Exploring Deep Space: A GR Analysis

In summary: I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
  • #1
Satyam
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Thank you all for clearing my doubt before. There is a question I want to ask on space and time and this time it is not about the absolute time as I have understood fairly that space and time are always relative.
So Here it is according to GR It is very beautifully explained that Very massive objects manipultes space and time , as they bends the space- time fabric and as a consequence give rise to gravity. This shows how gravity actually behaves.
I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?
 
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  • #2
Satyam said:
I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?

I don't understand the question.
 
  • #3
PeterDonis said:
I don't understand the question.
How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
 
  • #4
Satyam said:
How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
There is no total emptiness. Energy counts, too, and gravitation acts infinitely. But what do you want to describe, if there is nothing to describe?
 
  • #5
Satyam said:
How we will acknowledge that space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric or in other words how to describe the domain of deep empty spaces in this ever expanding cosmos.?
It's all spacetime. The only difference is how curved it is and in what way it is curved.
 
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  • #6
Satyam said:
I want to ask you then what we will call or how we will acknowledge that space and time which has not been manipulated or in other words describe something in domain of deep empty spaces in this ever expanding cosmos.?
I am not sure what you are asking since you seem to be asking about two different spacetimes.

A spacetime without any mass or energy is called a vacuum spacetime. The simplest vacuum spacetime is the Minkowski spacetime which is flat (no curvature) everywhere.

The spacetime which describes the cosmos as a whole is the FLRW spacetime also called LCDM for a specific equation of state.
 
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  • #7
Satyam said:
space and time which has not been manipulated i.e the space and time fabric which has not been bend as there is no planet , star or massive object to manipulate the space time fabric

Ok, then you're talking about the flat Minkowski spacetime of special relativity. Which does not actually exist; it's an idealization only, useful for certain purposes.

Satyam said:
how to describe the domain of deep empty spaces in this ever expanding cosmos.?

As an appropriate curved spacetime geometry, since there is matter and energy in the universe. The fact that there might not be matter or energy in some particular region does not mean there is no spacetime curvature in that region; there can be spacetime curvature there due to the presence of matter or energy elsewhere in the universe.
 
  • #8
Dale said:
I am not sure what you are asking since you seem to be asking about two different spacetimes.

A spacetime without any mass or energy is called a vacuum spacetime. The simplest vacuum spacetime is the Minkowski spacetime which is flat (no curvature) everywhere.

The spacetime which describes the cosmos as a whole is the FLRW spacetime also called LCDM for a specific equation of state.
So are there actually two dimensions/ models of space-time. One is vacuum space-time and other FLRW. ?
 
  • #9
Ibix said:
It's all spacetime. The only difference is how curved it is and in what way it is curved.
I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
 
  • #10
Satyam said:
So are there actually two dimensions/ models of space-time. One is vacuum space-time and other FLRW. ?
No. There's one model of spacetime, a 4d manifold. Depending on what's in that spacetime it has different curvature, and we give names to the different curvatures we get under circumstances. Spacetime around a non-rotating black hole is called Schwarzschild spacetime. Spacetime in a large enough empty region is flat and is called Minkowski spacetime. Spacetime on a large enough scale that galaxies are too small to see is FLRW spacetime.
Satyam said:
I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
It's spacetime with zero curvature. We do not have a more fundamental model, so there isn't any further layer of explanation.
 
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  • #11
PeterDonis said:
Ok, then you're talking about the flat Minkowski spacetime of special relativity. Which does not actually exist; it's an idealization only, useful for certain purposes.
As an appropriate curved spacetime geometry, since there is matter and energy in the universe. The fact that there might not be matter or energy in some particular region does not mean there is no spacetime curvature in that region; there can be spacetime curvature there due to the presence of matter or energy elsewhere in the universe.
The space - time is always curved is hard to digest. Because the % occupied by matter and energy I'd only 5% of the total cosmos. The respective is dark matter and energy . Can we say that flat or unmanipulated space- time anddark matter and energy are same?
Here is the link of the blog.
https://en.m.wikipedia.org/wiki/Dark_matter
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
 
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  • #12
Satyam said:
The space - time is always curved is hard to digest. Because the % occupied by matter and energy I'd only 5% of the total cosmos.
Matter, energy, dark matter, dark energy. They all curve space time. The difference between the dark stuff and the non-dark stuff is that we can see the latter. Hence the names.
Can we say that flat or unmanipulated space- time anddark matter and energy are same?
No. Not even close.
Here is the link of the blog.
https://en.m.wikipedia.org/wiki/Dark_matter
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
The latter reference does not say what you think it says. Space-time curvature is a tensor, not a scalar. The fact that we live in an expanding universe means that the tensor is not identically zero.

However, we can observe some symmetries. And if we adopt the "co-moving" coordinate system where the expansion is uniform in all directions then we can slice space-time up into spatial slices (each corresponding to a moment in time according to our coordinate system) and ask whether these spatial slices are each flat. The curvature of a 3-dimensional space is a scalar. It can be positive, negative or zero. It is this curvature of these spatial slices which the latter article is speaking of. Not space-time curvature.
 
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  • #13
Satyam said:
So are there actually two dimensions/ models of space-time. One is vacuum space-time and other FLRW. ?
There are an infinite number of models of space-time corresponding to an infinite number of distributions of matter. Some of the more useful or easy to calculate models have names. You were asking about two of those (as far as I could tell).

Satyam said:
I'm asking about that space- time which is not curved. i.e what is the nature of that space-time which is not curved.
That is the flat Minkowski solution. However you also asked:
Satyam said:
domain of deep empty spaces in this ever expanding cosmos.?
Which is not flat and is the FLRW spacetime instead.

Satyam said:
Because the % occupied by matter and energy I'd only 5% of the total cosmos.
This is not correct. In the FLRW spacetime one of the assumptions is homogeneity which means that 100% of the cosmos is occupied by matter at the largest scales. Remember, we are talking about cosmological scales, so at cosmological scales every part of the universe contains a mix of matter, dark matter, energy, and dark energy. The percentages you mention describe the ratio of this mixture, not the spatial distribution which is homogenous.
 
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  • #14
Satyam said:
The space - time is always curved is hard to digest.
Gravity has infinite range as far as we are aware. So spacetime will be (possibly very slightly) curved everywhere if it is curved anywhere.
Satyam said:
Here some scientific theory have also proved that flat space-time exists. Have a look
https://en.m.wikipedia.org/wiki/Shape_of_the_universe
This says that there are spatially flat FLRW solutions, not that spacetime curvature is zero. These are not the same thing.
 
  • #15
Dale said:
There are an infinite number of models of space-time corresponding to an infinite number of distributions of matter. Some of the more useful or easy to calculate models have names. You were asking about two of those (as far as I could tell).

That is the flat Minkowski solution. However you also asked:
Which is not flat and is the FLRW spacetime instead.

This is not correct. In the FLRW spacetime one of the assumptions is homogeneity which means that 100% of the cosmos is occupied by matter at the largest scales. Remember, we are talking about cosmological scales, so at cosmological scales every part of the universe contains a mix of matter, dark matter, energy, and dark energy. The percentages you mention describe the ratio of this mixture, not the spatial distribution which is homogenous.
Can you throw more light on homogeneous spatial distribution and how would our universe look if it was heterogeneous..?
 
  • #16
Satyam said:
Can you throw more light on homogeneous spatial distribution and how would our universe look if it was heterogeneous..?
We might see different numbers of galaxies in different parts of the sky, or more galaxies further away than nearby. On average at large scales, we don't see this - the universe is pretty much the same in every direction.
 
  • #17
jbriggs444 said:
Matter, energy, dark matter, dark energy. They all curve space time. The difference between the dark stuff and the non-dark stuff is that we can see the latter. Hence the names.

No. Not even close.

The latter reference does not say what you think it says. Space-time curvature is a tensor, not a scalar. The fact that we live in an expanding universe means that the tensor is not identically zero.

However, we can observe some symmetries. And if we adopt the "co-moving" coordinate system where the expansion is uniform in all directions then we can slice space-time up into spatial slices (each corresponding to a moment in time according to our coordinate system) and ask whether these spatial slices are each flat. The curvature of a 3-dimensional space is a scalar. It can be positive, negative or zero. It is this curvature of these spatial slices which the latter article is speaking of. Not space-time curvature.
However if the observable universe is expanding which the results shows it is then it's volume must be increasing or the space in the universe is getting increasing.
For analogy we can say that if we put gas into a balloon it's volume get increased and as it volume increases it displaces the air around it. So it takes over air and displaces it as the volume increases.

So in the case of this cosmos as it is expanding then what are the characteristics of that domain in which it is expanding into..?
 
  • #18
Ibix said:
We might see different numbers of galaxies in different parts of the sky, or more galaxies further away than nearby. On average at large scales, we don't see this - the universe is pretty much the same in every direction.
Okay the universe is same in every direction is an indication of it's isotropic behaviour. What about it's homogeneity?
 
  • #19
Satyam said:
Okay the universe is same in every direction is an indication of it's isotropic behaviour. What about it's homogeneity?
Homogeneity means that it's the same everywhere, at all distances. That does imply isotropy too.
 
  • #20
Ibix said:
Homogeneity means that it's the same everywhere, at all distances. That does imply isotropy too.
Your statement is incorrect.
Isotropy is about exhibiting same properties in every direction while homogeneity is about uniform composition. Here are two examples
1. An example of something that is homogeneous but not isotropic is a space that is filled with a uniform electric or magnetic field. Because the field is uniform it is homogeneous, but because the field has a direction, it is not isotropic.

Similarly, it's easy to see how something can be isotropic but not homogeneous. For example, a spherically symmetric distribution of mass is isotropic for an observer at the center of the sphere, but is not necessarily homogenous.
 
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  • #21
Satyam said:
Your statement is incorrect.

No, his statement was correct.

Satyam said:
Isotropy is about exhibiting same properties in every direction while homogeneity is about uniform composition.

Homogeneity is not just about "uniform composition". It means uniformity everywhere in space, period. And that, as @Ibix said, implies isotropy as well; a universe which is the same at every point in space will also be the same in every direction from every point in space.
 
  • #22
PeterDonis said:
No, his statement was correct.
Homogeneity is not just about "uniform composition". It means uniformity everywhere in space, period. And that, as @Ibix said, implies isotropy as well; a universe which is the same at every point in space will also be the same in every direction from every point in space.
Ok Sir. I'm not here to debate anyone. Can you tell me more about spatial distribution of matter as my purpose was to get a clear picture of this.
 
  • #23
Satyam said:
An example of something that is homogeneous but not isotropic is a space that is filled with a uniform electric or magnetic field.

A region of space can be homogeneous in this sense, but the universe as a whole cannot; it's impossible to have a uniform EM field everywhere in the universe.

Satyam said:
Can you tell me more about spatial distribution of matter

For what spacetime? So far we have discussed four possibilities in this thread: flat Minkowski spacetime, Schwarzschild spacetime, FRW spacetime, and our actual universe (which is not exactly described by any of those). Which one are you asking about?
 
  • #24
PeterDonis said:
A region of space can be homogeneous in this sense, but the universe as a whole cannot; it's impossible to have a uniform EM field everywhere in the universe.
For what spacetime? So far we have discussed four possibilities in this thread: flat Minkowski spacetime, Schwarzschild spacetime, FRW spacetime, and our actual universe (which is not exactly described by any of those). Which one are you asking about?
How spatial distribution is homogeneous in our actual/ observable universe.
 
  • #25
Satyam said:
About our actual/ observable universe.

Then, as I said, our actual/observable universe is not described exactly by any of the spacetimes we have discussed, but FRW spacetime is closest. Our actual/observable universe is not exactly isotropic or homogeneous, but it is to a good approximation on scales of about 100 million light-years and larger. So an FRW spacetime is a good approximation to the actual spacetime geometry on these scales.
 
  • #26
Sir on what reference we are saying that it is homogeneous. In order to understand FLRW Model. It is important to grasp why it is considered homogeneous?
 
  • #27
Satyam said:
It is important to grasp why it is considered homogeneous?
Because that's a pretty good approximation to what we see through telescopes.
 
  • #28
Satyam said:
However if the observable universe is expanding which the results shows it is then it's volume must be increasing or the space in the universe is getting increasing.
When we talk about the universe expanding, we are not normally talking about an increase in the radius of the observable universe. Rather we are talking about the fact that all of the [large scale] things in the universe are getting farther apart.

If the universe as a whole is infinite, then it does not have a defined volume. So it is not correct to talk about its volume increasing or decreasing.
So in the case of this cosmos as it is expanding then what are the characteristics of that domain in which it is expanding into..?
There is no such domain. It is not that sort of expansion. It is not expanding to fill some existing empty space. It is simply expanding. Distances are getting greater. There is no need consider our universe as somehow embedded within a higher dimensional space in order to describe its expansion.

Edit...

You had invoked the balloon analogy, pointing out that when the balloon expends, it displaces air. This is a good example of what it means to have a lower-dimensional space embedded in a higher dimensional space. The surface of the balloon is a two dimensional space. We picture it embedded in a pre-existing three dimensional space. We do that because it is easy to imagine.

But there is no requirement for the three dimensional space to actually exist. One can describe all of the relevant properties of a two dimensional surface with a spherical topology without ever considering it to exist within a three dimensional space. One can do it with a two dimensional coordinate system (like latitude and longitude). The trick is to use a distance metric that is different from the euclidean ##\sqrt{x^2 + y^2}## one. [One also has to split it up into multiple patches -- that's what we call a manifold].

Same for our four-dimensional space-time. We can describe the relevant properties in terms of a metric rather than in terms of some euclidean hyper-space within which it is hypothetically embedded.
 
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  • #29
Satyam said:
In order to understand FLRW Model. It is important to grasp why it is considered homogeneous?

The FRW model is homogeneous by construction; it is a model explicitly constructed to be homogeneous.

Our actual universe, as I said, is not exactly homogeneous, but is homogeneous to a good approximation on scales of about 100 million light years and larger. We know that from astronomical observations.
 
  • #30
Satyam said:
Can you throw more light on homogeneous spatial distribution and how would our universe look if it was heterogeneous..?
If the universe were not spatially homogenous and isotropic then it would look different at different directions and distances (after accounting for light travels time). For instance, if the universe had an edge and if we were close to it then we would not see distant objects in that direction.

Satyam said:
So in the case of this cosmos as it is expanding then what are the characteristics of that domain in which it is expanding into..?
We have no evidence that such a domain exists. It certainly is not necessary for general relativity.
 
  • #31
jbriggs444 said:
When we talk about the universe expanding, we are not normally talking about an increase in the radius of the observable universe. Rather we are talking about the fact that all of the [large scale] things in the universe are getting farther apart.

If the universe as a whole is infinite, then it does not have a defined volume. So it is not correct to talk about its volume increasing or decreasing.

There is no such domain. It is not that sort of expansion. It is not expanding to fill some existing empty space. It is simply expanding. Distances are getting greater. There is no need consider our universe as somehow embedded within a higher dimensional space in order to describe its expansion.

Edit...

You had invoked the balloon analogy, pointing out that when the balloon expends, it displaces air. This is a good example of what it means to have a lower-dimensional space embedded in a higher dimensional space. The surface of the balloon is a two dimensional space. We picture it embedded in a pre-existing three dimensional space. We do that because it is easy to imagine.

But there is no requirement for the three dimensional space to actually exist. One can describe all of the relevant properties of a two dimensional surface with a spherical topology without ever considering it to exist within a three dimensional space. One can do it with a two dimensional coordinate system (like latitude and longitude). The trick is to use a distance metric that is different from the euclidean ##\sqrt{x^2 + y^2}## one. [One also has to split it up into multiple patches -- that's what we call a manifold].

Same for our four-dimensional space-time. We can describe the relevant properties in terms of a metric rather than in terms of some euclidean hyper-space within which it is hypothetically embedded.
I thought we do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper like an 'infinite' sheet of paper and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus i.e like a doughnut. The surface of the torus is also spatially flat, but it is finite. So we have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.
 
  • #32
Satyam said:
I thought we do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper like an 'infinite' sheet of paper and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus i.e like a doughnut. The surface of the torus is also spatially flat, but it is finite. So we have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.
Again, that is not a flat Universe. That is a flat spatial slice of a universe. I did not make a claim one way or the other about the size of such a slice.
 
  • #33
Satyam said:
Sir on what reference we are saying that it is homogeneous. In order to understand FLRW Model. It is important to grasp why it is considered homogeneous?
The frame where it is homogenous and isotropic is called the comoving frame or comoving coordinates. Those are the standard coordinates for cosmology.

Regarding if it is important: I would say yes. The assumption of homogeneity and isotropy greatly constrains the form of the possible solutions. That is what makes it one of the few analytically tractable spacetime models.
 
  • #34
Isotropy everywhere implies homogeneity everywhere. However homogeneity (everywhere) does not imply isotropy. Consider a geometrically flat cylinder. It is homogeneous but not isotropic.
 
  • #35
jbriggs444 said:
Again, that is not a flat Universe. That is a flat spatial slice of a universe. I did not make a claim one way or the other about the size of such a slice.
The surface of the torus is termed as flat and surface is a slice of 3d as it is 2d. The point on which I want to drag your attention is that the universe can be in the form of torus and as there are no ends to it , it can be termed as endless universe. But being endless doesn't mean it is infinite.
We don't know yet the universe is finite or infinite.

jbriggs444 said:
If the universe as a whole is infinite, then it does not have a defined volume. So it is not correct to talk about its volume increasing or decreasing.
Is this correct to term universe as infinite and then making a statement based on that..?
 
<h2>1. What is GR Analysis?</h2><p>GR Analysis stands for General Relativity Analysis, which is a mathematical framework used to describe the effects of gravity on the motion of objects in space. It is based on Albert Einstein's theory of general relativity and is used to study the behavior of objects in deep space.</p><h2>2. How is GR Analysis used in exploring deep space?</h2><p>GR Analysis is used to study the gravitational effects of massive objects such as stars, galaxies, and black holes on the motion of other objects in space. It helps scientists understand the curvature of space-time and how it affects the trajectory of objects in deep space.</p><h2>3. What are some of the challenges of exploring deep space using GR Analysis?</h2><p>One of the main challenges is the vast distances involved in deep space exploration. This makes it difficult to gather accurate data and requires advanced technologies to study the effects of gravity. Another challenge is the complexity of the mathematical equations involved in GR Analysis, which require a high level of expertise to understand and interpret.</p><h2>4. What are some recent discoveries made using GR Analysis in deep space exploration?</h2><p>GR Analysis has helped scientists discover the existence of gravitational waves, which are ripples in space-time caused by the collision of massive objects. It has also provided evidence for the existence of black holes and has been used to study the expansion of the universe and the behavior of dark matter.</p><h2>5. How does GR Analysis contribute to our understanding of the universe?</h2><p>GR Analysis is a crucial tool in understanding the fundamental laws of the universe. It has helped us gain insights into the behavior of objects in deep space, the structure of the universe, and the nature of gravity. It also plays a significant role in the development of new technologies for space exploration and has led to many groundbreaking discoveries in the field of astrophysics.</p>

1. What is GR Analysis?

GR Analysis stands for General Relativity Analysis, which is a mathematical framework used to describe the effects of gravity on the motion of objects in space. It is based on Albert Einstein's theory of general relativity and is used to study the behavior of objects in deep space.

2. How is GR Analysis used in exploring deep space?

GR Analysis is used to study the gravitational effects of massive objects such as stars, galaxies, and black holes on the motion of other objects in space. It helps scientists understand the curvature of space-time and how it affects the trajectory of objects in deep space.

3. What are some of the challenges of exploring deep space using GR Analysis?

One of the main challenges is the vast distances involved in deep space exploration. This makes it difficult to gather accurate data and requires advanced technologies to study the effects of gravity. Another challenge is the complexity of the mathematical equations involved in GR Analysis, which require a high level of expertise to understand and interpret.

4. What are some recent discoveries made using GR Analysis in deep space exploration?

GR Analysis has helped scientists discover the existence of gravitational waves, which are ripples in space-time caused by the collision of massive objects. It has also provided evidence for the existence of black holes and has been used to study the expansion of the universe and the behavior of dark matter.

5. How does GR Analysis contribute to our understanding of the universe?

GR Analysis is a crucial tool in understanding the fundamental laws of the universe. It has helped us gain insights into the behavior of objects in deep space, the structure of the universe, and the nature of gravity. It also plays a significant role in the development of new technologies for space exploration and has led to many groundbreaking discoveries in the field of astrophysics.

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