# Explaining Weak & Null Singularities in Black Holes

• Dmitry67
In summary: The weak singularity at the Cauchy horizon is not an instantaneous infinite blip, but it is a point where the metric becomes scalar and tidal effects are no longer finite.
Dmitry67
I understand the concept of a spacetime (future) singularity in a BH
I understand what is a ring singularity in Kerr'sblack hole

Could anyone explain (for dummies) what is meant by "weak" and "null" singularity?

Null means that the singularity is not spacelike nor timelike, but light-like. Weak means that the tidal deformations do not diverge at the singularity. It may happen at the inner horizon of a perturbed charged black hole, as studied in Poisson and Israel, "Internal structure of black holes", Phys. Rev. D41 (1990), 1796-1809.

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Thank you
The what is 'singular' there?

Dmitry67 said:
Thank you
The what is 'singular' there?

Spacetime.

It probably is easier to give somewhat general examples "singular spacetime" than to give a generic definition of a spacetime singularity.

For example, a spacetime is singular if there is a timelike curve having bounded acceleration (i.e, a worldline an observer could follow) that ends after a finite amount of proper time, and that is inextendable. Singular spacetimes have "edges".

What does inextendable mean? This depends on how "differentiable" the differentiable manifold used to model spacetime is.

Spacetimes usually are taken to be suitably smooth differentiable manifolds. If differentiability of the metric is relaxed to continuity of the metric, then spacetimes can be extended through some singularities. Since second derivatives of the metric are used to construct curvature, we could have a continuous metric (like the absolute value function) that, when differentiated twice, gives a distribution that involves a Dirac delta function. Then, tidal forces don't build up in a continuous way.

Thank you
Still, it is not clear to me. I read in some sources that bluesheet is not fatal and observer can survive falling thru cauchy horizon. So for an observer metrics is not singular? As I understand, geodesics there just lead inside the second horizon, and they don't 'end' after finite time?

Dmitry67 said:
Thank you
Still, it is not clear to me. I read in some sources that bluesheet is not fatal and observer can survive falling thru cauchy horizon.

If a curvature singularity blows up like a Dirac delta function, then integration produces only a finite contribution to the tidal deformation of an object, which, if the object is robust enough, it can withstand.
Dmitry67 said:
So for an observer metrics is not singular? As I understand, geodesics there just lead inside the second horizon, and they don't 'end' after finite time?

This depends on the differentiability condition imposed on the spacetime manifold.

Dmitry67 said:
Thank you
Still, it is not clear to me. I read in some sources that bluesheet is not fatal and observer can survive falling thru cauchy horizon. So for an observer metrics is not singular? As I understand, geodesics there just lead inside the second horizon, and they don't 'end' after finite time?

Poisson and Israel have shown that perturbations of a charged black hole due to ingoing radiation lead to a nonscalar singularity, and if also outgoing radiation is present then a phenomenon dubbed mass inflation arises and the singularity becomes scalar (the Weyl curvature scalar diverges), though the metric is still regular and tidal effects integrated on the infalling body worldline are finite (for this reason the singularity is called weak).

Thus, it seems possible that spacetime can be classically continued beyond the Cauchy horizon, even if general relativity cannot predict it. A fully quantum theory of gravity is required to exactly model the Cauchy horizon and its vicinity.

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George Jones said:
If a curvature singularity blows up like a Dirac delta function, then integration produces only a finite contribution to the tidal deformation of an object, which, if the object is robust enough, it can withstand.

Is the weak singularity at the Cauchy horizon pretty much an instantaneous infinite blip (like an upside-down capital T) on the scalar curvature or is there expected to be some gradient of change? If there is a gradient of change, would this have to be confined within the event horizon or might some small degree of mass-inflation be detected outside the BH?

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## 1. What is a singularity in a black hole?

A singularity in a black hole is a point where the gravitational pull becomes infinitely strong and the laws of physics break down. It is considered the center of a black hole, where the mass is concentrated and the density is infinite.

## 2. What is a weak singularity in a black hole?

A weak singularity in a black hole is a type of singularity where the gravitational pull is not strong enough to cause the laws of physics to break down. In other words, the density is not infinite at this point, but it is still very high.

## 3. How do weak singularities form in black holes?

Weak singularities form in black holes when the gravitational pull is not strong enough to overcome the forces of repulsion between particles. This can occur when the black hole is rotating or when there is a high level of charge.

## 4. What is a null singularity in a black hole?

A null singularity in a black hole is a type of singularity where the gravitational pull is zero, and the laws of physics can still be applied. It is also known as a "soft" singularity.

## 5. How are null singularities different from weak and strong singularities?

Null singularities are different from weak and strong singularities because they do not have infinite density or a breakdown of the laws of physics at their center. They are also not considered true singularities, as they can potentially be avoided or passed through without being destroyed.

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