Rotating Electric Classical Solutions of 2+1 D U(1) Einstein Maxwell Chern-Simons

TL;DR

This paper explores rotating electric solutions in 2+1 dimensional Einstein-Maxwell-Chern-Simons theory, revealing how the Chern-Simons term influences solution properties, including charge, angular momentum, and the presence of horizons, with implications for topological effects in gravity.

Contribution

It provides a detailed analysis of classical rotating solutions in 2+1D Einstein-Maxwell-Chern-Simons theory, highlighting the role of the Chern-Simons term and the effects of different gauge sector signs.

Findings

Existence of a rotating electric point particle solution.

Chern-Simons term restricts the cosmological constant to positive values.

Solutions exhibit horizons and divergent mass, with properties depending on parameter ratios.

Abstract

We study electric stationary radial symmetric classical solutions of the U(1) Einstein Maxwell Chern-Simons theory coupled to a gravitational massless scalar field with a cosmological constant in 2+1 dimensions. Generic aspects of the theory are discussed at an introductory level. We study solutions for both negative sign (standard) and positive sign (ghost) of the gauge sector concluding that although the expressions for the solutions are the same, the constants as well as the physics change significantly. It is found a rotating electric point particle. For the standard sign and specific values of the parameters corresponding to solutions with positive mass the singularity is dressed (in the sense that itself constitutes an horizon). The space-time curvatures can be both positive or negative depending on the dominance of the scalar or topologically massive matter. The Chern-Simons term is responsible for interesting features, besides only allowing for rotating solutions, it imposes restrictive bounds on the cosmological constant $\Lambda$ such that it belongs to a positive interval and is switch on and off by the topological mass $m^2$. Furthermore the charge, angular momentum and mass of the particle solution are expressed uniquely as functions of the ratio between the cosmological constant and the topological mass squared $x=\Lambda/m^2$. The main drawback of our particle solution is that the mass is divergent. Our background is a rotating flat space without angular deficit. We briefly discuss parity and time-inversion violation by the Chern-Simons term which is explicit in the solutions obtained, their angular momentum only depends on the relative sign between the Chern-Simons term and the Maxwell term. Trivial solutions are briefly studied holding non-singular extended configurations.