Could the mass of a singularity be described as an empty set

1. Dec 2, 2014

Quds Akbar

Could the mass of a singularity be described or defined as an empty set, or else what is the term to describe it (in at least one sentence).

2. Dec 2, 2014

Matterwave

What would this mean? I have no idea what "the mass is an empty set" means.

Probably the best way to describe the mass of the singularity (in the Schwarzschild metric) is simply the parameter M which appears in the Schwarzschild metric. I am not familiar enough with the other metrics to give a good description.

3. Dec 2, 2014

mathman

Mass is a term describing a physical property. The empty set is a purely mathematical term. The question doesn't make much sense.

4. Dec 2, 2014

Quds Akbar

So how can I describe it's mass in one word/sentence?

5. Dec 2, 2014

Quds Akbar

"In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced."
An empty set means there is no answer, zero as an answer is not an empty set. Think of it as an empty box with no answer. Zero is considered an answer and so is any other number.

6. Dec 2, 2014

Matterwave

So your question is actually "could the mass of the singularity of a black hole be undefined?"

7. Dec 3, 2014

Staff Emeritus
Colorless green ideas sleep furiously.

8. Dec 3, 2014

William Donald

It could be honestly anything. Beyond the event horizon of a black hole; we have no understanding of what happens. The laws of physics are completely torn apart. The singularity could possibly be a one-dimensional point with an empty set. But then again, if it's empty, then there would be no mass, even though there is an enormous amount of gravity, correct?

9. Dec 3, 2014

e.bar.goum

The density of a black hole (well, the singularity.**) is undefined. The mass of a black hole isn't anything that exotic. It'll be the mass of whatever collapsed + whatever it has accreted - evaporation (negligible).

We can even measure the mass of black holes through looking at the orbits of nearby stars. e.g. for Sgr A* http://onlinelibrary.wiley.com/doi/10.1002/asna.200385084/pdf

You're asking the wrong question, basically.

** People calculate a "density" by taking the ratio of mass to volume of the event horizon, but I don't like that.

10. Dec 3, 2014

Quds Akbar

In a way, so yeah, somehow.

11. Dec 3, 2014

Quds Akbar

That's a good way to think about it, but I mean mathematically. Since infinity times zero has no answer(technically)

12. Dec 3, 2014

Drakkith

Staff Emeritus
Why would it be undefined? The mass is a non-zero, non-infinite value, unlike the density, radius, and volume of the singularity,

13. Dec 3, 2014

Chronos

An electron is considered a point particle, but, still has a finite mass, charge, etc. Does that mean the electron is a 'charge singularity'? I doubt anyone thinks of it that way. I am, however, curious if you could derive the size of a black hole singularity based on logic similar to that used to derive the size of an electron.

14. Dec 4, 2014

irk

Not being top expert in this but explanation I heard is that 'naked' electron is considered point particle and its charge is infinite or 'most likely infinite' or at least 'huge' but theory assumes infinite so indeed it is a point singularity. The charge we observe is not the charge of 'naked' point electron but a result of interaction of the point charge with the surrounding vacuum which is polarized by the charge (meaning the naked charge is surrounded by the opposite screen charge) and what is seen on outside is a finite residual charge. Something similar could be with the mass.