Confusion about killing horizon in Carroll

In summary, Carroll's work on the "killing horizon" focuses on the idea of the event horizon as a boundary where time and space become distorted to the point of being "deadly" for anything crossing it. This adds to our understanding of black holes and their behavior, and how they shape the universe. However, there are misconceptions about the killing horizon, such as it being a physical barrier and having a literal "killing" effect on objects. The killing horizon also relates to the singularity within a black hole, marking the boundary of this region where the laws of physics break down. Carroll's work on the killing horizon has implications for our understanding of the universe, including advancements in research on black holes, matter and energy in
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In the opening paragraph of section 6.3 Carroll defines a killing horizon to be a null hypersurface Σ where some killing vector field χμ becomes null. Later (on page 247 if you have the book) when distinguishing between static and stationary space times, he says that in a stationary, but not static spacetime, we still have the killing field Kμ = (∂t)μ , but it won't become null at the killing horizon. How is that possible? By definition that seems wrong. How do you have a killing horizon if that's not where your killing field becomes null?

TIA
 
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NVM got it ;-)
 

1. What is the "killing horizon" in Carroll's work?

The "killing horizon" is a term used in General Relativity to describe the boundary of a black hole. It is the point at which the escape velocity exceeds the speed of light, making it impossible for any object or information to escape from within the black hole's event horizon.

2. How does Carroll's work contribute to our understanding of the killing horizon?

Carroll's work focuses on the concept of the event horizon as a "killing horizon," meaning that it is a boundary where time and space are distorted to the point of being "deadly" for anything crossing it. This adds to our understanding of black holes and their behavior, as well as their role in shaping the universe.

3. Are there any misconceptions about the killing horizon in Carroll's work?

One common misconception is that the killing horizon is a physical barrier that objects cannot cross. In reality, it is a mathematical concept used to describe the boundary of a black hole, and objects can still pass through it. Additionally, Carroll's work may be misinterpreted as suggesting that the event horizon has a literal "killing" effect on objects, when it is actually a result of extreme gravitational forces.

4. How does the killing horizon relate to the singularity within a black hole?

The killing horizon is often used to define the boundary of the singularity within a black hole. The singularity is the point at the center of a black hole where the laws of physics break down. The killing horizon is the boundary of this region, marking the point of no return for anything that crosses it.

5. What implications does Carroll's work on the killing horizon have for our understanding of the universe?

Carroll's work on the killing horizon has greatly advanced our understanding of black holes and their role in shaping the universe. It has also led to further research and theories about the behavior of matter and energy in extreme gravitational conditions. Additionally, it has shed light on the concept of time and how it is affected by the presence of black holes.

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