Rotating black holes in higher dimensions with a cosmological constant

Area of Science:

• Theoretical Physics
• General Relativity
• String Theory

Background:

• Black holes are fundamental objects in astrophysics and theoretical physics.
• Understanding black hole metrics is crucial for testing theories of gravity.
• Higher-dimensional theories and string theory require generalized black hole solutions.

Purpose of the Study:

• To present a generalized metric for rotating black holes in higher dimensions.
• To incorporate a cosmological constant and arbitrary angular momenta into the black hole metric.
• To explore the mathematical structures arising from these solutions, particularly compact Einstein spaces.

Main Methods:

• Derivation of the black hole metric in both Kerr-Schild and Boyer-Lindquist coordinates.
• Analysis of the metric in the Euclidean-signature case.
• Construction of associated compact Einstein spaces over S2 bundles.

Main Results:

• A comprehensive metric for rotating black holes with a cosmological constant and arbitrary angular momenta in D dimensions.
• Identification of infinitely many smooth compact Einstein spaces for odd D >= 5 in the Euclidean-signature case.
• The metric is presented in two standard coordinate systems for broader applicability.

Conclusions:

• The derived metric provides a powerful tool for studying higher-dimensional rotating black holes.
• The discovery of new compact Einstein spaces has significant implications for string theory and M-theory.
• This work unifies several concepts in higher-dimensional gravity and theoretical physics.