Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies

TL;DR

This paper investigates hidden symmetries in complex black hole solutions within general relativity, revealing how nonholonomic deformations can eliminate quantum anomalies and extend classical conserved quantities to quantum regimes.

Contribution

It introduces new classes of off-diagonal black hole solutions with hidden symmetries and demonstrates how to remove quantum anomalies through geometric deformations.

Findings

Existence of hidden symmetries in off-diagonal black hole solutions.

Construction of new black hole solutions with ellipsoidal and solitonic deformations.

Quantum anomalies can be eliminated via geometric deformations.

Abstract

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.