A nonsingular black hole model is a mathematical theory of black holes that avoids certain theoretical problems with the standard black hole model, including information loss and the unobservable nature of the black hole event horizon.

Avoiding paradoxes in the standard black hole model

For a black hole to physically exist as a solution to Einstein's equation, it must form an event horizon in finite time relative to outside observers. This requires an accurate theory of black hole formation, of which several have been proposed. In 2007, Shuan Nan Zhang of Tsinghua University proposed a model in which the event horizon of a potential black hole only forms (or expands) after an object falls into the existing horizon, or after the horizon has exceeded the critical density. In other words, an infalling object causes the horizon of a black hole to expand, which only occurs after the object has fallen into the hole, allowing an observable horizon in finite time.[1][2] This solution does not solve the information paradox, however.
Alternative black hole models

Nonsingular black hole models have been proposed since theoretical problems with black holes were first realized. Today some of the most viable candidates for the end result of the collapse of a star with mass well above the Chandrasekhar limit include the gravastar and the dark energy star.

While black holes were a well-established part of mainstream physics for most of the end of the 20th century, alternative models received new attention when models proposed by George Chapline and later by Lawrence Krauss, Dejan Stojkovic, and Tanmay Vachaspati of Case Western Reserve University showed in several separate models that black hole horizons could not form.[3][4]

Such research has attracted much media attention,[5] as black holes have long captured the imagination of both scientists and the public for both their innate simplicity and mysteriousness. The recent theoretical results have therefore undergone much scrutiny and most of them are now ruled out by theoretical studies. For example, several alternative black hole models were shown to be unstable in extremely fast rotation,[6] which, by conservation of angular momentum, would be a not unusual physical scenario for a collapsed star (see pulsar). Nevertheless, the existence of a stable model of a nonsingular black hole is still an open question.
Hayward metric

The Hayward metric is the simplest description of a black hole which is non-singular. The metric was written down by Sean Hayward as the minimal model which is regular, static, spherically symmetric and asymptotically flat.[7]

Zhang, Shuang Nan; Tang, Sumin (2007-07-06). "Witnessing matter falling into a black hole by a distant observer". Tsinghua University. Retrieved 2007-11-03.[permanent dead link]
Zhang, Shuang Nan; Liu, Yuan (2008). "Observe matter falling into a black hole". AIP Conf. Proc. 968: 384–391.arXiv:0710.2443. Bibcode:2008AIPC..968..384Z. doi:10.1063/1.2840436. S2CID 15169576.
Chapline, George (July 1998). "The Black Hole Information Puzzle and Evidence for a Cosmological Constant".arXiv:hep-th/9807175.
Vachaspati, Tanmay; Dejan Stojkovic; Lawrence M. Krauss (June 2007). "Observation of Incipient Black Holes and the Information Loss Problem". Physical Review D. 76 (2): 024005.arXiv:gr-qc/0609024. Bibcode:2007PhRvD..76b4005V. doi:10.1103/PhysRevD.76.024005. S2CID 119333620.
Rockets, Rusty (2007-06-22). "Rethinking Black Holes". Science A Gogo. Retrieved 2007-11-03.
Cardoso, Vitor; Paolo Pani; Mariano Cadoni; Marco Cavaglia (2008). "Ergoregion instability rules out black hole doubles". Physical Review D. 77 (12): 124044.arXiv:0709.0532. Bibcode:2008PhRvD..77l4044C. doi:10.1103/PhysRevD.77.124044. S2CID 119119838.
Hayward, Sean A. (26 January 2006). "Formation and evaporation of non-singular black holes". Physical Review Letters. 96 (3): 031103.arXiv:gr-qc/0506126. Bibcode:2006PhRvL..96c1103H. doi:10.1103/PhysRevLett.96.031103. PMID 16486679. S2CID 15851759.


Black holes

Schwarzschild Rotating Charged Virtual Kugelblitz Primordial Planck particle


Extremal Electron Stellar
Microquasar Intermediate-mass Supermassive
Active galactic nucleus Quasar Blazar


Stellar evolution Gravitational collapse Neutron star
Related links Tolman–Oppenheimer–Volkoff limit White dwarf
Related links Supernova
Related links Hypernova Gamma-ray burst Binary black hole


Gravitational singularity
Ring singularity Theorems Event horizon Photon sphere Innermost stable circular orbit Ergosphere
Penrose process Blandford–Znajek process Accretion disk Hawking radiation Gravitational lens Bondi accretion M–sigma relation Quasi-periodic oscillation Thermodynamics
Immirzi parameter Schwarzschild radius Spaghettification


Black hole complementarity Information paradox Cosmic censorship ER=EPR Final parsec problem Firewall (physics) Holographic principle No-hair theorem


Schwarzschild (Derivation) Kerr Reissner–Nordström Kerr–Newman Hayward


Nonsingular black hole models Black star Dark star Dark-energy star Gravastar Magnetospheric eternally collapsing object Planck star Q star Fuzzball


Optical black hole Sonic black hole


Black holes Most massive Nearest Quasars Microquasars


Black Hole Initiative Black hole starship Compact star Exotic star
Quark star Preon star Gamma-ray burst progenitors Gravity well Hypercompact stellar system Membrane paradigm Naked singularity Quasi-star Rossi X-ray Timing Explorer Timeline of black hole physics White hole Wormhole

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