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

[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).

 

[Matterwave]

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).

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.

 

[mathman]

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

 

[Quds Akbar]

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

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

 

[Quds Akbar]

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.

"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.

 

[Matterwave]

"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.

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

 

[Vanadium 50]

Colorless green ideas sleep furiously.

 

[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?

 

[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.

 

[Quds Akbar]

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

In a way, so yeah, somehow.

 

[Quds Akbar]

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?

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

 

[Drakkith]

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

In a way, so yeah, somehow.

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

 

[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.

 

[irk]

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.

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.