# Understanding of the theory of relativity

maximus
a vauge question:

i am, admititly, far from a complete understanding of the theory of relativity and special relativity but could someone humor me by explaining exactly why the T.ofR. perdicts its own break down at a singularity.

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because in the spherical case of a black hole, the singularity is located in the center, and represents infinite gravitational curvature.

More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply. So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.

Instanton

Originally posted by instanton
More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply. So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.

Instanton
Even more precisely GR defines the Universe (except
fot the particles ) as a single continous geometrical
entity. However, if the mass in a singularity is
infinite then space-time has a "hole" in it, and
that kin'na ruins the "suit"...

Live long and prosper.

pellman
A singularity is an infinity - in this case, an infinite space-time curvature. Usually when a theory predicts an infinite value it is interpreted as a failure of the theory in that case, e.g., the infinite self-energy of an electron in classical EM. Thus we say, that the theory "breaks down" inside a black hole.

Originally posted by maximus

...could someone humor me by explaining exactly why the T.ofR. perdicts its own break down at a singularity.

The phrasing of your question hides the issue because singularities by definition signal a breakdown in any theory. But to answer the intended question, there are theorems in GR predicated on very reasonable assumptions proving that singularities are a generic feature of realistic cosmologies since realistic distributions of mass-energy will develop black holes.

Originally posted by instanton

...[GR] is suppose to be [but can't be] applied everywhere in spacetime...

No, GR is not required to be applicable everywhere.

Originally posted by instanton

...[GR] predicts regions where it can't be applied.

Originally posted by pellman

A singularity is an infinity - in this case, an infinite space-time curvature.

We currently have no completely satisfactory way of characterizing GR singularities since they indicate a breakdown in spacetime and thus cannot be ascribed location. In fact, geometrical pathologies like the blowing up of curvature scalars or bad behaviour of curvature or metric components can never classify the infinite variety of spacetime singularities, and global methods where singularities are viewed as bounding spacetime don't work either. By far the most satisfactory tool - and in fact the one on which the aforementioned singularity theorems are based - is "geodesic incompleteness" which captures the intuitive idea of the existence of particles in free fall ending or beginning (like entering or exiting a black hole singularity for example) at some finite time. Depending on the behaviour of curvature along such geodesics, the corresponding singularities may be classified as scalar curvature, parallelly propagated curvature, or non-curvature singularities.

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Originally posted by steinitz

No, GR is not required to be applicable everywhere.

Well I never said it is. Read the original question more carefully.

Instanton

Originally posted by instanton
More precisly the existence of singularity on spacetime means there is a region of spacetime that physical theory doesn't apply.

So, you have a theory that is suppose to be applied everywhere in spacetime, that predicts regions where it can't be applied.

Instanton

Both of these remarks are misleading as I've indicated. With someone else I might have ignored the second remark. But you claim to be a graduate student and I therefore expect more precision from you.

Originally posted by steinitz
Both of these remarks are misleading as I've indicated. With someone else I might have ignored the second remark. But you claim to be a graduate student and I therefore expect more precision from you.

Maybe I should've been more precise. What I meant was following. The original question was about the statement we often hear "exactly why the T.ofR. perdicts its own break down at a singularity." In my opinion the statement implies GR suppose to be applied in whole spacetime, but predicts the region which it can not be. It is just my interpretation of the statement Maximus quoted, not my blided belief on classical GR.

Now, you pointed out I read more carefully of the original question and I realize I do not really know what the statement exactly means. As you said singularities are characterized by geodesic incompleteness. What precisely is wrong with that? It maybe weird, but I can not really think of any concrete reason. Maybe you have better idea.

Instanton

Originally posted by instanton As you said singularities are characterized by geodesic incompleteness. What precisely is wrong with that?

What is wrong with what?

Infinities indeed are usually the indicators that something is forgotten to be taken into consideration (often not known yet phenomenon which is nevertheless important).

In case of gravitational singularities it can be angular momentum (of black hole), or minimum allowed by math angular momentum, or quantum nature of gravity, or vacuum fluctuations, etc

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