Gravitational radiations of generic isolated horizons and non-rotating dynamical horizons from asymptotic expansions

TL;DR

This paper uses a four-dimensional asymptotic expansion approach to analyze gravitational radiation from generic isolated and non-rotating dynamical horizons, comparing results with Bondi-Sachs and Ashtekar-Kirshnan formalisms.

Contribution

It introduces a novel four-dimensional asymptotic expansion method for studying gravitational radiation near horizons, linking horizon analysis with null infinity techniques.

Findings

Derived quasi-local energy-momentum expressions for horizons

Compared flux formulas with Bondi-Sachs and Ashtekar-Kirshnan results

Highlighted similarities between horizon and null infinity radiation

Abstract

Instead of using a three dimensional analysis on quasi-local horizons, we adopt a four dimensional asymptotic expansion analysis to study the next order contributions from the nonlinearity of general relativity. From the similarity between null infinity and horizons, the proper reference frames are chosen from the compatible constant spinors for an observer to measure the energy-momentum and flux near quasi-local horizons. In particular, we focus on the similarity of Bondi-Sachs gravitational radiation for the quasi-local horizons and compare our results to Ashtekar-Kirshnan flux formular. The quasi-local energy momentum and flux of generic isolated horizons and non-rotating dynamical horizons are discussed in this paper.