B How Planetary Bodies Affect Space Time

[BL4CKB0X97]

Hello.

I was thinking about gravity and how matter bends the ST (space time) creating gravity.which lead on to singularities. I wondered how much mass it would take to either make a hole in spacetime, or how much it would take to make a black hole. So I googled it.

This is where my confusion became apparent.

Firstly: Are black holes literal holes in St, or are they just warps(I think it's the right Word) so much that matter can't get out, like a spider in a bath tub.

Secondly: it is not just mass that effects ST , but energy too. Is it every type of energy in a scenic body? Such as as the Kinetic energy, potential energy and electric?

Even links to useful websites and papers will be great. Thanks.

 

[mfb]

Black holes are very strong deformations in spacetime. They are not literal holes. They just share the property "if you throw something in, it doesn't come out again".

Every type of energy affects spacetime. The source of spacetime deformation is the stress-energy tensor. Mass doesn't even appear explicitly there, it just acts via its energy.

 

[BL4CKB0X97]

Black holes are very strong deformations in spacetime. They are not literal holes. They just share the property "if you throw something in, it doesn't come out again".

Every type of energy affects spacetime. The source of spacetime deformation is the stress-energy tensor. Mass doesn't even appear explicitly there, it just acts via its energy.

Thanks.

 

[pervect]

Hello.

I was thinking about gravity and how matter bends the ST (space time) creating gravity.which lead on to singularities. I wondered how much mass it would take to either make a hole in spacetime, or how much it would take to make a black hole. So I googled it.

This is where my confusion became apparent.

Firstly: Are black holes literal holes in St, or are they just warps(I think it's the right Word) so much that matter can't get out, like a spider in a bath tub.

Except at the singularity itself, which is excluded from the space-time, the space-time around a black hole has a geometry. So I would go with "warped" as the less misleading description. The exclusion of the singularity could be regarded as a sort of "pinprick" in space-time, limited to a single point that's removed from the space-time in the classical view.

Secondly: it is not just mass that effects ST , but energy too. Is it every type of energy in a scenic body? Such as as the Kinetic energy, potential energy and electric?

Even links to useful websites and papers will be great. Thanks.

The mathematical entity that warps space-time is called the "stress energy tensor". It's found on the right hand side of Einstein's Field equations (EFE), $G_{\mu\nu} = 8 \pi T_{\mu\nu}$. The left hand side $G_{\mu\nu}$ is the Einstein tensor, it is derived from the curvature of space-time. The right hand side, $T_{\mu\nu}$ is the stress energy tensor, which can be described as the density (or flow) of energy-momentum. This view is summed up informally in Wheeler's famous quote "Spacetime tells matter how to move; matter tells spacetime how to curve."

One place the stress-energy tensor is mentioned in Baez's paper "The Meaning of Einstein's equation" , <link>. As Baez remarks, it's probably too difficult to get into the details of general realtivity (GR) unless one is already familiar with special relativity (SR). The origin of the stress-energy tensor comes from SR, though introducing it in detail is usually deferred to GR textbooks. To give a vague verbal description, SR first suggest that energy and momentum should be unified in the same manner as space and time are. I don't know your background, but I would suspect that the whole idea of unifying space and time into a single entity is something you've seen referred to, but the motivations probably seems mysterious at this point.

Without going into too much details, though, the stress-energy tensor, the entity on the right hand side of the EFE's, can be described as the density, or flow (different authors use different words) of energy-momentum. Non-intuitively, pressure is part of the stress-energy tensor as well, so another overview of the EFE's is to say that energy, momentum, and pressure all curve space-time.

 

[BL4CKB0X97]

Except at the singularity itself, which is excluded from the space-time, the space-time around a black hole has a geometry. So I would go with "warped" as the less misleading description. The exclusion of the singularity could be regarded as a sort of "pinprick" in space-time, limited to a single point that's removed from the space-time in the classical view.
The mathematical entity that warps space-time is called the "stress energy tensor". It's found on the right hand side of Einstein's Field equations (EFE), $G_{\mu\nu} = 8 \pi T_{\mu\nu}$. The left hand side $G_{\mu\nu}$ is the Einstein tensor, it is derived from the curvature of space-time. The right hand side, $T_{\mu\nu}$ is the stress energy tensor, which can be described as the density (or flow) of energy-momentum. This view is summed up informally in Wheeler's famous quote "Spacetime tells matter how to move; matter tells spacetime how to curve."

One place the stress-energy tensor is mentioned in Baez's paper "The Meaning of Einstein's equation" , <link>. As Baez remarks, it's probably too difficult to get into the details of general realtivity (GR) unless one is already familiar with special relativity (SR). The origin of the stress-energy tensor comes from SR, though introducing it in detail is usually deferred to GR textbooks. To give a vague verbal description, SR first suggest that energy and momentum should be unified in the same manner as space and time are. I don't know your background, but I would suspect that the whole idea of unifying space and time into a single entity is something you've seen referred to, but the motivations probably seems mysterious at this point.

Without going into too much details, though, the stress-energy tensor, the entity on the right hand side of the EFE's, can be described as the density, or flow (different authors use different words) of energy-momentum. Non-intuitively, pressure is part of the stress-energy tensor as well, so another overview of the EFE's is to say that energy, momentum, and pressure all curve space-time.

That helps a lot,exactly what I needed. Thanks.