Wind-Finslerian structure of black holes

TL;DR

This paper extends the Finslerian geometric framework to include black hole horizons and interiors, using wind-Finslerian structures to analyze null geodesics and frame-dragging effects in various black hole models.

Contribution

It introduces wind-Finslerian structures to describe black hole horizons and interiors, connecting recent mathematical advances to physical models of black holes.

Findings

Finslerian indicatrix identifies horizons and ergosurfaces.

Enhanced visualization of null geodesics in black hole regions.

Application to spherically symmetric and Kerr black holes.

Abstract

Recently, there has been an increasing interest in the Finslerian interpretation of null geodesics in the exterior regions of stationary black holes, particularly through the Zermelo navigation problem and the Randers metric. In this work, we show that recent mathematical advancements in wind-Finslerian structures, which involve the critical and strong Zermelo navigation problems and their connections to Kropina and Lorentz-Finsler metrics, enable the extension of the Finslerian framework to encompass horizons and their interior regions of black holes. The Finslerian indicatrix, a key element of this framework, serves as an effective tool for identifying frame-dragging effects and the location of horizons and ergosurfaces. We illustrate our results with explicit physical examples, focusing on spherically symmetric black holes, Kerr black holes, and analog models of gravity. Our findings provide new insights into the ``river model'' of black holes, offering enhanced visual representations of null geodesics on the ergosurfaces, horizons, and within their interior regions.