Semiclassical vs. Exact Solutions of Charged Black Hole in Four Dimensions and Exact O(d,d) Duality

TL;DR

This paper derives an exact four-dimensional charged black hole solution using WZW coset models, revealing the persistence of singularities and potential violations of cosmic censorship, and explores exact duality transformations in string theory.

Contribution

It presents the first exact all-orders solution for a charged 4D black hole in string theory and derives precise $O(d,d)$ duality transformations for WZW coset models.

Findings

Singularity persists in the exact solution, unlike in 2D black holes.

In some gauge ranges, the spacetime exhibits naked singularities.

Exact $O(d,d)$ transformations are derived, including corrections beyond one-loop order.

Abstract

We derive a charged black hole solution in four dimensions described by $SL(2,R)\times SU(2)\times U(1)/U(1)^2$ WZW coset model. Using the algebraic Hamiltonian method we calculate the corresponding solution that is exact to all orders in ${1\over k}$. It is shown that unlike the 2D black hole, the singularity remains also in the exact solution, and moreover, in some range of the gauge parameter the space-time does not fulfil the cosmic censor conjecture, $i.e.$ we find a naked singularity outside the black hole. Exact dual models are derived as well, one of them describes a 4D space-time with a naked singularity. Using the algebraic Hamiltonian approach we also find the exact to all orders $O(d,d)$ transformation of the metric and the dilaton field for general WZW coset models and show the correction with respect to the transformations in one loop order.