Frequency shift of light emitted from growing and shrinking black holes

TL;DR

This paper introduces a numerical method to analyze how the frequency of light signals changes when emitted near a Schwarzschild black hole undergoing growth or shrinkage due to accretion, revealing variability dependent on accretion timescales.

Contribution

It presents a novel numerical approach combining Einstein's equations with scalar field shells to study frequency shifts during black hole accretion and contraction.

Findings

Frequency shift variability depends on accretion timescale.

Photon energy changes are influenced by scalar field shell thickness.

Method enables detailed analysis of light signals near dynamic black holes.

Abstract

In this paper we present a method to study the frequency shift of signals sent from near a Schwarzschild black hole that grows or shrinks through accretion. We construct the numerical solution of Einstein's equations sourced by a spherical shell of scalar field, with positive energy density to simulate the growth and with negative energy density to simulate the shrink of the black hole horizon. We launch a distribution of null rays at various time slices during the accretion and estimate their energy along their own trajectories. Spatially the bundles of photons are distributed according to the distribution of dust, whose dynamics obeys Euler equations in the test field limit during the evolution of the black hole. With these elements, we construct the frequency shift of photons during the accretion process of growth or contraction of the hole, which shows a variability that depends on the thickness of the scalar field shell or equivalently the time scale of the accretion.