# Is singularity without black hole possible?

I read things related to the topic I am asking and I found the idea of a "Naked Singularity" but naked singularities can't be created without black hole.

I need to know whether it is logical to think about a singularity that can exist without a black hole. Can some other gravitational waves or gravitational effects create a singularity without a black hole?

• "I actually need to know is this is possible to make a spacetime singularity but its not addicted to anything." Addicted? What do you mean by "addicted"?
– hft
Commented Jul 27, 2022 at 2:51
• An example of a spacelike singularity with a horizon is in an uncharged, non-rotating black hole. An example of a spacelike singularity without a horizon is the Big Bang. Commented Jul 27, 2022 at 3:02
• I've tried to edit your question further to clarify what you're asking (and I have also nominated it for re-opening.) Please feel free to edit it further or roll back my changes if I have misinterpreted your meaning. Commented Jul 27, 2022 at 13:32
• There are easy-to create models with naked singularities in them. The mathematically simplest one is a charged black hole with $Q > M$ (the horizon of a charged black hole is located at $M \pm \sqrt{M^{2} - Q^{2}}$) Commented Jul 27, 2022 at 13:35

### What is a (naked) singularity?

It is common to think of singularities as being points of infinite curvature on spacetime, or points where gravity is infinite. Using this understanding, it is definitely very difficult to understand how a naked singularity would be a possibility: if gravity is infinite at a singularity, then surely it must be strong enough at a distance from it so as to form a black hole, right?

The thing is: that is not the definition of a singularity. In General Relativity, it doesn't make sense to say "the curvature is infinite at this point", for the curvature tensor is defined in a way such that is must be finite at all points of spacetime. The trick with singularities is that they are not points on spacetime. And this is one of the many reasons General Relativity is hard.

The actual definition of a singularity is roughly the following:

A spacetime is said to be singular if there is an unextendible geodesic that ends at finite affine parameter.

In other words, the spacetime is singular if you can find some observer whose worldline ends at finite proper time (this is actually only a particular case). It is as if you were walking through spacetime with your personal clock and then, at finite time, you suddenly are not at spacetime anymore (no clue where you are or even on whether you exist, but you're not on spacetime). In this sense, singularities are "holes" in spacetime.

Thinking about singularities in this way makes things a bit more clear. One way of creating a "hole" would be to have a region in which curvature is blowing up: the "blow-up point" is then a "hole" in spacetime, a singularity. However, that isn't the only case. As long as you have "holes", you can get singularities. (As a remark, there are naked singularities which are curvature blow-ups. Schwarzschild spacetime with a negative mass is one example).

Intuitively, that is one way of thinking about naked singularities: they are "holes" in spacetime that are not hidden behind a black hole. The issues about these things are that just as an observer can "fall into a hole", you could also have stuff "coming out of the hole". If the singularity is behind a black hole, no one minds, because whatever might come out is trapped inside the black hole and you won't have anything weird. If, on the other hand, the singularity is naked, it means you can't really predict what will happen on the spacetime, because you can't predict what comes out of the hole.

### Can one create a naked singularity?

As for whether one can create a naked singularity, that is an open question! As mentioned in another answer, the cosmic censorship conjectures are mathematical conjectures about the structure of General Relativity that state that, under physical conditions, the formation of naked singularities is impossible. Being conjectures, we're still not sure of whether they are true: it could be that they hold and it could be that they do not.

In plain English, the meaning of the two Cosmic Censorship Conjectures is

1. Weak Cosmic Censorship Conjecture: under physical assumptions, no naked singularity can arise from gravitational collapse.
2. Strong Cosmic Censorship Conjecture: under physical assumptions on the matter and initial conditions of a spacetime, it must hold that it is completely determined by these initial conditions.

The Weak Cosmic Censorship Conjecture is an assumption in many (if not all) of the theorems of Black Hole Thermodynamics, and hence the fact that no mathematical contradictions have been found in Black Hole Thermodynamics suggests that the Conjecture might actually be true. Philosophical reasoning for believing in these conjectures also comes from the belief that the universe should be predictable and causal.

For more details on these themes, you might want to check Wald's General Relativity (especially Secs. 9.1 and 12.1) and his 1993 review paper on the Weak Cosmic Censorship Conjecture.

Naked singularities are thought to be nonphysical, and most physicists argue that any singularity must be enclosed by an event horizon. For example, as you have pointed out, inside a black hole.

There are theories that suggest the possibility of naked singularities, for example, loop quantum gravity$$^1$$. There are also those who suggest that the universe would never "allow" a naked singularity, to begin with. This is known as the cosmic censorship hypothesis developed by Roger Penrose.

This hypothesis has two (mathematically independent) conjectures, and from the link:

1. The weak cosmic censorship hypothesis asserts there can be no singularity visible from future null infinity. In other words, singularities need to be hidden from an observer at infinity by the event horizon of a black hole. Mathematically, the conjecture states that, for generic initial data, the maximal Cauchy development possesses a complete future null infinity.

2. The strong cosmic censorship hypothesis asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory. In other words, the classical fate of all observers should be predictable from the initial data. Mathematically, the conjecture states that the maximal Cauchy development of generic compact or asymptotically flat initial data is locally inextendible as a regular Lorentzian manifold. Taken in its strongest sense, the conjecture suggests locally inextendibility of the maximal Cauchy development as a continuous Lorentzian manifold [very Strong Cosmic Censorship]$$^2$$.

As stated, each of these are mathematically independent, and each has a spacetime i.e., one for which the weak cosmic censorship holds true and the strong cosmic censorship is violated and exactly vice-versa.

$$^1$$ LQG is unverified.

$$^2$$ The "strongest version" stated there has since been disproven for the case of a rotating black hole with no charge.