Black holes do not exist.

Abstract

We reconsider classical features of Schwarzschild and Kerr metrics, basis of the Black Hole model, through new space and time coordinates which transform the object into a space bridge linking two folds of the universe, PT symmetrical. In addition, such change gives a fast mass transfer through such spheroidal throat, one way membrane, which makes the black hole model questionable. Back to TOV model we assume that the physical criticity at r = 0,942 Rs, occuring before geometrical criticity, corresponds to real physics. We associate this to the fast establishment of a small space bridge between the two folds, through which matter in excess would be immediatly transfered, transformed into negative mass, and consquently spread away. So that such space bridge would correspond to an instant picture of a fast transient phenomenon, that would keep neutron stars’mass above 3 solar masses. The discussion is extended to so- called « Giant Black Holes ».

Full text

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!
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Black holes do not exist
Jean-Pierre Petit1
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Introduction$!
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The$topology$associated$to$the$Schwarzschild$solution!
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ρ
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Rs
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!!
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r)dt 2−2Rs
r
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θ
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θ
d
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2)
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!!
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δ
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ρ
Rs
⎡
⎣
⎢⎤
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δ
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d!
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ρ
1+Log ch
ρ
c2dt 2−2+Log ch
ρ
1+Log ch
ρ
th 2
ρ
d
ρ
2
+2
δ
c dt d
ρ
1+Log ch
ρ
−Rs
2( 1 +Log ch
ρ
)2(d
θ
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θ
d
ϕ
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δ
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(16)!
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Rs
−1 ) with
δ
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r)r2+2
δ
Rs
r
c dt d r −r2(d
θ
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ϕ
2)
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!
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d
ϕ
= ± dr
r2
λ
2−1
h2+Rs
h2r−1
r2+Rs
r3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!X"LY!
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!#!!
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dt =
λ
r−
δ ν
Rs
λ
2−1+Rs
r
c
ν
(r−Rs)
λ
2−1+Rs
r
dr
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!XNKY!
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!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
dt 
λ ν
c
r−
δ ν
Rs
(r−Rs)
dr
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!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
J=(R(+)+R(−))d4x
D4
∫
δ
J=0
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!XNNY!
-&40-=0+1!=*/!#!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
R(+)=−R(−)R
µν
(+)=R
µν
(−)=0
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!XNRY!
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F(+)
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!
The$fate$of$a$neutron$star$that$overcomes$its$limit$of$stabilityE!!
!
F=! 7+! '*5.%+! 4)+! +P4+/3&%! 6')7&/8-')0%1! 9+4/0'! -*%540*3! XeY! 4*! 4)+! =*%%*7032! 034+/3&%!
6')&/8-')0%1!9+4/0'!-*%540*3!#!
(24)
7+!2+4!&!2+*9+4/0'&%!/+./+-+34&40*3!*=!&!-.)+/+,!7)*-+!/&105-!0-!
r
n
,!=0%%+1!$D!'*3-4&34!
1+3-04D!
ρ
!9&4+/0&%!,!-5//*531+1!$D!A*01E!C)+!-4&$0%04D!'*31040*3!0-!#!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Rs=8
π
G
ρ
3c2r
n
3<r
n<3
8
π
G
ρ
=ˆ
R
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!XNdY!
!
'*//+-.*31032!4*!=025/+!NE!!
!

!
!
a!
!
!
Fig.2$:$Subcritical$neutron$star,$schematical!
!
F3!'*3-4&34!1+3-04D!2/*74)!4)+!47*!/&100!$+'*9+-!+G5&%!4*!4)+!/&105-!*=!4)+!-4&/,!-*!4)&4!
7+!)&A+!&!1*5$%+!2+*9+4/0'&%!'/040'04DE!6++!=025/+!RE!!
Fig.3 : Double geometrical criticity.
The famous TOV equation [6] gives the pressure versus radius in such object.
d p
dr
=−
ρ
+p
c2
⎛
⎝
⎜⎞
⎠
⎟m+4
π
G p r 3
c4
⎛
⎝
⎜⎞
⎠
⎟
r(r−2m)
=−
ρ
+p
c2
⎛
⎝
⎜⎞
⎠
⎟Rs
2
+4
π
G p r 3
c4
⎛
⎝
⎜⎞
⎠
⎟
r(r−Rs)
(26)
When integrating this differential equation, we get figure 4.

!
!
g!
Fig.4 : Physical criticity in a neutron star
For
r
n=0.9428 Rs
a physical criticity appears, before geometrical criticity. Classically one
considers the two values as just quite close. If we assume this is physics, it means that
something happens in the center of the star when this physical critical condition is reached. In
former papers we developped the concept of joints variations for the so-called constants of
physics ( [7], [8], [9] ). Then such very important increase of pressure would go with the
increase of c to infinite and create a bridge between the two sectors, the one for positive
energy and mass particles, the other for negative energy and mass particles. The challenging
decoding of Schwarzschild metric would then correspond to some instant picture of a fast
process, to be built from the set of field equations introduced in [10].
A control mechanism for neutron stars’masses.
The universe contains a very large number of objects, at distance, of even in our galaxy.
When some theoretician predicts the existence of some object, if he is right, it will be
discovered late or soon. As an example Fritz Zwicky predicted the phenomenon of supernova
in 1931. He observed the first in 1937, then he found one more four months later. Three years
after he had evidenced 12. Now we have thousands. Same thing for neutron stars, exo-planets.
The existence of black hole was conjectured in 1963, when Kerr built his axisymmetrical
metric solution. Half century have passed, and we have very few stellar black holes
candidates. In fact, they are more black holes in poplar journals that in the sky. A control
mechanism for neutron stars could justify such absence. According to this model, when a

!
!
L!
neutron star receives matter from a companion star, and get a pressure jump at its center, a
small space bridge opens there. Matter flows in at large density and relativistic density. The
sign of such mass is inverted, so that it escapes the star. It does not any longer interfer with
this dense material for matters with opposite signs only interact through gravitational force.
Subsidiarily it becomes invisible to our eyes and telescopes. Then the mass of neutron stars
should be limited to 3 solar masses, instead 3.3 .
What about « giant black holes » ?
h+&-5/+9+34-!*=!A+%*'040+-!*=!=&-4!-4&/-,!*/$04032!'%*-+!4*!4)+!'+34+/!*=!2&%&P0+-!0310'&4+!
4)&4!!*$@+'4-!7)*-+!9&--+-!7*5%1!/&32+!$+47++3!"Ka! &31!"KL!-*%&/!9&--+-!-)*5%1!$+!
%*'&4+1!4)+/+!j"RkE!C)+!-'0+340=0'!'*995304D!1+'01+1!4*!'&%%!04!T!20&34!$%&'(!)*%+-!VE!>54!
&/+!4)+D!$%&'(!)*%+-!l!?*7!1*!4)+D!=*/9!l!F!)&A+!-522+-4+1!&!-'+3&/0*!03!j""kE!^/*9!9D!
.*034! *=! A0+7,! 4)+! 530A+/-+! 0-! =0%%+1! $D! .*-040A+! &31! 3+2&40A+! 9&--+-E! F3! "Lda! ?E>*310!
j"Nk! -)*7+1! 4)&4! 4)0-! '*)&$04&40*3! 7&-! 09.*--0$%+,! 15+! 4*! 4)+! ./+.*-4+/*5-! /53&7&D!
.)+3*9+3*3E! F=! 4)+! 530A+/-+! 0-! '*3-01+/+1! &-! &! hM! 9&30=*%1! 704)! &! -032%+! 9+4/0',!
-*%540*3! *=! f03-4+03Q-! +G5&40*3,! &31! 0=! 47*! 9&--+-! 704)! *..*-04+! -023-! +3'*534+/! 4)+!
.*-040A+!*3+!+-'&.+-!7)0%+!4)+!3+2&40A+!*3+!/53-!&=4+/!04E!C)0-!'*//+-.*31-!4*!4)+!&%%+2+1!
T!/53&7&D!.)+3*9+3*3!VE!6)0=4032! 4*!&!$09+4/0'!/+./+-+34&40*3!Xjgk,!jLk,!j"Kk! Y!7+!=031!
10==+/+34! 4)+! 2/&A04&40*3&%! 034+/&'40*3! %&7-#! 9&--+-! 704)! -&9+! -023-! 9545&%%D! &44/&'4,!
4)/*52)!`+74*3Q-!%&7E!h&--+-!704)!*..*-04+!-023-!9545&%%D!/+.+%!4)/*52)!&340S`+74*3Q-!
%&7E! C)0-! 9*1+%! =5%%D! ')&%%+32+-! 4)+! 1&/(! 9&44+/! 9*1+%E! i*034! 2/&A04&40*3&%! 03-4&$0%04D!
+P.%&03-! I]6,! 2&%&P0+-Q! '*3=03+9+34,! =%&43+--! *=! 4)+0/! /*4&40*3! '5/A+-! &31! %&/2+!
2/&A04&40*3+%!%+3-!+==+'4-,!9&03%D!09.54+1!4*!3+2&40A+!%+3-032!jgkE!!H3!'*-9*%*20'&%!-'&%+-!
04!+P.%&03-!4)+!*$-+/A+1!&''+%+/&40*3!*=!4)+!530A+/-+,!704)*54!3++1!4*!9D-4+/0*5-!T!1&/(!
+3+/2D!VE!!
W*5.%+1! =0+%1! +G5&40*3-! -D-4+9! 9&D! ./*15'+! @*034! 9+4/0'! *-'0%%&40*3-! 15/032! 4)+!
+P.&3-0*3!./*'+--E!F4!7*5%1! 9*10=D!4)+!-4/+32)4!*=! 4)+!'*3=03+9+34!*=!2&%&P0+-,!15+! 4*!
4)+0/! +3A0/*39+34! *=! 03A0-0$%+! 3+2&40A+! 9&--E! F=! 95')! 7+&(+3+1,! 4)+! '*3=03+9+34!
$+'*9+-! 3*! %*32+/! +3-5/+1! &31! 7+! 2+4! 0//+25%&/! 2&%&P0+-E! F=! -4/*32%D! /+03=*/'+1! 04!
'/+&4+-!&3!&335%&/!1+3-04D! 7&A+! 7)0')! =*'5-! 4*7&/1-! 4)+! '+34+/! *=! 4)+! 2&%&PDE! >D! 4)+!
7&D,!4)+!1+3-04D!7&A+!4/022+/-!D*532!-4&/-Q!$0/4)E!C)+D!0*308+!4)+!2&-!&31!'/+&4+!)02)!
9&23+40'!O+D3*%1-!359$+/!'*31040*3-,!-*!4)&4!4)+!/032!'*%%+'4-!4)+!9&23+40'!%023+-!&-!&!
.+&-&34!2&4)+/-!'*/3!+&/-E!C)0-!/+03=*/'+-!4)+!9&23+40'!=0+%1E!<)+3!4)+!/032!/+&')+-!4)+!
'+34+/,!04!=*/9-!&!$&%%!*=!)*4!2&-! 03!7)0')!]&7-*3!'*31040*3-!*''5/-!03!4)+!$5%(E!^5-0*3!
1+$/0-! &/+! +@+'4+1! &%*32! 47*! 10&9+4/&%%D! *..*-04+! %*$+-E! <+! 2+4! &! m6HE! C)+! 9&23+40'!
=0+%1!2/&10+34!&'4-!&-! &! 3&45/&%!.&/40'%+!&''+%+/&4*/!&31!4)+! *$@+'4!0-!4)+!-*5/'+!*=! )02)!
+3+/2D!.&/40'%+-,!'*-90'!/&D-E!!
6*=4! ./*'+--! 7*5%1! '&5-+! 2&-! %*--,! 0=! 4)+! '*3=03+9+34! 0-! 7+&(%D! /+15'+1E! 6*=4!
/+03=*/'+9+34!7*5%1!-+31!2&-!4*!4)+!'+34+/!*=!4)+!2&%&PD,!&4!9*1+/&4+!A+%*'04DE!C)0-!2&-!
7*5%1E! C)+! 9&--! '*34/*%! 9+')&30-9! +A*(+1! &$*A+! 7*5%1! %0904! 04-! 2/*74)! &31! 7*5%1!
.%&'+!04!03!-5$S'/040'&%! '*3=025/&40*3!
R≤0.942 Rs
E!F=!-*9+!9&44+/! 7*5%1!.&--!$D,!7)+3!
'&.45/+1,!04-!+%+'4/*3-,!&''+%+/&4+1,!7*5%1!+904!/&10&40*3,!nS/&D-!E!>54!4)+!7&A+%+324)!*=!
4)+!/&10&40*3! +9044+1! $D! 4)+! *$@+'4! 7*5%1! $+!2/+&4%D! +3%&2+1! $D! 2/&A04&40*3&%! /+1-)0=4!
+==+'4E!!
H3! &3*4)+/! )&31,! -5')! -5.+/9&--0A+! *$@+'4-! 9&D! )&A+! $++3! =*/9+1! A+/D! +&/%D! $D!
2/&A04&40*3&%! 03-4&$0%04D,! &4! 4)+! A+/D! $+203032! *=! 4)+! %0=+! *=! 2&%&P0+-E! c''*/1032! 4*! 4)+!
'%&--0'&%!4)+*/D!4)&4!7*5%1!20A+!20&34!$%&'(!)*%+-E!W*3-01+/032!4)0-!3+7!.*034!*=!A0+7!04!

!
!
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7*5%1!20A+!-5$S'/040'&%!*$@+'4-,!15+!4*!4)+!+A*(+1!9&--!'*34/*%!./*'+--E!!
Conclusion$
!
64&/4032! =/*9! 4)+! 9*1+%! *=! $%&'(! )*%+,! $&-+1! *3! 6')7&/8-')0%1! &31! :+//! 9+4/0'-! 7+!
034/*15'+!47*!-5''+--0A+!')&32+-!*=!'**/103&4+-E!C)+!=0/-4!/+A+&%-!4)+! 4/5+! 531+/%D032!
4*.*%*2D! *=! 4)0-! =*5/! 109+3-0*3&%! )D.+/-5/=&'+,! +%0903&4032! -0325%&/04D,! -)*7032! 4)&4!
4)0-!%&-4!'*9+-!=/*9!&!7/*32!')*0'+!*=!-.&'+!'**/103&4+!&31!0-!3*4!&3!034/03-0'!&44/0$54+E!!
!
C)+!)*/08*3,!0-!-40%%!&!*3+S7&D!9+9$/&3+!7)0')!$+'*9+-!4)+!901!.&/4!*=!&!-.&'+!$/012+!
%03(032! 4)+! 47*! WBC! -D99+4/0'&%! h03(*7-(0&3! -+'4*/-! *=! &! $09+4/0'! -4/5'45/+E! <)+3!
4/+-.&--032,!9&44+/!2+4-!3+2&40A+!9&--E!!
!
c!-+'*31!')&32+!*=!409+S9&/(+/,!03-.0/+1!$D!4)+!*3+!034/*15'+1!$D!f110324*3!(++.-!4)+!
9+4/0'!]*/+3480&3!&4!03=0304+E!C*!4)+!&80954&%!:+//Q-!=/&9+S1/&22032!+==+'4!04!&11-!/&10&%!
=/&9+S1/&22032E! C)+! =/++! =&%%! 409+! *=! &! 4+-4! .&/40'%+! 4*7&/1-! 4)+! 6')7&/8-')0%1! 4)/*&4!
-.)+/+!$+'*9+!=0304+,!7)0')!9&(+-!4)+!$%&'(!)*%+!9*1+%!G5+-40*3&$%+E!E!!
!
C)+! CHI! 9*1+%! ./+10'4-! 4)&4! 7)+3! 4)+! /&105-! *=! &! 3+54/*3! -4&/! /+&')+-! KELMN! O-! 4)+!
./+--5/+!&4!4)+!'+34/+!$+'*9+-!03=0304+E!<+!&--59+!04!'*//+-.*31-!4*!&!.)D-0'&%!'/040'04D,!
7)0')!7*5%1!&..+&/-!before!2+*9+4/0'&%!'/040'04D!&31!./+A+34!4)+!$0/4)!*=!&!-0325%&/04DE!
<+! '*3@+'45/+! 4)&4! 4)0-! ./+--5/+! /0-+! 2*+-! 704)! &! /0-+! *=! 4)+! %*'&%! -.++1! *=! %02)4! 4*!
03=0304D! &31! '&5-+! &! 2+*9+4/0'&%! -5/2+/D! 7)0')! 9*10=0+-,! 15/032! &! -)*/4! 409+! 4)+!
2+*1+-0'!1+-023!704)! %*'&%!9&--!03A+/-0*3!./*'+--E! C)0-!G5+-40*3-!$%&'(!)*%+! 9*1+%,!&-!
/+'+34%D!1*3+!$D!6E!?&7(032![14]E!!
!
C)0-!9+')&30-9!7*5%1!%0904!4)+!3+54/*3!-4&/Q-!9&--!4*!R!-*%&/!9&--+-E!<+!-522+-4!4)&4!
-090%&/!9+')&30-9!'*5%1!4&(+!.%&'+!&4!4)+!'+34+/!*=!2&%&P0+-!&31!1/&03032!*==!&%%!9&44+/!
03!+P'+--,!4/&3-=*/9032!04!034*!3+2&40A+!9&--!&31!./+A+34032!4)+!$0/4)!*=!&!-0325%&/04DE!E!
!
References$
$
j"k! :E! 6')7&/8-')0%1! ! T!o$+/! 1&-! U/&A04&40*3&%! +03+-! h&--+3.53(4+-! 3&')! 1+/!
f03-4+03+-')+3!C)+*/D!V!6048$+/E!B/+5--E!c(&1E!<0--E!>+/%03,!.E"gLS"Le!X"L"eY!
!
jNk!OE!BE!:+//,!!T!U/&A04&40*3&%!^0+%1!*=!&!6.033032!h&--!&-!&3!fP&9.%+! *=! c%2+$/&0'&%%D!
6.+'0&%!h+4/0'-$»$!B)D-E!O+AE!]+4E!"",!NRaSNRg!X"LeRY!
!
jRk!cE6&()&/*A,!T!WB!A0*%&40*3!&31!$&/D*30'!&-D99+4/D!*=!4)+!p30A+/-+!V!q)fC^!B0-r9&!d!
#!RNSRd!X"LeaY!s!C/&15'40*3!ifCB!]+44E!d!#!NMSNa!X"LeaY!!
!
jMk! cE! 6E! f110324*3,! T!c! '*9.&/08*3! *=! <04)+)+&1r-! &31! f-03-4+03r-! =*/95%t!V! `&45/+!
113!#!"LN!X"LNMY!!
!
jdk!iEhE! 6*5/0&5,! T!64/5'45/+! *=! 1D3&90'&%! -D-4+9-!V! >0/()&5-+/! f1E! X"LLgY!&31! _53*1!

!
!
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f1E!X"LaMY!
!
jek!iEOE!H..+3)+09+/!&31!?E63D1+/,!uH3!'*34035+1!U/&A04&40*3&%!W*34/&'40*3v!B)D-E!O+AE!
56,!Mdd!X"LRLY!
!
jak! iEBEB+404,! T!c3! 034+/./+4&40*3! *=! '*-9*%*20'&%! 9*1+%! 704)! A&/0&$%+! %02)4! A+%*'04D!V!
h*1+/3!B)D-0'-!]+44+/-!c,!I*%E!R,!3w"e,!.E"dNa!X"LggY!
!
jgk! iEBEB+404,! T!C703! p30A+/-+! '*-9*%*2D!V! c-4/*3*9D! &31! 6.&'+! 6'0+3'+,! NNe! ..E! NaRS
RKa!X"LLdY!
!
jLk!iEBE!B+404,! BEh01D!x!^E]&31-)+&4!T!C703!9&44+/!&2&03-4!1&/(! 9&44+/E!F34+/3E!h++4E!*3!
c4/*.)D-E!&31!W*-9E!y<)+/+!0-!4)+!9&44+/!l!y!V!h&/-+0%%+!i53+!NdSNL!XNKK"Y!
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j"Kk! ! iEBEB+404,! T!C)+! 90--032! 9&-! ./*$%+9!V! F%! `5*A*! W09+34*! >,! I*%E! "KL! ! .EeLaSa"K!!
X"LLMY!
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j""k!!iEBEB+404,!T!H3!&!.+/15!%&!9*040z!1+!%Qp30A+/-!V!f1E!c%$03!h0')+%!X"LLaY!
!
j"Nk!?E>*310,!T!`+2&40A+!9&--!03!U+3+/&%!O+%&40A04D!V!O+AE!*=!h*1E!B)D-E!NL!3wR!X"LdaY!
!
j"Rk!6'){1+%!O!+4!&%E!c31!#!c!-4&/!03!&!"dEN!*/$04!&/*531!&!-5.+/9&--0A+!$%&'(!)*%+!&4!4)+!
'+34/+!*=!4)+!h0%(D!<&D,!`&45/+,!M"L,!"a!*'4E!eLMSeLe!XNKKNY!
!
j"Mk! 6E?&7(032!#! F3=*/9&40*3! B/+-+/A&40*3! &31! <+&4)+/! ^*/+'&-4032! =*/! >%&'(! ?*%+-E!
&/n0A!#!"MK"Edae"!XNN!@&3E!NK"MY!
!
$$
Annex$:$Didactic$model$
F4!'&3!$+!5-+=5%!4*!20A+!-*9+!09&2+-!*=!4)+!./*'+--E!!
Fig.5 : The two surfaces figures the gravitational potential, « in mirror ».

!
!
"N!
Fig. 6 : Stellar wind brings matter
Fig.7 : Matter in excess is evacuated. Its mass is inverted
and it spreads away.
Fig.8 : Stand by in sub-critical conditions
!
!