<p>The question is really about how to turn a loose question into something that has an answer; to some degree this is a logic and philosophy question rather than astronomy, so don't get surprised if it gets closed.</p>
<p>The key thing here is the concepts &quot;really exists&quot; and &quot;with respect to relative frame of reference&quot;  - what does that mean?</p>
<p>In relativity theory there are many possible frames of reference, typically described that what different kinds of observers would observe or as different coordinate systems for the same underlying spacetime. The theory describes how to translate from one frame to another one.</p>
<p>Can something really exist just in relation to some frames of reference? In pure special relativity events and objects have existence independent of the observers, so there the answer is no. There are still things like simultaneity that are bound to particular frames and do not translate, and there are events that cannot be seen from other events due to lightspeed limitations.</p>
<p>In general relativity frames can be curved in complicated ways and whole parts of spacetime can be invisible to some frames. An obvious example is black hole interiors: events there cannot signal to observers located outside. Choosing other coordinate systems can allow reasoning about the whole spacetime, but most do not correspond to anything an actual physical observer could ever observe: they are frames of reference for idealized mathematical observers.</p>
<p>So, does the singularity &quot;really exist&quot; in a frame of reference? Yes, mathematically it is not a problem to extend the spacetime manifold towards the <span class="math-container">$r=0$</span> singularity. Note that you cannot include it in the spacetime manifold: it is in a sense the edge, just as the number <span class="math-container">$1$</span> is not part of the set of numbers <span class="math-container">$&lt;1$</span> despite there being numbers coming arbitrarily close. But it makes sense to speak of a region in spacetime where curvature diverges to infinity as one approaches the edge, so most people slightly sloppily talks about the singularity as being inside whatever reference frame is being used. Mathematicians will disagree.</p>
<p>Note that this is more philosophy of relativity theory issue than a discussion of what is actually going on in actual black holes. Answering this kind of question requires formalizing the words into terms of the theory we use, and then checking the revised question against the theory.</p>

CC BY-SA 4.0
2021-06-11T12:15:10.533Z
The singularity isn't in the past light cone of any observer, even one inside the event horizon. So it's a bit like next Tuesday, it doesn't exist until you get there. ;) Does it even make sense to say that something exists if it doesn't exist yet in your reference frame?
PM 2Ring
CC BY-SA 4.0
2021-06-11T17:26:42.873Z
@PM2Ring - Good point about it always being in the future light-cone. I think this really shows the difference between the frames commonly used in theory that do not correspond to any possible physical observers, and the much more restricted frames of the observers. But whether next Tuesday truly exists is a battle between the presentists, the growing block theorists, and the block universe people in philosophy of time.
Anders Sandberg
CC BY-SA 4.0
2021-06-11T11:34:07.420Z
2021-06-11T11:34:07.420Z
Anders Sandberg
<p>How can one describe this phenomena?
What are the factors that we should consider for solving such a problem?</p>

CC BY-SA 4.0
2021-06-11T12:11:06.727Z
From https://physics.stackexchange.com/a/144458/123208 A singularity in GR is like a piece that has been cut out of the manifold. It's not a point or point-set at all. Because of this, formal treatments of singularities have to do a lot of nontrivial things to define stuff that would be trivial to define for a point set. For example, the formal definition of a timelike singularity is complicated, because it has to be written in terms of light-cones of nearby points.
PM 2Ring
<astrophysics><cosmology><supermassive-black-hole><singularity>
Does black hole singularity really exists with respective to relative frame of reference?
Sivaditya Varma
# Does black hole singularity really exists with respective to relative frame of reference?

(Asked by: username_0 on 2021-06-11)

How can one describe this phenomena?
What are the factors that we should consider for solving such a problem?

**Tags:** astrophysics, cosmology, supermassive-black-hole, singularity

> **Comments:**
> **username_1**: From https://physics.stackexchange.com/a/144458/123208 A singularity in GR is like a piece that has been cut out of the manifold. It's not a point or point-set at all. Because of this, formal treatments of singularities have to do a lot of nontrivial things to define stuff that would be trivial to define for a point set. For example, the formal definition of a timelike singularity is complicated, because it has to be written in terms of light-cones of nearby points.  

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## 1 answers

### Answer by username_2 on 2021-06-11. Score: 1

The question is really about how to turn a loose question into something that has an answer; to some degree this is a logic and philosophy question rather than astronomy, so don't get surprised if it gets closed.

The key thing here is the concepts "really exists" and "with respect to relative frame of reference" - what does that mean?

In relativity theory there are many possible frames of reference, typically described that what different kinds of observers would observe or as different coordinate systems for the same underlying spacetime. The theory describes how to translate from one frame to another one.

Can something really exist just in relation to some frames of reference? In pure special relativity events and objects have existence independent of the observers, so there the answer is no. There are still things like simultaneity that are bound to particular frames and do not translate, and there are events that cannot be seen from other events due to lightspeed limitations.

In general relativity frames can be curved in complicated ways and whole parts of spacetime can be invisible to some frames. An obvious example is black hole interiors: events there cannot signal to observers located outside. Choosing other coordinate systems can allow reasoning about the whole spacetime, but most do not correspond to anything an actual physical observer could ever observe: they are frames of reference for idealized mathematical observers.

So, does the singularity "really exist" in a frame of reference? Yes, mathematically it is not a problem to extend the spacetime manifold towards the $r=0$ singularity. Note that you cannot include it in the spacetime manifold: it is in a sense the edge, just as the number $1$ is not part of the set of numbers $<1$ despite there being numbers coming arbitrarily close. But it makes sense to speak of a region in spacetime where curvature diverges to infinity as one approaches the edge, so most people slightly sloppily talks about the singularity as being inside whatever reference frame is being used. Mathematicians will disagree.

Note that this is more philosophy of relativity theory issue than a discussion of what is actually going on in actual black holes. Answering this kind of question requires formalizing the words into terms of the theory we use, and then checking the revised question against the theory.

> **Comments:**
> **username_1**: The singularity isn't in the past light cone of any observer, even one inside the event horizon. So it's a bit like next Tuesday, it doesn't exist until you get there. ;) Does it even make sense to say that something exists if it doesn't exist yet in your reference frame?  
> **username_2**: @username_1 - Good point about it always being in the future light-cone. I think this really shows the difference between the frames commonly used in theory that do not correspond to any possible physical observers, and the much more restricted frames of the observers. But whether next Tuesday truly exists is a battle between the presentists, the growing block theorists, and the block universe people in philosophy of time.  

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