Question on Black Hole Metrics

In summary, the concept of a black hole does not make sense in a non-asymptotically flat spacetime. This is because the definition of an event horizon relies on the concept of null infinity, which does not exist in a non-AF spacetime. However, there are some solutions, such as Schwarzschild deSitter, which could be considered as representing a black hole in a non-AF universe.
  • #1
skippy1729
Are there any exact solutions known for a black hole in a universe which is NOT asymptotically flat?
 
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  • #2
Yes and no. Technically, the notion of a black hole doesn't make sense in a non AF spacetime. An event horizon is defined as the boundary of the past of future null infinity, but there's no such thing as null infinity if the spacetime is not AF. (Intuitively, a black hole is a region of spacetime from which nothing can escape--but if there's no infinity, what does "escape" even mean?)

However, there are some solutions, like Schwarzschild deSitter, which most people would say represent "a black hole in a non-AF universe".
 
  • #3
Sam Gralla said:
An event horizon is defined as the boundary of the past of future null infinity, but there's no such thing as null infinity if the spacetime is not AF. (Intuitively, a black hole is a region of spacetime from which nothing can escape--but if there's no infinity, what does "escape" even mean?)
So you think radially rising light has some kind of apogee?
 

1. What is a black hole metric?

A black hole metric is a mathematical representation of the spacetime geometry around a black hole. It describes how the curvature of space and time is affected by the presence of a black hole and how objects move in this curved spacetime.

2. How is the metric of a black hole calculated?

The metric of a black hole is calculated using Einstein's field equations, which relate the curvature of spacetime to the distribution of matter and energy within it. The specific calculation depends on the mass, spin, and charge of the black hole.

3. What are the different types of black hole metrics?

The most commonly studied black hole metrics are the Schwarzschild metric, which describes a non-rotating, uncharged black hole, the Kerr metric, which describes a rotating black hole, and the Reissner-Nordström metric, which describes a charged black hole. There are also more complex metrics that take into account multiple black holes, or the effects of gravitational waves.

4. What can black hole metrics tell us about black holes?

Black hole metrics can tell us about the properties of black holes, such as their mass, spin, and charge. They can also give us insights into how objects move around black holes and how spacetime is affected by their presence. Additionally, black hole metrics have been used to make predictions about observable phenomena, such as gravitational lensing and the emission of Hawking radiation.

5. Why are black hole metrics important in understanding the universe?

Black hole metrics play a crucial role in our understanding of the universe as they provide a way to study and predict the behavior of these extreme objects. They also help us to test and refine our understanding of gravity and the laws of physics in the extreme conditions near black holes. Furthermore, black hole metrics are important in the study of cosmology, as black holes are thought to play a significant role in the evolution of galaxies and the large-scale structure of the universe.

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