jfxwcdd aovfrafot fok d fok twn bnostfotpnsatavc pfrfjctcrs. [mc jfgoctab stcdk twn hnrj as gavco ey

H: Psao5 kk (6;)

ao wmabm P as tmc jfgoctab jnonpndc bmfrgc. Dfttcr stcdk hnrjtngctmcr watm tmc daoc cdcjcot (x) ajpdy

H :5P5

r

; . (63)



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Caostcao stcdk cquftanos frc

G :[ (68)

ao wmabm

[ : 6

5

D ;HHDH

(67)

ao wmabmDH : DH. Noc bfo smnw tmft usaogD (H) gavco ao (x),tmc Caostcao cquftano fkjat tmc Mfywfrk rcgudfr edfbi mndc jctrabprnvakaog: 5P

5

(5jd5);/2. [mc wcfi stcdk dajat nh tmc Dfgrfogafo (x)

bfo ec hnuok ey cxpfokaog tmc Dfgrfogafo fenut H: 0 wmabm

rcfksD (H) : 8H

2/5

d52/5+

65H1/;

d51/; + N H2 . (6=)


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y g pp g



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Ao tmc scbnok pfrt nh tmc pfpcr wc usc tmc stfokfrk jctmnk nhjfiaog f tajcdaic tmao-smcdd wnrjmndc fok jfic f tajcdaictmao-smcdd dnbftck ft r:f (f?rm) ey but r4f hrnj tmc Mfywfrk

rcgudfr edfbi mndc fok pfst twn bnpy nh at ft r:f. No tmc smcddtmc spfbctajc as bmnsco tn ec

ks5 : k5 +f ()5

k5 + sao5 k5

(61)

ao wmabm as tmc prnpcr tajc no tmc smcdd.[n jfic f bnosastcot 5 + 6kajcosanofd tajcdaic smcdd watm tmctwn 2 + 6kajcosanofd wc mfvc tn hudstdd tmc Dfobzns bnokatanoswmabm frc tmc Caostfao cquftanos no tmc smcdd

Ila

YIZ la : =Rla (50)

ao wmabm Y]Z :]5 ]6 fok Ila as tmc cxtraosab burvfturc tcosnr aocfbm pfrt nh tmc tmao-smcdd fok I kcontcs atstrfbc. Rla astmc



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cocrgy jnjcotuj tcosnr no tmc smcdd subm tmft R : nrcocrgy kcosaty R :p:R

as tmc prcssurc kcosaty.

J.Mfdadsny, R.M.Jfzmfrajnusfva, F.Nvguo CJS[mao-Rmcdd Mfywfrk EM

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Ila as tmc cxtraosab burvfturc kcstock ey

I()al

:o()

5xal

+

x

a

x

l

r:f

(56)

watm tmc onrjfd uoat vcbtnr

o() : g h

x

h

x 6/5 h

x . (55)

frc hnuok fs hnddnws

ot:

gttf ()

t

5

+grr6/5

H

t

r:f

. (52)

Spno usaog

t

5

: 6

h (f) 6 + 6

h (f)f5 , (5;)


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at ajpdacsot: (f) . (53)

Rajadfrdy noc stoks tmft

or : gtt

H

t

H

t +grr

H

r

H

r

6/5 Hr

r:f

(58)

: h(f) + f5h (f) , fok oa : 0, hnr fdd a. (57)Ontc tmftI :[rfbc

Ila

fok Rla :kafg(,py, p) as tmc cocrgy

jnjcotuj tcosnr no tmc tmao-smcdd. [mc pfrfjctrab cquftano nh

tmc mypcrsurhfbc as gavco ey

h (x, f ()) :x f () : 0. (5=)

Fhtcr tmc uoat k

onrjfd, noc stoks tmc cxtraosabburvfturctcosnr


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bnjpnocots hrnj tmc kcstoatano

Ial :

o

5x

a

l +

x

a

x

l r:f

. (51)

At hnddnws tmft

I : ot5t

5+ t

x

x

r:f

or5r

5+ r

x

x

r:f

ot 5t5 + 5ttr t rr:f or 5

r5 + rttt t +

rrrr r

r:f

(20)

: h+ 5f5h + f5 , (26)

Fdsn

Iaa : o

5x

5a+

x

a

x

a

r:f

: h (f) + f5mm.

(25)J.Mfdadsny, R.M.Jfzmfrajnusfva, F.Nvguo CJS[mao-Rmcdd Mfywfrk EM

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fok tmcrchnrc

I: [rfbcIla: Iaa:

h+ 5fh + f

5+ ;h (f) + f5

m

m. (22)

[mc surhfbc cocrgy-jnjcotuj bnjpnocots nh tmc tmao-smcdd frc

Rla :

6

=

Ila

Ila

(2;)

wmabm yacdk

: R : 5

h (f) + f5m

m

, (23)

Ra

a :pa :

6

= h+ 5f

h(f) + f5 + 5h

(f

) + f5m

m. (28)

Noc bfo cxpdabatdy stok

: 65fh (f) + f5 (27)


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fok

p: 6

;

h (f) + f5

f +

f+h (f) /5

h(f) + f5. (2=)

Bnoscqucotdy tmc cocrgy fok prcssurc kcosatacs ao f stftabbnostgurftano ft f:f0 frc gavco ey

0

:

6

5f0h(f

0) (21)

fok

p0 : 6

;

h (f0)

f0+h (f0) /5

h(f0). (;0)

[n aovcstagftc tmc stfeadaty nh subm wnrjmndc wc fppdy f daocfrpurtcreftano ao wmabm fhtcr tmft tmc hnddnwaog stftc cquftano

p:() (;6)J.Mfdadsny, R.M.Jfzmfrajnusfva, F.Nvguo CJS[mao-Rmcdd Mfywfrk EM

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watm fo freatrfry cquftano () as hnddnwck ey tmc tmao smcdd. Aofkkatano tn tmas rcdftano ectwcco pfok tmc cocrgy bnoscrvftanodfw fdsn ajpnscs

Ral9l: 0 (;5)

wmabm ao bdnsck hnrj at fjnuots tn

Ral,l+R

ilail +Railil: 0 (;2)

nr cquavfdfotdy, fhtcr tmc daoc cdcjcot (x),

f5

+p

f5

: 0. (;;)

[mas cquftano bfo ec rcwrattco fs

f5 +X(f) : 0 (;3)

ao X(f) as gavco ey

X(f) :h

;5f55 (;8)


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fok as tmc cocrgy kcosaty fhtcr tmc pcrtureftano. Cq. (x) as f nockajcosanofd cquftano nh jntano ao wmabm tmc nsbaddftnry jntano hnrf ao tcrjs nh fenut f:f0 as tmc bnoscqucobc nh mfvaog f:f0

tmc cquadaerauj pnaot wmabm jcfos X (f0) : 0 fok X (f0) 0. Aotmc scqucd wc bnosakcr h6(f0) :h5(f0) fok tmcrchnrc ft f:f0,noc stoks X0 :X

0 : 0. [n aovcstagftc X

(f0) 0 wc usc tmcgavco p:() tn stoks

: kkf

: 5

f(+) (;7)

fok

: 5

f5(+) 2 + 5

. (;=)

Mcrcao : kk . Haofddy

X (f0) :h0 =5

(0+ 5p0)5 + 50(0+p0)

6 + 5 (0)

(;1)


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wmabm wc mfvc usck 0 :p0.


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Ucbcotdy twn nh us fofdyzck tmc cffcbt nh tmc Gfuss-Enooctpfrfjctcr ao tmc stfeadaty nh [RW ao magmcr kajcosanofd CGEgrfvaty . Ao tmft pfpcr snjc spcbastb jnkcd nh jfttcr mfs ecco

bnosakcrck subm fs DG, BG, GBG, JGBG fok DG. Ao tmas wnri wcgn bdnscdy tn tmc sfjc stftc huobtanos fok wc fofdyzc tmc cffcbt nhMfywfrks pfrfjctcr ao tmc stfeadaty nh tmc [RW bnostrubtckfenvc.



Daocfr gfs (DG)
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Daocfr gfs (DG)

Hagurc< Rtfeadaty nh [RW suppnrtck ey DG ao tcrjs nhf0 fok 0 hnr



Daocfr gfs (DG)
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Daocfr gfs (DG)

: 0.00, 0.60, 0.77 fok 0.10. [mc vfduc nhj: 6. [mc cffcbt nhMfywfrks bnostfot as tn aobrcfsc tmc stfeadaty nh tmc [RW. Wc ontc tmfttmc stfedc rcganos frc smnwo eyRfok tmc jctrab huobtano as pdnttck tnn.

Ao tmc bfsc nh f daocfr stftc huobtano a.c.,

:0( 0) +p0

ao wmabm 0 as f bnostfot pfrfjctcr, noc stoks (0) :0. Hag. 6kaspdfys tmc rcgano nh stfeadaty ao tcrjs nh0 fok f0 hnr kaffcrcotvfducs nh Mfywfrks pfrfjctcr.



Bmfpdygao gfs (BG)
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p yg g ( )

Hagurc< Rtfeadaty nh [RW suppnrtck ey BG ao tcrjs nhf0 fok 0 hnr



Bmfpdygao gfs (BG)
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p yg g ( )

: 0.00, 0.60, 0.77 fok 0.10. [mc vfduc nhj: 6. [mc cffcbt nhMfywfrks bnostfot as tn aobrcfsc tmc stfeadaty nh tmc [RW. Wc fdsn pdnttmc jctrab huobtano tn bnjpfrc tmc mnrazno nh tmc edfbi mndc fok tmc

dnbftano nh tmc tmrnft.

Hnr Bmfpdygao gfs (BG) tmc stftc huobtano as gavco ey

:0 6

6

0

+p0

wmcrc 0 as f bnostfot pfrfjctcr, ajpdacs (0) : 050 . Ao Hag. 5

wc pdnt tmc stfeadaty rcgano ao tcrjs nh0 fok f0 hnr kaffcrcotvfducs nh.



Gcocrfdazck Bmfpdygao gfs (GBG)
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Hagurc< Rtfeadaty nh [RW suppnrtck ey GBG ao tcrjs nhf0 fok hnr



Gcocrfdazck Bmfpdygao gfs (GBG)
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[mc stftc huobtano nh tmc Gcocrfdazck Bmfpdygao gfs bfo ec bfstaotn

() :0 6

6

0

+p

0

ao wmabmfok0 frc bnostfot. [n scc tmc cffcbt nh pfrfjctcr aotmc stfeadaty wc sct tmc bnostfot 0 subm tmft ecbnjcs

() :p00

.

Fhtcr wc hnuok (0) : p00 , ao Hag. 2 wc pdnt tmc stfeadatyrcganos nh tmc [RW suppnrtck ey f GBG ao tcrjs nh fok f0 watmvfranus vfducs nh.



Jnkastck Gcocrfdazck Bmfpdygao gfs (JGBG)
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Hagurc< Rtfeadaty nh [RW suppnrtck ey JGBG ao tcrjs nhf0 fok 0 hnr



Jnkastck Gcocrfdazck Bmfpdygao gfs (JGBG)
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: 0.00, 0.60, 0.77 fok 0.10. [mc vfduc nhj: 6 fok 0 :0 : 6. [mccffcbt nh Mfywfrks bnostfot as tn aobrcfsc tmc stfeadaty nh tmc [RW. Wcfdsn pdnt tmc jctrab huobtano tn bnjpfrc tmc mnrazno nh tmc edfbi mndc

fok tmc dnbftano nh tmc tmrnft.

F jnrc gcocrfdazck hnrj nh BG as bfddck tmc Jnkastck GcocrfdazckBmfpdygao gfs (JGBG) wmabm as gavco ey

() :0( 0) 0

6 6

0

+p0

ao wmabm 0, 0 fok frc hrcc pfrfjctcrs. Noc tmco, stoks

(0) :0+0

0

+60.

[n gn hurtmcr wc sct 0 : 6 fok : 6 fok ao Hag. ; wc smnw tmcstfeadaty rcganos ao tcrjs nhfok f0 watm vfranusvfducsnh.



Dngfratmjab gfs (DG)
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Hagurc< Rtfeadaty nh [RW suppnrtck ey DG ao tcrjs nhf0 fok 0 hnr



Dngfratmjab gfs (DG)
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Ao nur dfst cquftano nh stftc wc bnosakcr tmc Dngfratmjab gfs (DG)wmabm as gavco ey

() :0do 0 +p0

ao wmabm 0 as f bnostfot. Hnr DG noc stoks

(0) : 00

.

Ao Hag. 3 wc pdnt tmc stfeadaty rcgano hnr tmc [RW suppnrtck ey DGfok tmc cffcbt nh Mfywfrks pfrfjctcr as smnwo bdcfrdy.


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BnobdusanoWc mfvc stukack vfranus fspcbts nh tmao-smcddwnrjmndcs bnostrubtck hrnj tmc Mfywfrk rcgudfr edfbi mndc ao;-kajcosanofd spmcrabfd syjjctrab stftab spfbctajc watm tmc snurbc

nh onodaocfr jfgoctab jnonpndc stcdk. Ao f onodaocfr Jfgoctabstcdk. Wc mfvc pdnttck fok p hnr kaffcrcot vfducs nh pfrfjctcrsJ, V fok f : f0 tn smnw tmc prcscobc nh cxntab jfttcr bnostockwatmao tmc smcdd nh tmc wnrjmndc. [mc ofturc nh tmc wnrjmndc(fttrfbtavc fok rcpudsavc) mfs ecco aovcstagftck hnr stxck vfducs nh

pfrfjctcrs J fok V. [mc fjnuot nh cxntab jfttcr rcquarck tnsuppnrt tmc wnrjmndc as fdwfys f brubafd assuc. Wc mfvc smnwo tmcvfraftano nh cxntab jfttcr grfpmabfddy watm rcspcbt tn bmfrgc fokjfss.

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Thin-shell wormholes from the regular Haywardregular black hole Seminar