Generators of Internal Lorentz Transformations and of General Affine Coordinate Transformations in Teleparallel Theory of (2+1)-Dimensional Gravity --- Cases with Static Circularly Symmetric Space-Times---

TL;DR

This paper investigates the generators of internal Lorentz and affine transformations in a (2+1)-dimensional teleparallel gravity theory, providing explicit expressions for conserved quantities in static circularly symmetric solutions and commenting on the definability of momentum and boosts.

Contribution

It introduces explicit forms of generators and conserved quantities in a teleparallel (2+1)-dimensional gravity context, addressing previous claims about momentum and boosts.

Findings

Explicit expressions for spin angular momentum, energy-momentum, and extended orbital angular momentum.

Analysis of the definability of momentum and boosts in finite energy solutions.

Critical commentary on Deser's claim regarding three-dimensional Einstein gravity.

Abstract

In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions of gravitational field equation. The \lq \lq spin" angular momentum, the energy-momentum and the \lq \lq extended orbital angular momentum" are explicitly given for each solution. Also, we give a critical comment on Deser's claim that neither momentum nor boosts are definable for finite energy solutions of three-dimensional Einstein gravity.