Non-singular black holes beyond General Relativity and their characteristic image features

Abstract

This thesis centres on non-singular black-hole spacetimes derived in all three different approaches to black holes beyond General Relativity and their characteristic image features. This topic has sparked considerable interest in past years with the tremendous development of observational tests of General Relativity in the strongest gravitational fields induced by neutron stars and black holes. The thesis begins with a brief overview of the current classical theory of gravity, General Relativity, and its main black-hole solutions. We then elaborate on the successes and flaws of General Relativity for different gravitational field strengths, which motivate the proliferation of both classical gravity and quantum gravity theories beyond General Relativity within the fundamental approach. We shortly describe two complementary and largely theory-agnostic approaches to black holes beyond General Relativity, the parameterised approach and the principled-parameterised approach, and review horizonless compact objects as alternatives to black holes. We then move on to describe the principles and outcomes of imaging compact objects and apply them to non-singular black holes, horizonless spacetimes and parameterised black holes. We find that spacetimes beyond General Relativity generically exhibit peculiar image features, especially imprinted in photon rings, which distinguish them from the classical black holes. This serves as a motivation to analyse the detectability of a second thin photon ring in synthetic image data produced with a simple flux density profile by current and future radio telescope arrays. We find that we can only tell apart two thin photon rings with the current array if we use super-resolution techniques, while we can do so without restrictions with plannedextensions of the array on Earth and in space. Next, we review a simple scenario of spherically symmetric gravitational collapse in General Relativity and build on its shortcomings to perform a regular upgrade of the classical dynamical spacetime in the fundamental approach and in the principled-parameterised approach. We investigate their various properties which seem to indicate that the upgraded dynamical spacetimes are future null-geodesically complete and might allow (quantum) modifications to be visible by an asymptotic observer but may suffer from a mass-inflation instability in their interior. In the final part, we discuss the existing axisymmetric and stationary black-hole metrics within the parameterised approach given their symmetry constraints and emphasise that circularity and an additional hidden constant of motion are superfluous. We thus put forward a new parametric spacetime which does not assume those superfluous symmetries while encompassing the existing parameterisations. We do so in two coordinate sets and examine their pros and cons. Finally, we highlight the connection between the absence of those two superfluous symmetries and the presence of peculiar image features, making a case for analyses of image data collected by future radio telescope arrays to consider our more general parameterisation.

Date of Award	17 Dec 2024
Original language	English
Awarding Institution	University of Southern Denmark
Supervisor	Astrid Eichhorn (Supervisor)