arXiv subjects

Frederick Alford

Publications and source records attributed to Frederick Alford.

3 recordsLinked to original sources

arXiv2023

A Rigorous Study of Hawking Radiation on Collapsing Charged Spherically Symmetric Spacetimes

In this paper, we give a rigorous mathematical treatment of the late time Hawking radiation of massless bosons emitted by a class of collapsing, spherically symmetric, charged models of black hole formation, including both extremal and sub-extremal black holes. We will also prove a bound on the rate at which the radiation emitted approaches this late time limit. This includes an integrable decay rate of radiation emitted by extremal black holes, for which the late time limit vanishes. Thus, we show that the total expected quantity of any massless boson emitted by an extremal \RNS black hole is finite.

gr-qc↗

arXiv2023

The Scattering Map on Collapsing Charged Spherically Symmetric Spacetimes

In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $ϕ$ to the wave equation on the exterior of collapsing spherically symmetric charged matter clouds. We then proceed to define the scattering map on this spacetime, and look at the implications of our boundedness results on this map. More specifically, we first construct a class of spherically symmetric charged collapsing matter cloud exteriors, and then consider solutions to the wave equation with Dirichlet (reflective) boundary conditions on the surface of these clouds. We then show that the energy of $ϕ$ remains uniformly bounded going forwards or backwards in time, and that the scattering map is bounded going forwards but not backwards. Therefore, the scattering map is not surjective onto the space of finite energy on $\mathcal{I}^+\cup\mathcal{H}^+$. Thus there does not exist a backwards scattering map from finite energy radiation fields on $\mathcal{I}^+\cup\mathcal{H}^+$ to finite energy radiation fields on $\mathcal{I}^-$ for these models. These results will be used to give a treatment of Hawking radiation in a companion paper [2].

gr-qc↗

arXiv2020

The Scattering Map on Oppenheimer--Snyder Spacetime

In this paper we analyse the boundedness of solutions $ϕ$ of the wave equation in the Oppenheimer--Snyder model of gravitational collapse in both the case of a reflective dust cloud and a permeating dust cloud. We then proceed to define the scattering map on this space-time, and look at the implications of our boundedness results on this scattering map. Specifically, it is shown that the energy of $ϕ$ remains uniformly bounded going forward in time and going backwards in time for both the reflective and the permeating cases, and it is then shown that the scattering map is bounded going forwards, but not backwards, and is therefore not surjective onto the space of finite energy on $\mathcal{I}^+\cup\mathcal{H}^+$. Thus there does not exist a backwards scattering map from finite energy radiation fields on $\mathcal{I}^+\cup\mathcal{H}^+$ to finite energy radiation fields on $\mathcal{I}^-$. We will then contrast this with the situation for scattering in pure Schwarzschild.

gr-qc↗