No black-hole theorem in three-dimensional gravity

Area of Science:

• Theoretical Physics
• General Relativity
• Quantum Gravity

Background:

• Black hole solutions in (2+1)-dimensional gravity typically require a negative cosmological constant.
• Understanding the fundamental properties and constraints of black holes in lower dimensions is crucial for theoretical physics.

Purpose of the Study:

• To investigate the existence of black holes in (2+1)-dimensional gravity theories that satisfy the dominant energy condition.
• To explain the common requirement of a negative cosmological constant for known black hole solutions.

Main Methods:

• Theoretical analysis of (2+1)-dimensional gravity.
• Application of the dominant energy condition to gravitational field equations.

Main Results:

• Demonstration that (2+1)-dimensional gravity theories satisfying the dominant energy condition forbid the existence of black holes.
• This finding provides a theoretical explanation for why known black hole solutions necessitate a negative cosmological constant.

Conclusions:

• The dominant energy condition is a fundamental constraint that prevents black hole formation in (2+1)-dimensional gravity.
• Further research may explore alternative gravity theories or dimensions where black holes can exist under different energy conditions.