Exploring BTZ Black Hole & Geodesics

In summary: 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.
  • #1
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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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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 [itex]\Lambda[/itex] that actually applied to them.
 

FAQ: Exploring BTZ Black Hole & Geodesics

What is a BTZ black hole?

A BTZ black hole is a type of black hole that was first proposed by Bañados, Teitelboim, and Zanelli in 1992. It is a three-dimensional black hole solution to Einstein's field equations in general relativity. It is named after the first initials of the three scientists who discovered it.

How is a BTZ black hole different from a regular black hole?

A BTZ black hole is different from a regular black hole in several ways. Firstly, it exists in a three-dimensional space instead of the four-dimensional space of a regular black hole. Additionally, it has a constant negative curvature, whereas a regular black hole has a singularity at its center. The event horizon of a BTZ black hole is also different, as it has a fixed radius and is shaped like a cylinder, while the event horizon of a regular black hole is spherical.

What is the significance of studying BTZ black holes?

Studying BTZ black holes is important for several reasons. Firstly, they provide a simplified model for studying the properties and behavior of black holes in general. Additionally, they have helped researchers gain a better understanding of the holographic principle and the connection between gravity and quantum mechanics. Moreover, they have potential applications in string theory and may help us understand the nature of space and time.

What are geodesics in relation to BTZ black holes?

In general, a geodesic is the shortest path between two points in a curved space. In the context of BTZ black holes, geodesics refer to the paths that particles follow as they travel around the black hole's event horizon. These paths are influenced by the curvature of space and the gravitational pull of the black hole.

How do BTZ black holes form?

BTZ black holes are not thought to form in the same way as regular black holes. Instead, they are considered to be mathematical solutions to Einstein's field equations. However, some theories suggest that they may arise in certain situations, such as in the collision of high-energy particles or in the early universe during the period of inflation.

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