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{{short description|Hypothesized alternative to black hole}}
In [[astrophysics]], the '''Gravastar''' theory is a proposal by [[Emil Mottola]] and [[Pawel Mazur]] to replace the [[black hole]]. Instead of a [[star]] collapsing into a pinpoint of [[space]] with virtually infinite [[density]], the gravastar theory proposes that as an object gravitationally collapses, space itself undergoes a [[phase transition]] preventing further collapse, being transformed into a spherical void surrounded by a form of super-dense [[matter]].
A '''gravastar''' is an object hypothesized in [[astrophysics]] by [[Pawel O. Mazur]] and [[Emil Mottola]] as an alternative to the [[black hole]] theory. It has usual black hole metric outside of the horizon, but [[de Sitter metric]] inside. On the [[Horizon (general relativity)|horizon]] there is a thin shell of matter. The term "gravastar" is a [[portmanteau]] of the words "gravitational vacuum star".<ref name="notblackholes">. This solution of Einstein equations is stable and has no singularities.
{{cite web
|url=http://www.lanl.gov/news/releases/archive/02-035.shtml
|archive-url=https://web.archive.org/web/20061213095149/http://www.lanl.gov/news/releases/archive/02-035.shtml
|archive-date=13 December 2006
|title=Los Alamos researcher says 'black holes' aren't holes at all
|publisher=[[Los Alamos National Laboratory]]
|access-date=10 April 2014
}}
</ref> Further theoretical considerations of gravastars include the notion of a nestar (a second gravastar ''nested'' within the first one).<ref name="SA-20240220">{{cite news |last=McRae |first=Mike |title=Bubble-Like 'Stars Within Stars' Could Explain Black Hole Weirdness |url=https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |date=20 February 2024 |work=[[ScienceAlert]] |url-status=live |archiveurl=https://archive.today/20240220150012/https://www.sciencealert.com/bubble-like-stars-within-stars-could-explain-black-hole-weirdness |archivedate=20 February 2024 |accessdate=20 February 2024 }}</ref><ref>{{cite journal |last1=Jampolski |first1=Daniel |last2=Rezzolla |first2=Luciano |date=2024-02-15 |title=Nested solutions of gravitational condensate stars |journal=Classical and Quantum Gravity |volume=41 |issue=6 |page=065014 |doi=10.1088/1361-6382/ad2317 |arxiv=2310.13946 |bibcode=2024CQGra..41f5014J |s2cid=264426808 |url=https://iopscience.iop.org/article/10.1088/1361-6382/ad2317}}</ref>


== Structure ==
The theory is a newcomer to the field which has generated little interest among astrophysicists. It was the topic of a conference proceeding, but has not been the topic of any scientific paper. The lack of interest comes from the fact that the concept requires one to accept a very speculative theory of [[quantum gravity]] yet provides no real benefit over black holes. Furthermore, there is no theoretical reason from quantum gravity that space should behave in the way that Mottola and Mazur assume.
In the original formulation by Mazur and Mottola,<ref>{{cite journal |last1=Mazur |first1=Pawel O. |last2=Mottola |first2=Emil |title=Gravitational Condensate Stars: An Alternative to Black Holes |journal=Universe |year=2023 |volume=9 |issue=2 |page=88 |doi=10.3390/universe9020088 |arxiv=gr-qc/0109035 |bibcode=2023Univ....9...88M |doi-access=free }}</ref> gravastars contain a central region featuring a {{nowrap|{{math| ''p'' {{=}} −''ρ''}} }}{{Technical inline|date=March 2024}} (where p is pressure and ρ is energy density), and false vacuum or "dark energy", a thin shell of {{nowrap|{{math| ''p'' {{=}} ''ρ''}} }} perfect fluid, and a true vacuum {{nowrap|{{math| ''p'' {{=}} ''ρ'' {{=}} 0}} }} exterior. The dark energy-like behavior of the inner region prevents collapse to a singularity and the presence of the thin shell prevents the formation of an event horizon, avoiding the infinite blue-shift. The inner region has thermodynamically no [[entropy (thermodynamics)|entropy]] and may be thought of as a gravitational [[Bose–Einstein condensate]]. Severe red-shifting of photons as they climb out of the gravity well would make the fluid shell also seem very cold, almost absolute zero.


In addition to the original thin shell formulation, gravastars with continuous pressure have been proposed. These objects must contain anisotropic stress.<ref>{{cite journal |last1=Cattoen |first=Celine |last2=Faber |first2=Tristan |last3=Visser |first3=Matt |date=2005-09-25 |title=Gravastars must have anisotropic pressures |journal=Classical and Quantum Gravity |volume=22 |number=20 |pages=4189–4202 |doi=10.1088/0264-9381/22/20/002 |bibcode=2005CQGra..22.4189C |arxiv=gr-qc/0505137|s2cid=10023130 }}</ref>
The gravastar's name origin is simply: GRAvitational VAcuum STAR.


Externally, a gravastar appears similar to a black hole: It is visible by the high-energy radiation it emits while consuming matter, and by the [[Hawking radiation]] it creates.{{citation needed|date=December 2017}} Astronomers search the sky for [[X-ray]]s emitted by infalling matter to detect black holes. A gravastar would produce an identical signature. It is also possible, if the thin shell is transparent to radiation, that gravastars may be distinguished from ordinary black holes by different [[gravitational lensing]] properties as null geodesics may pass through.<ref>{{cite journal |last1=Sakai |first1=Nobuyuki |last2=Saida |first2=Hiromi |last3=Tamaki |first3=Takashi |date=2014-11-17 |title=Gravastar shadows |journal=Phys. Rev. D |volume=90 |issue=10 |page=104013 |doi=10.1103/physrevd.90.104013 |arxiv=1408.6929 |bibcode=2014PhRvD..90j4013S|s2cid=119102542 }}</ref>
Mottola and Mazur have suggested that gravastars would be the solution for the [[black hole information paradox]]: the tremendous amounts of [[entropy]] that a black hole is said to have (a black hole apparently has a [[billion]], billion times more entropy than the star it formed from) cannot yet be explained; there does not seem to be anywhere inside a black hole where such entropy would exist. The Gravastar is theorized to have very low amounts of entropy, thereby eliminating the need to answer the question.


Mazur and Mottola suggest that the violent creation of a gravastar might be an explanation for the origin of our [[universe]] and many other universes, because all the matter from a collapsing star would implode "through" the central hole and explode into a new dimension and expand forever, which would be consistent with the current theories regarding the [[Big Bang]].<ref>{{cite news |first=Marcus |last=Chown |date=7 June 2006 |title=Is space-time actually a superfluid? |magazine=[[New Scientist]] |language=en-US |url=https://www.newscientist.com/article/mg19025551-000-is-space-time-actually-a-superfluid/ |access-date=2017-11-04 |url-access=subscription |url-status=live |archive-url=https://web.archive.org/web/20160412232613/https://www.newscientist.com/article/mg19025551-000-is-space-time-actually-a-superfluid/ |archive-date=2016-04-12 |quote="It’s the big bang," says Mazur. "Effectively, we are inside a gravastar."}} {{cite web |title=alternative URL |website=bibliotecapleyades.net |url=https://www.bibliotecapleyades.net/ciencia/time_travel/esp_ciencia_timetravel12.htm}}</ref> This "new dimension" exerts an outward pressure on the Bose–Einstein condensate layer and prevents it from collapsing further.
The violent creation of a gravastar might be an alternate explanation for [[gamma ray burst]]s, adding yet one more speculative possibility to the dozens if not hundreds of ideas that have been proposed as the cause of GRB's.


Gravastars also could provide a mechanism for describing how [[dark energy]] accelerates the [[expansion of the universe]]. One possible hypothesis uses Hawking radiation as a means to exchange energy between the "parent" universe and the "child" universe, and so cause the rate of expansion to accelerate, but this area is under much speculation.{{citation needed|date=December 2017}}
However, the consensus among astrophysicists is that there are much less radical and speculative ways of resolving both issues.


Gravastar formation may provide an alternative explanation for sudden and intense [[gamma-ray burst]]s throughout space.{{citation needed|date=December 2017}}
A problem with the theory over the creation of a gravastar is whether or not a star would be capable of shedding enough entropy upon implosion.


LIGO's observations of gravitational waves from colliding objects have been found either to not be consistent with the gravastar concept,<ref>{{cite journal |last1=Chirenti |first1=Cecilia |last2=Rezzolla |first2=Luciano |date=2016-10-11 |title=Did GW150914 produce a rotating gravastar? |journal=Physical Review D |volume=94 |issue=8 |page=084016 |doi=10.1103/PhysRevD.94.084016 |arxiv=1602.08759 |bibcode=2016PhRvD..94h4016C |s2cid=16097346 |url=https://link.aps.org/doi/10.1103/PhysRevD.94.084016 |quote=We conclude it is not possible to model the measured ringdown of GW150914 as due to a rotating gravastar.}}</ref><ref>{{Cite news |title=Did LIGO detect black holes or gravastars? |date=October 19, 2016 |website=[[ScienceDaily]] |url=https://www.sciencedaily.com/releases/2016/10/161019082757.htm |access-date=2017-11-04 |language=en}}</ref><ref>{{cite news |title=LIGO's black hole detection survives the gravastar test |date=2016-10-26 |website=Extreme Tech |url=https://www.extremetech.com/extreme/237917-ligos-black-hole-detection-survives-the-gravatstar-test |access-date=2017-11-04 |language=en-US}}</ref> or to be indistinguishable from ordinary black holes.<ref>{{cite news |title=Was gravitational wave signal from a gravastar, not black holes? |date=2016-05-04 |magazine=New Scientist |url=https://www.newscientist.com/article/mg23030724-100-was-gravitational-wave-signal-from-a-gravastar-not-black-holes/ |access-date=2017-11-04 |language=en-US |quote=Our signal is consistent with both the formation of a black hole and a horizonless object – we just can’t tell.}}</ref><ref>{{cite journal |last1=Cardoso |first1=Vitor |last2=Franzin |first2=Edgardo |last3=Pani |first3=Paolo |date=2016-04-27 |title=Is the gravitational-wave ringdown a probe of the event horizon? |journal=Physical Review Letters |volume=116 |issue=17 |page=171101 |doi=10.1103/PhysRevLett.116.171101 |issn=0031-9007 |arxiv=1602.07309 |bibcode=2016PhRvL.116q1101C |pmid=27176511|s2cid=206273829 }}</ref>
Externally, a gravastar appears similar to a black hole: it is visible only by the high-energy emissions it creates while consuming matter. Astronomers observe the sky for [[X-ray]]s emitted by infalling matter to detect black holes, and a gravastar would produce an identical signature.


==In comparison with black holes==
Inside a gravastar, space-time would be "totally warped" by the extreme conditions there and the inner space would exert an outward force, like [[dark energy]]. Around this void would be a "[[bubble]]" of incredibly dense and durable matter. The phase of this matter is theorized to be similar to an extreme form of [[Bose-Einstein condensate]] in which all matter ([[protons]], [[neutrons]], [[electrons]], etc.) goes into what is called a [[quantum state]] creating a "super-atom".
By taking quantum physics into account, the gravastar hypothesis attempts to resolve contradictions caused by conventional [[black hole]] theories.<ref>
{{cite news
|url=http://edition.cnn.com/2002/TECH/space/01/22/gravastars/index.html
|title= Is black hole theory full of hot air?
|date= 22 January 2002
|publisher=[[CNN.com]]
|access-date=10 April 2014
|last=Stenger
|first=Richard
}}
</ref>


===Event horizons===
According to the theorizers [[Emil Mottola]] and [[Pawel Mazur]] the [[universe]] itself could very well be the inside of a giant gravastar.
In a gravastar, the [[event horizon]] is not present. The layer of positive pressure fluid would lie just outside the 'event horizon', being prevented from complete collapse by the inner false vacuum.<ref name="notblackholes"/> Due to the absence of an event horizon the time coordinate of the exterior vacuum geometry is everywhere valid.


===Dynamic stability of gravastars===
Another alternative to the gravastar is the [[Dark-energy star]]. In [[April 2005]], [[George Chapline]], a physicist at the Lawrence Livermore National Laboratory in California, claimed that "It's a near certainty that black holes don't exist." Chapline argued that a massive star doesn't simply collapse to form a black hole; instead, its space-time fills with [[dark energy]]. The extremely powerful surface gravity of the proposed [[dark-energy star]] would be like that of a black hole's, however, the dark energy may cause matter to eventually "bounce back."
In 2007, theoretical work indicated that under certain conditions gravastars as well as other alternative black hole models are not stable when they rotate.<ref>{{cite journal |arxiv=0709.0532 |author1=Vitor Cardoso |author2=Paolo Pani |author3=Mariano Cadoni |author4=Marco Cavaglia |title=Ergoregion instability of ultra-compact astrophysical objects |year=2008 |doi=10.1103/PhysRevD.77.124044 |volume=77 |issue=12 |journal=Physical Review D |page=124044 |bibcode= 2008PhRvD..77l4044C |s2cid=119119838 }}</ref> Theoretical work has also shown that certain rotating gravastars are stable assuming certain angular velocities, shell thicknesses, and compactnesses. It is also possible that some gravastars which are mathematically unstable may be physically stable over cosmological timescales.<ref>{{cite journal |last=Chirenti |first=Cecilia |author2=Rezzolla, Luciano |title=Ergoregion instability in rotating gravastars |journal=Physical Review D |date=October 2008 |volume=78 |issue=8 |page=084011 |doi=10.1103/PhysRevD.78.084011 |arxiv=0808.4080 |bibcode=2008PhRvD..78h4011C |s2cid=34564980 |url=http://pubman.mpdl.mpg.de/pubman/item/escidoc:52853:2/component/escidoc:52854/PRD78-084011.pdf |access-date=10 April 2014 |archive-url=https://web.archive.org/web/20160304040157/http://pubman.mpdl.mpg.de/pubman/item/escidoc:52853:2/component/escidoc:52854/PRD78-084011.pdf |archive-date=4 March 2016 |url-status=dead }}</ref> Theoretical support for the feasibility of gravastars does not exclude the existence of black holes as shown in other theoretical studies.<ref>{{cite journal |arxiv=0803.4200 |author1=Rocha |author2=Miguelote |author3=Chan |author4=da Silva |author5=Santos |author6=Anzhong Wang |title=Bounded excursion stable gravastars and black holes |journal=Journal of Cosmology and Astroparticle Physics |date=2008|volume=2008 |issue=6 |page=025 |doi=10.1088/1475-7516/2008/06/025 |bibcode=2008JCAP...06..025R |s2cid=118669175 }}</ref>
<!-- TODO: talk about entropy -->

==See also==
* [[Acoustic metric]]
* [[Acoustic Hawking radiation]] from [[sonic black hole]]s
* [[Black star (semiclassical gravity)]]
* [[Dark-energy star]]

==References==
{{reflist|25em}}

==Further reading==
{{Refbegin}}
*{{cite book|last=Camenzind|first=Max|title=Compact objects in astrophysics white dwarfs, neutron stars and black holes.|date=2007|publisher=Springer|location=Berlin|isbn=9783540499121|pages=442&ndash;445}}
* {{cite news
| url=http://www.nature.com/news/2005/050328/full/050328-8.html
| author=George Chapline
| publisher=Nature News
| title=Black holes 'do not exist'
| date=2005-03-28
}}
* {{cite journal|arxiv=gr-qc/0109035|author1=Mazur|author2=Emil Mottola|title=Gravitational Condensate Stars: An Alternative to Black Holes|journal=Universe |year=2023 |volume=9 |issue=2 |page=88 |doi=10.3390/universe9020088 |bibcode=2023Univ....9...88M |doi-access=free }} The original paper by Mazur and Mottola
*{{cite web
| url=http://www.fc.up.pt/pessoas/luis.beca/phisky/PhiSky%20Wiltshire.pdf
| title=Stable gravastars — an alternative to black holes?
|author1=Visser, Matt |author2=Wiltshire, David L. | access-date=2004-10-02
}}
*{{cite book|last=Zanotti|first=Luciano Rezzolla, Olindo|title=Relativistic hydrodynamics|date=2013|publisher=[[Oxford University Press]]|location=Oxford|isbn=9780198528906|pages=599&ndash;603|edition=1. publ.}}
{{Refend}}


==External links==
==External links==
* [https://arxiv.org/find/grp_physics/1/abs:+gravastar/0/1/0/all/0/1 Papers about gravastars on gr-qc]
*[http://www.fc.up.pt/pessoas/luis.beca/phisky/PhiSky%20Wiltshire.pdf Stable gravastars – an alternative to black holes?]
*[http://www.nature.com/news/2005/050328/full/050328-8.html George Chapline article in Nature News]


{{Black holes}}
{{Star}}
{{Portal bar|Astronomy|Spaceflight|Outer space|Solar System}}
[[Category:Stellar black holes]]
[[Category:Black holes]]
[[Category:Black holes]]
[[Category:Stellar mass black holes]]
[[Category:Quantum gravity]]
[[Category:Star types]]

[[Category:Hypothetical stars]]
[[de:Gravastern]]
[[Category:Fringe physics]]

Latest revision as of 07:13, 23 March 2024

A gravastar is an object hypothesized in astrophysics by Pawel O. Mazur and Emil Mottola as an alternative to the black hole theory. It has usual black hole metric outside of the horizon, but de Sitter metric inside. On the horizon there is a thin shell of matter. The term "gravastar" is a portmanteau of the words "gravitational vacuum star".[1] Further theoretical considerations of gravastars include the notion of a nestar (a second gravastar nested within the first one).[2][3]

Structure[edit]

In the original formulation by Mazur and Mottola,[4] gravastars contain a central region featuring a p = −ρ [jargon] (where p is pressure and ρ is energy density), and false vacuum or "dark energy", a thin shell of p = ρ perfect fluid, and a true vacuum p = ρ = 0 exterior. The dark energy-like behavior of the inner region prevents collapse to a singularity and the presence of the thin shell prevents the formation of an event horizon, avoiding the infinite blue-shift. The inner region has thermodynamically no entropy and may be thought of as a gravitational Bose–Einstein condensate. Severe red-shifting of photons as they climb out of the gravity well would make the fluid shell also seem very cold, almost absolute zero.

In addition to the original thin shell formulation, gravastars with continuous pressure have been proposed. These objects must contain anisotropic stress.[5]

Externally, a gravastar appears similar to a black hole: It is visible by the high-energy radiation it emits while consuming matter, and by the Hawking radiation it creates.[citation needed] Astronomers search the sky for X-rays emitted by infalling matter to detect black holes. A gravastar would produce an identical signature. It is also possible, if the thin shell is transparent to radiation, that gravastars may be distinguished from ordinary black holes by different gravitational lensing properties as null geodesics may pass through.[6]

Mazur and Mottola suggest that the violent creation of a gravastar might be an explanation for the origin of our universe and many other universes, because all the matter from a collapsing star would implode "through" the central hole and explode into a new dimension and expand forever, which would be consistent with the current theories regarding the Big Bang.[7] This "new dimension" exerts an outward pressure on the Bose–Einstein condensate layer and prevents it from collapsing further.

Gravastars also could provide a mechanism for describing how dark energy accelerates the expansion of the universe. One possible hypothesis uses Hawking radiation as a means to exchange energy between the "parent" universe and the "child" universe, and so cause the rate of expansion to accelerate, but this area is under much speculation.[citation needed]

Gravastar formation may provide an alternative explanation for sudden and intense gamma-ray bursts throughout space.[citation needed]

LIGO's observations of gravitational waves from colliding objects have been found either to not be consistent with the gravastar concept,[8][9][10] or to be indistinguishable from ordinary black holes.[11][12]

In comparison with black holes[edit]

By taking quantum physics into account, the gravastar hypothesis attempts to resolve contradictions caused by conventional black hole theories.[13]

Event horizons[edit]

In a gravastar, the event horizon is not present. The layer of positive pressure fluid would lie just outside the 'event horizon', being prevented from complete collapse by the inner false vacuum.[1] Due to the absence of an event horizon the time coordinate of the exterior vacuum geometry is everywhere valid.

Dynamic stability of gravastars[edit]

In 2007, theoretical work indicated that under certain conditions gravastars as well as other alternative black hole models are not stable when they rotate.[14] Theoretical work has also shown that certain rotating gravastars are stable assuming certain angular velocities, shell thicknesses, and compactnesses. It is also possible that some gravastars which are mathematically unstable may be physically stable over cosmological timescales.[15] Theoretical support for the feasibility of gravastars does not exclude the existence of black holes as shown in other theoretical studies.[16]

See also[edit]

References[edit]

  1. ^ a b . This solution of Einstein equations is stable and has no singularities. "Los Alamos researcher says 'black holes' aren't holes at all". Los Alamos National Laboratory. Archived from the original on 13 December 2006. Retrieved 10 April 2014.
  2. ^ McRae, Mike (20 February 2024). "Bubble-Like 'Stars Within Stars' Could Explain Black Hole Weirdness". ScienceAlert. Archived from the original on 20 February 2024. Retrieved 20 February 2024.
  3. ^ Jampolski, Daniel; Rezzolla, Luciano (2024-02-15). "Nested solutions of gravitational condensate stars". Classical and Quantum Gravity. 41 (6): 065014. arXiv:2310.13946. Bibcode:2024CQGra..41f5014J. doi:10.1088/1361-6382/ad2317. S2CID 264426808.
  4. ^ Mazur, Pawel O.; Mottola, Emil (2023). "Gravitational Condensate Stars: An Alternative to Black Holes". Universe. 9 (2): 88. arXiv:gr-qc/0109035. Bibcode:2023Univ....9...88M. doi:10.3390/universe9020088.
  5. ^ Cattoen, Celine; Faber, Tristan; Visser, Matt (2005-09-25). "Gravastars must have anisotropic pressures". Classical and Quantum Gravity. 22 (20): 4189–4202. arXiv:gr-qc/0505137. Bibcode:2005CQGra..22.4189C. doi:10.1088/0264-9381/22/20/002. S2CID 10023130.
  6. ^ Sakai, Nobuyuki; Saida, Hiromi; Tamaki, Takashi (2014-11-17). "Gravastar shadows". Phys. Rev. D. 90 (10): 104013. arXiv:1408.6929. Bibcode:2014PhRvD..90j4013S. doi:10.1103/physrevd.90.104013. S2CID 119102542.
  7. ^ Chown, Marcus (7 June 2006). "Is space-time actually a superfluid?". New Scientist. Archived from the original on 2016-04-12. Retrieved 2017-11-04. It's the big bang," says Mazur. "Effectively, we are inside a gravastar. "alternative URL". bibliotecapleyades.net.
  8. ^ Chirenti, Cecilia; Rezzolla, Luciano (2016-10-11). "Did GW150914 produce a rotating gravastar?". Physical Review D. 94 (8): 084016. arXiv:1602.08759. Bibcode:2016PhRvD..94h4016C. doi:10.1103/PhysRevD.94.084016. S2CID 16097346. We conclude it is not possible to model the measured ringdown of GW150914 as due to a rotating gravastar.
  9. ^ "Did LIGO detect black holes or gravastars?". ScienceDaily. October 19, 2016. Retrieved 2017-11-04.
  10. ^ "LIGO's black hole detection survives the gravastar test". Extreme Tech. 2016-10-26. Retrieved 2017-11-04.
  11. ^ "Was gravitational wave signal from a gravastar, not black holes?". New Scientist. 2016-05-04. Retrieved 2017-11-04. Our signal is consistent with both the formation of a black hole and a horizonless object – we just can't tell.
  12. ^ Cardoso, Vitor; Franzin, Edgardo; Pani, Paolo (2016-04-27). "Is the gravitational-wave ringdown a probe of the event horizon?". Physical Review Letters. 116 (17): 171101. arXiv:1602.07309. Bibcode:2016PhRvL.116q1101C. doi:10.1103/PhysRevLett.116.171101. ISSN 0031-9007. PMID 27176511. S2CID 206273829.
  13. ^ Stenger, Richard (22 January 2002). "Is black hole theory full of hot air?". CNN.com. Retrieved 10 April 2014.
  14. ^ Vitor Cardoso; Paolo Pani; Mariano Cadoni; Marco Cavaglia (2008). "Ergoregion instability of ultra-compact astrophysical objects". Physical Review D. 77 (12): 124044. arXiv:0709.0532. Bibcode:2008PhRvD..77l4044C. doi:10.1103/PhysRevD.77.124044. S2CID 119119838.
  15. ^ Chirenti, Cecilia; Rezzolla, Luciano (October 2008). "Ergoregion instability in rotating gravastars" (PDF). Physical Review D. 78 (8): 084011. arXiv:0808.4080. Bibcode:2008PhRvD..78h4011C. doi:10.1103/PhysRevD.78.084011. S2CID 34564980. Archived from the original (PDF) on 4 March 2016. Retrieved 10 April 2014.
  16. ^ Rocha; Miguelote; Chan; da Silva; Santos; Anzhong Wang (2008). "Bounded excursion stable gravastars and black holes". Journal of Cosmology and Astroparticle Physics. 2008 (6): 025. arXiv:0803.4200. Bibcode:2008JCAP...06..025R. doi:10.1088/1475-7516/2008/06/025. S2CID 118669175.

Further reading[edit]

External links[edit]