A Kerr/CFT Correspondence in Twistor Space

TL;DR

This paper explores a novel twistor string model for Kerr spacetimes, linking null geodesics, twistor geometry, and conformal field theory to derive black hole entropy relations.

Contribution

It introduces a twistor string framework for Kerr geometry, connecting null geodesics with conformal field theory and black hole entropy calculations.

Findings

Twistor string models correspond to principal null geodesics in Kerr spacetime.

Conformal field theory derived from twistor models matches Bekenstein-Hawking entropy.

Effective central charge and temperature are key to entropy agreement.

Abstract

Ingoing and outgoing principal null geodesics in Kerr spacetimes are characterized as part of parametrized families of strings in complex Kerr geometry and are associated with holomorphic curves in twistor space with help of the Kerr theorem. They are defined on 2-dimensional twistor manifolds, one for outgoing and one for ingoing principal null congruences, and are solutions of free twistor string models on these 2-dimensional twistor manifolds. Such a twistor string model implies a conformal field theory and, assuming the applicability of the Cardy formula, agreement with the Bekenstein-Hawking area law can be achieved depending on the effective central charge and temperature. A couple of (ambi)twistor string candidate models are examined.