N-spheres: regular black holes without apparent horizons, static wormholes with event horizons and gravastars with a tube-like core

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N-spheres regular black holes without apparent
horizons, static wormholeswith event horizons
and gravastars with a tube-like core

• O. B. Zaslavskii,Department of Mechanics and
  Mathematics, Kharkov V. N. Karazin National
  University

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Alternative under BH horizon - singular or
regular centre?
Third option tube like geometry, everywhere
regular
Regular BH classical model of
elementary particle Lorentz electron
Outside black hole. Inside tube-like core
Poincare-Lorentz electron
Pure electromagnetic forces
Exterior Reissner-Nordström (RN).
Interior Bertotti-Robinson (BR) metric
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Matching 2 regions to replace bad siingular
inner region by good one Appearance of surface
stresses shell at
is Lanczos tensor.
BR metric
a)
extremal limit of non-extremal RN BH (O. .Z., PRL
1996, PRD 1997)
b)
no horizon
Smooth gluing m(outside)m(inside)
c)
extremal
q (outside)q(inside)
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For smooth gluing is impossible
but becomes possible in horizon liomit in case
c) only , RN is extremal BR as limiting form of
RN throat
In horizon limit no bare sources. Wheelers idea
mass without mass, charge without charge
Mass defect for external observer me (extremal
RN)
Proper mass
Classical analogue of electron in GR extremal
charged black hole with infinitely long tube
inside
(O. Z. PRD 2004)
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Geometry
sphere of constant radius
R-region
N-region
T-region
Generalization of RN BR gluing
inside
For an external observer object of finite areal
radius and ADM mass Inside tube of constant
radius and infinite proper mass
N sphere (cf. T sphere, Ruban, 1969)
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Behavior of surface stresses.
It follows from 00 and 11 Einstein equations for
inner (-) region that
And 22 equation gives us
Vacuum-like
1)
a)
c)
b)
2)
3)
a)
or
Examples. 1) with
BR, 2) with
Nariai
3) string dust
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Goal smooth gluing (at least, asymtotically)
1. Exterior black hole
Non-extremal. Types of guing 1a, 2, 3a. Then in
limit
Extremal. 1b
2. Wormholes

• Non-traversable, horizon BH N-region BH, BH
  BH
• Horizon non-extremal or extremal
• Even not-traversable WH safe for one-way travel

b) Traversable. N-region WH. Type 1c
3. No horizon. Gravastars. Types 1c, 3b
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Some properties
Example. Case 3a 2D Rindler x sphere rconst
Usually Rindler coordinates
Minlowski infinity
Now rconst, 2D infinity has nothing to do with
r-infinity, an observer at r-infinity cannot
see what happen inside shell
Event (acceleration) hotizon without apparent
horizon
Black hole trapped region. Wormhole
antitrapped Now rconst in both directions,
intermediate case
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Summary

• Composite objects interpolating between BH and
  gravastars horizon in the limit. Event horizons
  without apparent ones.
• N-gravastar with infinite tube-like core.
• Not-traversable and traversable wormholes with
  tube inside.
• Mass defect finite ADM mass but infinite proper
  mass.
• Geometry N2xS2, where N22D Rindler (p0), AdS
  (plt0) or dS (pgt0).
• Quantum backreaction retains general form of
  metric.
• Black holes with regular core, mass without mass,
  classical model of elementary particle