(2+1)-dimensional charged black hole in topologically massive electrodynamics.

Area of Science:

• Theoretical Physics
• General Relativity
• Quantum Field Theory

Background:

• The 2+1 dimensional black hole coupled to a Maxwell field exhibits two distinct charge types: Coulomb and topological.
• Topological charge, arising from noncontractible cycles, typically decouples from gravitational effects.
• The standard Maxwell field potential grows logarithmically with the radial coordinate.

Purpose of the Study:

• To investigate the impact of introducing a Chern-Simons term for the Maxwell field on charged black holes in 2+1 gravity.
• To analyze how this modification affects the nature and gravitational interaction of black hole charges.
• To explore the construction of charged black holes under these new conditions.

Main Methods:

• Coupling a Maxwell field to a 2+1 black hole solution.
• Introducing a Chern-Simons term into the Maxwell field dynamics.
• Analyzing the behavior of Coulomb and topological charges at the black hole horizon and at infinity.
• Imposing regularity conditions on the black hole horizon.

Main Results:

• The flux integral at infinity becomes equivalent to the topological charge.
• Regularity conditions at the black hole horizon necessitate the vanishing of the Coulomb charge.
• In 2+1 topologically massive electrodynamics, black holes can only support Maxwell field holonomies.

Conclusions:

• The inclusion of the Chern-Simons term fundamentally alters the nature of charge in 2+1 black hole solutions.
• Charged black holes in this modified theory are constructed from the vacuum through spacetime identifications, exclusively supporting topological charge.
• This work highlights a unique mechanism for generating charged black holes in lower-dimensional gravity.