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 In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...

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 Tsinghua University (; abbr. THU) is a national public research university in Beijing, China. The university is funded by the Ministry of Education. The university is a member of the C9 League, Double First Class University Plan, Projec ...

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. 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 result of the collapse of a star with mass well above the

Chandrasekhar limit The Chandrasekhar limit () is the maximum mass of a stable white dwarf star. The currently accepted value of the Chandrasekhar limit is about (). White dwarfs resist gravitational collapse primarily through electron degeneracy pressure, compa ...

include the

gravastar 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 th ...

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 Lawrence Maxwell Krauss (born May 27, 1954) is an American theoretical physicist and cosmologist who previously taught at Arizona State University, Yale University, and Case Western Reserve University. He founded ASU's Origins Project, now c ...

, Dejan Stojkovic, and Tanmay Vachaspati of Case Western Reserve University showed in several separate models that black hole horizons could not form. Such research has attracted much media attention, 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, which, by conservation of

angular momentum In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...

, 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 that is

non-singular In the mathematical field of algebraic geometry, a singular point of an algebraic variety is a point that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined. In ca ...

. The metric was written down by Sean Hayward as the minimal model that is regular, static,

spherically symmetric In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...

and

asymptotically flat An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime. ...

Ayón-Beato–García metric

The Ayón-Beato–García model is the first exact charged regular black hole with a source. The model was proposed by Eloy Ayón Beato and Alberto García in 1998 based on the minimal coupling between a nonlinear electrodynamics model and

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, considering a static and

spacetime. Later the same authors reinterpreted the first non-singular black hole geometry, the Bardeen toy Model, as a nonlinear-electrodynamics-based regular black hole. Nowadays, it is known that the Ayón-Beato–García model may mimic the absorption properties of the

Reissner–Nordström metric In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass ''M''. T ...

, from the perspective of the absorption of massless test scalar fields.

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