Two-dimensional Quantum-Corrected Eternal Black Hole

TL;DR

This paper investigates quantum corrections to two-dimensional black hole geometry and thermodynamics within the RST model, revealing milder singularities and identical thermodynamic quantities for classical and quantum-corrected solutions.

Contribution

It provides exact solutions for quantum-corrected black holes in 2D, including a novel constant curvature space-time and analysis of thermodynamics with no quantum corrections to thermodynamic quantities.

Findings

Quantum-corrected metric is a deformation of classical solution.

Singularity is milder than in classical case.

Thermodynamics remains unchanged by quantum corrections.

Abstract

The one-loop quantum corrections to geometry and thermodynamics of black hole are studied for the two-dimensional RST model. We chose boundary conditions corresponding to the eternal black hole being in the thermal equilibrium with the Hawking radiation. The equations of motion are exactly integrated. The one of the solutions obtained is the constant curvature space-time with dilaton being a constant function. Such a solution is absent in the classical theory. On the other hand, we derive the quantum-corrected metric (\ref{solution}) written in the Schwarzschild like form which is a deformation of the classical black hole solution \cite{5d}. The space-time singularity occurs to be milder than in classics and the solution admits two asymptotically flat black hole space-times lying at "different sides" of the singularity. The thermodynamics of the classical black hole and its quantum counterpart is formulated. The thermodynamical quantities (energy, temperature, entropy) are calculated and occur to be the same for both the classical and quantum-corrected black holes. So, no quantum corrections to thermodynamics are observed. The possible relevance of the results obtained to the four-dimensional case is discussed.