Is the Schwarzschild Metric Always Applicable to Black Holes?

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SUMMARY

The Schwarzschild metric is a valid solution to the Einstein Field Equations (EFE) for non-rotating, uncharged black holes, predicting the formation of an event horizon when the object's surface lies within the Schwarzschild radius. However, it is not applicable below the surface of an object, as this region is not a vacuum. For real-world black holes formed from rotating stars, the Kerr metric is the appropriate solution, accounting for angular momentum. Thus, while the Schwarzschild metric is foundational, its limitations necessitate the use of the Kerr metric for rotating black holes.

PREREQUISITES
  • Understanding of Einstein Field Equations (EFE)
  • Familiarity with Schwarzschild metric and its implications
  • Knowledge of Kerr metric for rotating black holes
  • Concept of Schwarzschild radius and event horizons
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  • Study the derivation and applications of the Schwarzschild metric
  • Explore the Kerr metric and its significance in astrophysics
  • Investigate the implications of black hole rotation on spacetime
  • Learn about the observational evidence for black holes and their properties
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What do you put inside einstein field equation for black holes? Why is it that such black hole solution is not feasible?

Isnt the schwarzschild metric a solution for black holes? How is it not feasible?
 
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TimeRip496 said:
What do you put inside einstein field equation for black holes? Why is it that such black hole solution is not feasible?

Isnt the schwarzschild metric a solution for black holes? How is it not feasible?

Why are you saying that it's "not feasible"? The Schwarzschild metric is the solution to the EFE for (non-rotating, uncharged) masses, whether black holes or not. It doesn't apply below the surface of an object because it's a vacuum solution and below the surface isn't a vacuum, but if the object is dense enough that its surface lies inside the Schwarzschild radius, the Schwarzschild solution predicts that a a black hole will form, event horizon and all.

It it is true that any real world black hole formed by the collapse of a star will be rotating because the original star was rotating, and in that case you will want to use the Kerr metric instead of the Schwarzschild metric.
 

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