Sun can absorb almost 200,000 more Suns?

  • Context: Graduate 
  • Thread starter Thread starter victorvmotti
  • Start date Start date
  • Tags Tags
    Sun
Click For Summary

Discussion Overview

The discussion revolves around the theoretical limits of mass-energy that the Sun can contain without collapsing, as derived from Buchdahl's Theorem. Participants explore the implications of this theorem in the context of the Sun's current mass and radius, considering both theoretical calculations and physical realities.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Exploratory

Main Points Raised

  • Some participants assert that calculations based on Buchdahl’s Theorem suggest the Sun could absorb almost 200,000 more Suns without collapsing.
  • Others argue that with such an increase in mass, the Sun would become a black hole, with the event horizon at its current surface, indicating a collapse is inevitable.
  • A participant highlights that Buchdahl's Theorem assumes incompressible material and constant density, which does not apply to the Sun, suggesting the theoretical maximum mass may not be achievable.
  • Another participant notes that the only conditions of the theorem that the Sun satisfies are its mass and radius, implying limitations in applying the theorem directly to the Sun.
  • Quotations from Sean Carroll's work are presented, emphasizing that exceeding the mass limit leads to no static solutions in general relativity, which supports the idea of inevitable collapse into a black hole.
  • There is a discussion about the difference between "radius" and "circumference" of the Sun, with a participant indicating that while it could be a point of contention, it may not be significant enough to warrant further debate.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Buchdahl's Theorem to the Sun, with some agreeing on the theoretical limits while others emphasize the physical realities that prevent reaching those limits. The discussion remains unresolved regarding the implications of the theorem in the context of the Sun.

Contextual Notes

Participants note that Buchdahl's Theorem relies on assumptions that may not hold for the Sun, such as constant density and incompressibility, which could affect the validity of the maximum mass calculations.

victorvmotti
Messages
152
Reaction score
5
The maximum mass-energy allowable inside a sphere to ensure a static Star is obtained from Buchdahl’s Theorem:

M(max)=4/9*R/G*c^2

Calculations show that Sun can absorb almost 200,000 more Suns and remain it its current radius and stay away from collapsing.

Is this correct?
 
Astronomy news on Phys.org
With 200 000 times its mass, the sun would be a black hole where the event horizon would be roughly at the current surface of sun. For realistic objects, this is certainly beyond a collapse.

If you try to produce such an object by adding more and more mass from the outside, however, you produce a star with extremely strong stellar winds that will prevent more mass from getting added.
 
mfb said:
With 200 000 times its mass, the sun would be a black hole where the event horizon would be roughly at the current surface of sun. For realistic objects, this is certainly beyond a collapse.

If you try to produce such an object by adding more and more mass from the outside, however, you produce a star with extremely strong stellar winds that will prevent more mass from getting added.

I was essentially trying to picture a thought experiment here.

How much mass-energy could fit into the current radius of Sun, referring to the condition of a static Star obtained from Buchdahl’s Theorem, which sets the upper limit.
 
victorvmotti said:
The maximum mass-energy allowable inside a sphere to ensure a static Star is obtained from Buchdahl’s Theorem:

M(max)=4/9*R/G*c^2

Calculations show that Sun can absorb almost 200,000 more Suns and remain it its current radius and stay away from collapsing.

Is this correct?

Buchdahl's theorem assumes that the material the object (in this case the sun) is made of is incompressible and of constant density, i.e. that it's proper volume doesn't shrink under pressure. This isn't the case for the sun, so I wouldn't expect the theoretical maximum mass given by the theorem to be reached.
 
Pretty much the only conditions of the theorem that the sun satisfies are that it has a mass and a radius.
 
  • Like
Likes   Reactions: 1 person
Let me quote from Sean Carroll in his book Spacetime and Geometry.

After introducing the maximum mass-energy allowable equation on page 234 he writes:

"Thus, if we try to squeeze a greater mass than this inside a radius R, general relativity admits no static solutions; a star that shrinks to such a size must inevitably keep shrinking, eventually forming a black hole. We derived this result from the rather strong assumption that the density is constant, but it continues to hold when that assumption considerably weakened."
 
victorvmotti said:
Let me quote from Sean Carroll in his book Spacetime and Geometry.

After introducing the maximum mass-energy allowable equation on page 234 he writes:

"Thus, if we try to squeeze a greater mass than this inside a radius R, general relativity admits no static solutions; a star that shrinks to such a size must inevitably keep shrinking, eventually forming a black hole. We derived this result from the rather strong assumption that the density is constant, but it continues to hold when that assumption considerably weakened."

Your original post:
victorvmotti said:
Calculations show that Sun can absorb almost 200,000 more Suns and remain it its current radius and stay away from collapsing.

didn't state this. Your followup:
victorvmotti said:
How much mass-energy could fit into the current radius of Sun,

basically asserts correctly that Buchdal's theorem gives an upper limit to the mass that would fit into an object with the circumference of the sun. (We could quibble some over the difference between "radius of the sun" and "circumference of the sun", but I'm currently not thinking that the issue is important enough to argue about).

The point that the theoretical upper limit given by the theorem wouldn't be reached if you used the hydrogen/helium/other mix that the sun uses is the point I was trying to convey.

This isn't the case for the sun, so I wouldn't expect the theoretical maximum mass given by the theorem to be reached.
 
pervect said:
Your original post:

but I'm currently not thinking that the issue is important enough to argue about.

Can you explain the difference and why is it so?
 

Similar threads

  • · Replies 49 ·
2
Replies
49
Views
5K
Replies
17
Views
4K
  • · Replies 20 ·
Replies
20
Views
4K
  • · Replies 12 ·
Replies
12
Views
9K
  • · Replies 9 ·
Replies
9
Views
923
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 21 ·
Replies
21
Views
3K