Naked Singularities and the quest for the uncharted.

By Yukterez (Simon Tyran, Vienna). Source material for the Milky way background (also available on Commons): ESO/S.Brunier. Code for the relativistic raytracer and other angles: yukterez.net — Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=68252446

Much has been pondered over black holes and their possible cosmic origins since the times of the English clergyman John Mitchell, who seems to have speculated about the presence of bodies with such a great mass, through which not even light can escape. However, it wasn’t until the theory of gravitational collapse surfaced that these phenomenal works of nature were thrown back into the limelight. Stellar Nucleosynthesis has been credited with powering the star, lacking which the star rapidly crumbles under its own mass, which is termed as an “implosion” in astronomical terms. Even so, stellar nucleosynthesis, or its lack thereof, isn’t the only thing that causes a star to implode. Occasionally, extra matter that doesn’t raise the star’s core temperature partakes in such an act. This rapid collapse may be stemmed by the degeneracy pressure of star’s constituents, creating an exotic, denser state due to the compressed condensation of matter. Such a star formed is just one of the many compact star types known to man.

By NASA, ESA, Andrew Fruchter (STScI), and the ERO team (STScI + ST-ECF) — http://www.spacetelescope.org/images/heic9910a/, Public Domain, https://commons.wikimedia.org/w/index.php?curid=52133

This inevitably brings us to the question, “can’t the planetary nebula formed thus revitalize the ailing star?”

Nope.

By the time this happens, and with the humongous explosions and pulsations doing all they can to throw the nebulae matter far inwards into the galaxy, the star is likely to be stable on its own (if it hasn’t died by then). A study led by M. Rees and others surmised that the gravitational collapse of heavy stars is linked directly to the formation of stellar mass black holes, some as massive as 10³ M☉, considered the the ‘seeds’ of supermassive black holes found in the center of most galaxies.

By ESA/Hubble, CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=49042636

Quasar observers devised a relationship between such black holes and the galaxy circumscribing it. The ‘bulge’ visible in most galaxies is home to some of the most odious black holes the universe can spawn, all showing no visible signs of slowing down. To top it off, the galaxy has to pay up 0.2% of its total mass to the black hole. Quite an appetite, I’d say. Talk about an imploding star eating up its parent galaxy!

The last resort to stop these supermassive black holes dead in their tracks is something hiding in plain sight. Not from the astronomers, but in an idiom encountered in the last line by you, the readers!

Dead. Death of the stars. The death of a human is an eventful moment, let alone a massive whopper pledging allegiance to E.T to eat up the Milky Way.

Okay, that’s all I have for the itsy-bitsy gossip. But on the serious side of things, the only known method that exists to determine the mass of the condensed remnant is the Tolman-Oppenheimer-Volkoff limit, applying which, the only hope one has is praying the degeneracy pressure puts an end to such a spooky phenomenon. However, the chances of pulling off a successful save is extremely minimal, coupled with the fact that if the mass of these stars with their newfound appearance exceeds 3-4 M☉, we have a black hole in the making. An exceptional case of a facelift gone wrong.

If the remnant shows signs of becoming a quark star, the quark degeneracy pressure will forestall it from imploding spontaneously ever again.

Naked Singularities

As previously described, implosion is chiefly responsible for birthing these giants. The models explaining the act of implosion of a star into a neutron star or a black hole exist in abundance. Of these, the Laimaitre-Tolmann-Bondi Model is held in high spirits, particularly because it presents itself as a solution to the Einstein’s field equations for an expanding or collapsing spherical shell of dust under the influence of gravity. The model is embodied in an illustrious line element:

which represents the Einstein Field Equation for a spherical shell that is either expanding or collapsing under gravitational influence. More often than not, this is the quintessential key to finding out the standard Schwarzchild solution, or the Freidmann-Laimaitre equations. However, as established by matter of records, one could stumble upon naked singularities, as happened with Eardley et al in 1979, who numerically discerned such a case for the first time the world had seen.

But what exactly is a naked singularity?

Naked singularities are prime examples of gravitational singularities, which means they are points in spacetime that are of infinitely large curvature. So large, in fact, that they can’t be, or at least, by virtue of hypothesizing Einstein’s General relativity, should not be hidden behind an event horizon.

But here’s the catch. Even something as faint as the bleak possibility of even a trace of its existence would break down general relativity’s or even all of physics’ predictability itself. Think of it as the quintessential arcade game of getting a snake to eat so much that he could bite his own tail in the end. We want to explore naked singularities, but certainly not at the expense of having to disprove Einstein’s Theory of General Relativity and push the mathematical systems in place over the edge, into a perpetual uncertain void, maybe a black hole!

This fear caused one Roger Penrose to pen down the idea of cosmic censorship, of which the idea of strong cosmic censorship supported the theory that the space time could go no further down than the Cauchy Horizon, and attempted to close the can of worms called naked singularities, that could cause massive headaches for physicists.

“There’s nothing down there, trust me. Einstein! He’s always right!”

In fact, it was Penrose himself, who in 1965 demonstrated why a black hole must have a singularity. But he couldn’t prove that all singularities need to have an event horizon with a “point of no return”, and hence, a black hole over them. Caught in his own mathematical contraption, Penrose returned to his desk, emerging four years later with what he called “The Conjecture of Cosmic Censorship” which basically read that it was mathematically, physically, or otherwise impossible for a singularity to exist without an event horizon covering it up.

Even so much as a conjecture, many believed his hypothesis to be true, because it’s hard to imagine an infinitely dense particle sitting out in the spacetime without it deforming and forming an event horizon.

This conjecture earned him the support of noted theoretical physicist Stephen Hawking, who in the 90’s got so hyped up over this debate that he took on two of Caltech’s geniuses Kip Thorne and John Preskill over this premise and their slightly divergent views.

And naked singularities jinxed it again.

Hawking met with a similar roadblock as Penrose, finding mathematical evidence for an improbable, but not unlikely event that consisted of the black hole losing its mass due to evaporating or losing particles, as explained through Quantum Mechanics, leaving behind just the singularity. Quantum Mechanics, however, didn’t fall under the confines of the bet, leaving Hawking’s loss as debatable as naked singularities themselves.

Then the golden age of computer programming happened, and in 1997, computer models found out the “unlikely event” that Hawking was talking about. A naked singularity being produced from an imploding star under just the right parameters. The odds of it were, however, as slim as if you were to balance a carpentry nail on its tip.

If I didn’t tell you already, the good news is naked singularities can be normally formed, and be a common occurrence in universes that have multiple dimensions.

The bad news? Ours doesn’t.

Unless we find one that does, we’d have to make use of either Hawking’s favourite Quantum Mechanics, or Einstein’s brainchild, the theory of General Relativity, which work perfectly on their own, but suck when teamed together, because frankly, the only thing massive yet tiny at the same time is, you guessed it — a singularity!

Directly observing these singularities would provide us with invaluable insights that could enable physicists to derive a new equation that bridges these two, or discard them for good for a better theory that applies to not just ours, but every universe, if there exists such things outside the observable universe, which I believe does, and I’m ready to go full Stephen Hawking on anyone that thinks otherwise, so fight me for it!

References:

  1. Penrose, Roger (1969). “Gravitational collapse: The role of general relativity”. Nuovo Cimento. Rivista Serie. 1: 252–276. Bibcode:1969NCimR…1..252P

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