Can the BTZ Black Hole Solutions Be Valid with Different Cosmological Constants?

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Discussion Overview

The discussion revolves around the validity of BTZ black hole solutions when altering the cosmological constant from negative to zero or positive values. Participants explore the implications of these changes on the interpretation of geodesics and the nature of the solutions in relation to the vacuum field equations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant asserts that changing the cosmological constant in the BTZ solution is not valid as it would not yield a solution to the vacuum field equations.
  • Another participant questions whether the conical singularity at r=0 must be treated as a point particle for the solutions to be considered valid.
  • A different viewpoint suggests that while the cosmological constant can be changed, only one specific value accurately predicts the shape of our universe, referencing the Flatness Problem.
  • Some participants indicate that the geodesics would retain the same interpretation as in the BTZ solution due to the metric remaining unchanged.

Areas of Agreement / Disagreement

Participants express differing views on the validity of changing the cosmological constant in BTZ solutions, with no consensus reached on whether such changes yield valid solutions or how geodesics should be interpreted in these contexts.

Contextual Notes

There are unresolved questions regarding the treatment of conical singularities and the implications of different cosmological constants on the nature of the solutions and their compliance with the Einstein field equations.

erasrot
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Hi everybody. I am well aware that there is only one black hole in 2+1, i.e., the BTZ one. I also know that for vanishing and positive cosmological constants we get solutions with a conical singularity. My question is more about the interpretation of these last results. Assume that in the BTZ solution you just change the value of the cosmological constant from negative to zero or positive. Is that valid? How are the geodesics to be interpreted in these spacetimes? Is just like in any geodesically incomplete background?
 
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erasrot said:
Assume that in the BTZ solution you just change the value of the cosmological constant from negative to zero or positive. Is that valid? How are the geodesics to be interpreted in these spacetimes? Is just like in any geodesically incomplete background?

It wouldn't be a solution to the vacuum field equations. The geodesics would have the same interpretation as in the BTZ solution, because the metric would be the same.
 
Thanks for your answer. Do you mean that they are not vaccuum solutions because, to be a solution, the conical singularity at r=0 has to be treated as a point particle?
 
erasrot said:
Assume that in the BTZ solution you just change the value of the cosmological constant from negative to zero or positive. Is that valid? How are the geodesics to be interpreted in these spacetimes? Is just like in any geodesically incomplete background?

You can change it, but only one of the cosmological values most accurately predict the shape of out universe. If you read up on the Flatness Problem, you will find it. I believe it is +1. My memory could be failing me here, while since I read it.
 
erasrot said:
Thanks for your answer. Do you mean that they are not vaccuum solutions because, to be a solution, the conical singularity at r=0 has to be treated as a point particle?

No. I mean that they aren't vacuum solutions because they wouldn't satisfy the Einstein field equations with T=0 and the value of \Lambda that actually applied to them.
 

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