Naked singularity

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In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon.

When there exists at least one causal geodesic that, in the future, extends either to an observer at infinity or to an observer comoving with the collapsing cloud, and in the past terminates at the gravitational singularity, then that singularity is referred to as a naked singularity.<ref>Template:Cite book</ref> In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the curvature of spacetime caused by the singularity is so strong that light cannot escape. Hence, objects inside the event horizon—including the singularity itself—cannot be observed directly. In contrast, a naked singularity would be observable.

The theoretical existence of naked singularities is important because their existence would mean that it would be possible to observe the collapse of an object to infinite density. It would also cause foundational problems for general relativity, because general relativity cannot make predictions about the evolution of spacetime near a singularity. In generic black holes, this is not a problem, as an outside viewer cannot observe the spacetime within the event horizon.

Naked singularities have not been observed in nature. Astronomical observations of black holes indicate that their rate of rotation falls below the threshold to produce a naked singularity (spin parameter 1). GRS 1915+105 comes closest to the limit, with a spin parameter of 0.82-1.00.<ref name=space>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> It is hinted that GRO J1655−40 could be a naked singularity.<ref>Template:Cite journal</ref>

According to the cosmic censorship hypothesis, gravitational singularities may not be observable. If loop quantum gravity is correct, naked singularities may be possible in nature.

Predicted formationEdit

When a massive star undergoes a gravitational collapse due to its own immense gravity, the ultimate outcome of this persistent collapse can manifest as either a black hole or a naked singularity. This holds true across a diverse range of physically plausible scenarios allowed by general relativity. The Oppenheimer–Snyder–Datt (OSD) model illustrates the collapse of a spherical cloud composed of homogeneous dust (pressureless matter).<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> In this scenario, all the matter converges into the spacetime singularity simultaneously in terms of comoving time. Notably, the event horizon emerges before the singularity, effectively covering it. By allowing an inhomogeneous initial density profile, one can demonstrate a significant alteration in the behavior of the horizon. This leads to two distinct potential outcomes arising from the collapse of generic dust: the formation of a black hole, characterized by the horizon preceding the singularity; or the emergence of a naked singularity, where the horizon is delayed. In the case of a naked singularity, this delay enables null geodesics or light rays to escape the central singularity, where density and curvatures diverge, reaching distant observers.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> In exploring more realistic scenarios of collapse, one avenue involves incorporating pressures into the model. The consideration of gravitational collapse with non-zero pressures and various models including a realistic equation of state, delineating the specific relationship between the density and pressure within the cloud, has been thoroughly examined and investigated by numerous researchers over the years.<ref>Examples include:

From concepts drawn from rotating black holes, it is shown that a singularity, spinning rapidly, can become a ring-shaped object. This results in two event horizons, as well as an ergosphere, which draw closer together as the spin of the singularity increases. When the outer and inner event horizons merge, they shrink toward the rotating singularity and eventually expose it to the rest of the universe.

A singularity rotating fast enough might be created by the collapse of dust or by a supernova of a fast-spinning star. Studies of pulsars<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> and some computer simulations (Choptuik, 1997) have been performed.<ref>Template:Cite journal</ref> Intriguingly, it is recently reported that some spinning white dwarfs could realistically transmute into rotating naked singularities or black holes with a wide range of near- and sub-solar-mass values by capturing asymmetric dark matter particles.<ref>Template:Cite journal</ref> Similarly, spinning neutron stars could also be transmuted to slowly spinning near–solar-mass naked singularities by capturing asymmetric dark matter particles, if the accumulated cloud of dark matter particles in the core of a neutron star can be modeled as an anisotropic fluid.<ref>Template:Cite journal</ref> In general, the precession of a gyroscope and the precession of orbits of matter falling into a rotating black hole or a naked singularity can be used to distinguish these exotic objects.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>

Mathematician Demetrios Christodoulou, a winner of the Shaw Prize, has shown that contrary to what had been expected, singularities which are not hidden in a black hole could also occur.<ref>Template:Cite journal</ref> However, he then showed that such "naked singularities" are unstable.<ref name=instability>Template:Cite journal</ref>

MetricsEdit

File:Naked.Singularity,Overextremal.Kerr.Newman,Raytracing.png
Ray traced image of a hypothetical naked singularity in front of a Milky Way background. The parameters of the singularity are M=1, a²+Q²=2M². The singularity is viewed from its equatorial plane at θ=90° (edge on).
File:Black.Hole,Extremal.Kerr.Newman,Raytracing.png
Comparison with an extremal black hole with M=1, a²+Q²=1M²

Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum. Specifically, if the angular momentum is high enough, the event horizons could disappear. Transforming the Kerr metric to Boyer–Lindquist coordinates, it can be shown<ref>Hobson, et al., General Relativity an Introduction for Physicists, Cambridge University Press 2007, p. 300-305</ref> that the <math>r</math> coordinate (which is not the radius) of the event horizon is <math display="block">r_\pm = \mu \pm (\mu^2-a^2)^{1/2},</math> where <math>\mu = G M / c^2</math>, and <math>a=J/M c</math>. In this case, "event horizons disappear" means that the solutions are complex for <math>r_\pm</math>, or <math>\mu^2 < a^2</math>. However, this corresponds to a case where <math>J</math> exceeds <math>GM^{2}/c</math> (or in Planck units, Template:Nowrap, i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.

Disappearing event horizons can also be seen with the Reissner–Nordström geometry of a charged black hole. In this metric, it can be shown<ref>Hobson, et al., General Relativity an Introduction for Physicists, Cambridge University Press 2007, p. 320-325</ref> that the horizons occur at <math display="block">r_\pm = \mu \pm (\mu^2-q^2)^{1/2},</math> where <math>\mu = G M / c^2</math>, and <math>q^2 = G Q^2/(4 \pi \varepsilon_0 c^4)</math>. Of the three possible cases for the relative values of <math>\mu</math> and <math>q</math>, the case where <math>\mu^2 < q^2</math> causes both <math>r_\pm </math> to be complex. This means the metric is regular for all positive values of <math>r</math>, or in other words, the singularity has no event horizon. However, this corresponds to a case where <math>Q/\sqrt{4 \pi \varepsilon_0}</math> exceeds <math>M\sqrt{G}</math> (or in Planck units, Template:Nowrap, i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values.

See Kerr–Newman metric for a spinning, charged ring singularity.

EffectsEdit

A naked singularity could allow scientists to observe an infinitely dense material, which would under normal circumstances be impossible according to the cosmic censorship hypothesis. That is, without an event horizon of any kind, naked singularities could actually emit light.<ref>Template:Cite news</ref>

Cosmic censorship hypothesisEdit

{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} The cosmic censorship hypothesis says that every gravitational singularity will remain hidden by its event horizon. LIGO events, including GW150914, are consistent with these predictions. Although data anomalies would have resulted in the case of a singularity, the nature of those anomalies remains unknown.<ref>Template:Cite journal</ref>

Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature,<ref>M. Bojowald, Living Rev. Rel. 8, (2005), 11 Template:Webarchive</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> implying that the cosmic censorship hypothesis does not hold. Numerical calculations<ref>Template:Cite journal</ref> and some other arguments<ref>Template:Cite journal</ref> have also hinted at this possibility.

In fictionEdit

See alsoEdit

ReferencesEdit

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Further readingEdit

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