Effective Lagrangian and static black holes in 2D dilatonic gravity inspired by quantum effects

TL;DR

This paper develops an effective Lagrangian for 2D dilaton-Maxwell quantum gravity incorporating quantum effects, leading to new classical solutions including static black holes that could serve as remnants after Hawking radiation.

Contribution

It introduces a novel effective Lagrangian with curvature logarithms in 2D dilaton gravity, and investigates static black hole solutions influenced by quantum effects.

Findings

Derived an improved effective Lagrangian with curvature logarithms.

Found static black hole solutions potentially acting as Hawking radiation remnants.

Constructed effective Lagrangian for Gross-Neveu-dilaton gravity in 1/N expansion.

Abstract

We study the effective action in 2D dilaton-Maxwell quantum gravity. Working with the one-loop renormalizable subset of such theories, we construct the improved effective Lagrangian which contains curvature under logarithm. This effective Lagrangian leads to new classical dilatonic gravity inspired by quantum effects. The static black holes (BH) solutions which may play the role of a remnant after the Hawking radiation for such theory are carefully investigated. The effective Lagrangian for Gross-Neveu-dilaton gravity is also constructed (in 1/N expansion).