A note on positive energy of topologically massive gravity

TL;DR

This paper reviews how classical supergravity embeddability ensures positive energy in three-dimensional topologically massive gravity, providing explicit energy expressions and highlighting differences from Einstein gravity.

Contribution

It demonstrates that classical SUGRA embeddability guarantees positive energy in TMG and offers explicit formulas, contrasting with the non-manifest positivity in standard GR.

Findings

Positive energy E established for TMG via SUGRA embeddability

Explicit expressions for the energy E in TMG provided

E is not manifestly positive due to TMG's two-term structure

Abstract

I review how "classical SUGRA" embeddability establishes positive energy E for D=3 topologically massive gravity (TMG), with or without a cosmological term, a procedure familiar from D=4 Einstein gravity (GR). It also provides explicit expressions for E. In contrast to GR, E is not manifestly positive, due to the peculiar two-term nature of TMG.