Equations of general relativistic radiation hydrodynamics in Kerr space-time

TL;DR

This paper derives comprehensive equations for general relativistic radiation hydrodynamics in Kerr space-time, accounting for matter-radiation interactions and relativistic effects near rotating black holes.

Contribution

It presents a novel formulation of radiation hydrodynamics equations in Kerr space-time, incorporating frame-dragging, gravitational redshift, and relativistic effects with multiple reference frames.

Findings

Derived equations in Kerr space-time including matter-radiation interactions.

Incorporated frame-dragging and gravitational redshift effects.

Established a framework connecting comoving, LNRF, and Boyer-Lindquist frames.

Abstract

Equations of fully general relativistic radiation hydrodynamics in Kerr space-time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer-Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame-dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF.