Kerr black holes in horizon-generating form

Area of Science:

• General Relativity
• Black Hole Physics
• Differential Geometry

Background:

• Kerr and Schwarzschild black holes are fundamental solutions in General Relativity.
• Dual-null foliations provide a powerful framework for studying black hole dynamics.
• The Kruskal form simplifies the description of Schwarzschild black holes.

Purpose of the Study:

• To generalize the Kruskal form for Schwarzschild black holes to describe nondegenerate Kerr black holes.
• To introduce new coordinate systems for analyzing black hole horizons.
• To provide a framework for studying the geometry of Kerr black holes in dual-null foliations.

Main Methods:

• Development of new coordinate systems based on dual-null foliations.
• Introduction of an area radius for transverse surfaces.
• Generalization of the Regge-Wheeler radial function.

Main Results:

• New coordinates accurately describe nondegenerate Kerr black holes.
• The generalized Regge-Wheeler function depends solely on the original radial coordinate.
• The construction provides a unified approach to black hole horizons.

Conclusions:

• The new coordinate system offers a simplified and generalized description of Kerr black holes.
• This work extends our understanding of black hole geometry and dynamics.
• The findings have implications for theoretical physics and astrophysics.