String gravity in $D=4$

TL;DR

This paper derives a four-dimensional string-inspired gravity model with higher-derivative corrections, analyzes its impact on black hole solutions, and computes first-order corrections to Kerr black hole entropy.

Contribution

It shows that string theory leads to a generalized axidilaton gravity with specific higher-derivative couplings and calculates novel corrections to Kerr black hole entropy at second order in .

Findings

Derived the 4D string gravity action with scalar couplings to Gauss-Bonnet and Pontryagin densities.

Computed first-order ' corrections to Kerr black hole geometry.

Obtained second-order ' corrections to Kerr black hole entropy.

Abstract

We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $\alpha'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute the stringy corrections to the Kerr geometry and we obtain, for the first time, the corrections to the entropy of the Kerr black hole at order $\alpha'^2$. We check that the first law of black hole mechanics is satisfied and discuss several properties of the solution. Our results suggest that there exist black hole solutions with $J>M^2$ and therefore the extremal ratio $J/M^2$ must be modified positively.