The threshold of general relativity gravity

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Discussion Overview

The discussion revolves around the threshold of general relativity in relation to gravitational effects of massive objects, particularly focusing on the Schwarzschild radius and its implications for black holes. Participants explore theoretical aspects, including energy ratios, the nature of micro black holes, and the relationship between the universe and black holes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants reference Padmanabhan's work to discuss the limitations of Newtonian gravity for massive objects confined to small regions, suggesting that general relativity effects become significant.
  • There is a proposal to explore the relationship between mass and radius using the Schwarzschild metric or Einstein field equations, rather than relying solely on energy ratios.
  • Questions are raised about the existence of a lower limit on the Schwarzschild radius, particularly in the context of hypothetical micro black holes formed from extremely small sizes filled with large masses.
  • Some participants mention that while there is a theoretical lower limit for the Schwarzschild radius, the lack of a complete theory of quantum gravity complicates the discussion.
  • The idea of an upper limit on the Schwarzschild radius is introduced, with inquiries about whether the universe could be considered inside a black hole based on current energy density parameters.
  • Contrasting views emerge regarding the nature of the universe compared to black holes, with some asserting that the universe is isotropic and uniform, unlike the directional nature of black holes.
  • Discussions about string theory and quantum gravity reveal differing interpretations of their implications for the Schwarzschild radius and the Planck length.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the implications of the Schwarzschild radius, the nature of black holes, and the relationship between string theory and quantum gravity. The discussion remains unresolved with no consensus on several key points.

Contextual Notes

Limitations include the dependence on definitions of black holes, the unresolved nature of quantum gravity, and the speculative aspects of relating the universe to black holes.

victorvmotti
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In Padmanabhan's Theoretical Astrophysics by defining a ratio for comparing gravitational potential energy with rest-mass energy it is shown that if massive objects with M=10^33 gm are confined to small regions with R= 1km then we cannot use Newtonian gravity because the system has general relativity effects.

I wonder if we do not use an energy ratio and instead use only Schwarzschild metric or Einstein field equations can we infer the same ratio between mass and radius?

I already see that Schwarzschild vacuum solution is asymptotically flat because the ratio of Schwarzschild radius over radius vanishes if the radius coordinate approaches infinity.

But establishing the above mentioned ratio of mass and radius for the threshold of general relativity without using the energy argument is not immediately clear.
 
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victorvmotti said:
In Padmanabhan's Theoretical Astrophysics by defining a ratio for comparing gravitational potential energy with rest-mass energy it is shown that if massive objects with M=10^33 gm are confined to small regions with R= 1km then we cannot use Newtonian gravity because the system has general relativity effects.

I wonder if we do not use an energy ratio and instead use only Schwarzschild metric or Einstein field equations can we infer the same ratio between mass and radius?
For a given mass M, the Schwarzschild radius is Rs = 2GM/c2.

For m = 1033 gm, Rs = 2(6.6x10-8)(1033)/(3x1010)2 ≈ 105 cm = 1 km.
 
Is there any lower limit on Rs here?

I mean if we imagine a size almost equal to the hydrogen atom 0.5*10^-8 cm filled with a mass of 3.4*10^19 gm then what? Should we call this a candidate of a micro black hole?
 
victorvmotti said:
Is there any lower limit on Rs here?
I mean if we imagine a size almost equal to the hydrogen atom 0.5*10^-8 cm filled with a mass of 3.4*10^19 gm then what? Should we call this a candidate of a micro black hole?

Well one thing you should realize is there is a lower limit that we can apply Rs is one of debates of String Theory vs. Quantum Gravity.

For example, string theory would make the lower limit the "length of a string", but quantum gravity makes it a much smaller Plank length.

Now if you believe in Hawking Radiation is the dominant form of radiation from black holes(*), then a black hole the size of a hydrogen atom would only last for a couple of picoseconds or nanoseconds.*https://en.wikipedia.org/wiki/Eddington_luminosity anyone? ... darn tough crowd tonight for making Star Trek 2009 astrophysics jokes.
 
What about an upper limit on Rs?

Can we use the same ratio to determine if the whole universe is indeed inside a black hole?

What would be the mass here for the ratio and the related Rs?

Can we use the current epoch energy density parameter, that is \Omega = 1, then obtain the observable universe mass and see if the radius of the observable universe is less than Rs?
 
victorvmotti said:
What about an upper limit on Rs?
Can we use the same ratio to determine if the whole universe is indeed inside a black hole?
No, this is a common misconception. There is no similarity at all between the universe we observe and a black hole.

A black hole, after all, has an inside and an outside. At any point it has a preferred direction, namely the radial direction, and consequently at that point the collapse is not isotropic.

By contrast the universe we observe is uniform, apparently flat and infinite, and expanding at the same rate in all directions.
 
Last edited:
piareround said:
Well one thing you should realize is there is a lower limit that we can apply Rs is one of debates of String Theory vs. Quantum Gravity.

For example, string theory would make the lower limit the "length of a string", but quantum gravity makes it a much smaller Plank length.

I'm not a specialist in quantum gravity, but I don't think this is right. String theory *is* supposed to be a theory of quantum gravity, and the length of the strings in string theory is presumed to *be* the Planck length.
 
bcrowell said:
I'm not a specialist in quantum gravity, but I don't think this is right. String theory *is* supposed to be a theory of quantum gravity, and the length of the strings in string theory is presumed to *be* the Planck length.
Ben is right. (And he survived the Earthquake!) :wink:
 
  • #10
Bill_K said:
(And he survived the Earthquake!) :wink:

But I think my terrier is going to need therapy.
 

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