Gravitation and the fundamental nature of spacetime
File(s)
Author(s)
Albertini, Emma
Type
Thesis
Abstract
This Thesis investigates three gravitational theories that propose alternatives to the notion of spacetime as four-dimensional, diffeomorphism-invariant manifold.
Firstly, we study spherically symmetric configurations in ghost‐free de Rham–Gabadadze–Tolley massive gravity—a bimetric theory that breaks General Relativity’s diffeomorphism invariance by giving the graviton a mass. In the limit of small graviton mass, our result restricts non-relativistic matter so that the pressure is bounded from below in terms of the density and graviton mass in a manner that is at odds with a reasonable phenomenology.
Then, we examine higher-dimensional gravity, with extra compact dimensions, in the context of Kaluza-Klein theory. Focusing on vacuum solutions in five dimensions, we consider static black hole configurations and conjecture that, for fixed mass and sufficiently small compactification radius, the only solutions are homogeneous black strings. Supporting this conjecture, we derive bounds on inhomogeneities and develop a local rigidity theorem through elliptic analysis.
Finally, we turn to Causal Set Theory, a quantum gravity framework in which spacetime is fundamentally discrete at the Planck scale and is modelled as an irregular Lorentzian lattice. Within this setting, we develop a quantum field theory formalism, deriving a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. This result exhibits manifest causality and terminates at finite order in the interaction coupling, highlighting how the fundamental discreteness acts as a natural cut-off, eliminating the UV divergences.
Firstly, we study spherically symmetric configurations in ghost‐free de Rham–Gabadadze–Tolley massive gravity—a bimetric theory that breaks General Relativity’s diffeomorphism invariance by giving the graviton a mass. In the limit of small graviton mass, our result restricts non-relativistic matter so that the pressure is bounded from below in terms of the density and graviton mass in a manner that is at odds with a reasonable phenomenology.
Then, we examine higher-dimensional gravity, with extra compact dimensions, in the context of Kaluza-Klein theory. Focusing on vacuum solutions in five dimensions, we consider static black hole configurations and conjecture that, for fixed mass and sufficiently small compactification radius, the only solutions are homogeneous black strings. Supporting this conjecture, we derive bounds on inhomogeneities and develop a local rigidity theorem through elliptic analysis.
Finally, we turn to Causal Set Theory, a quantum gravity framework in which spacetime is fundamentally discrete at the Planck scale and is modelled as an irregular Lorentzian lattice. Within this setting, we develop a quantum field theory formalism, deriving a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. This result exhibits manifest causality and terminates at finite order in the interaction coupling, highlighting how the fundamental discreteness acts as a natural cut-off, eliminating the UV divergences.
Version
Open Access
Date Issued
2025-06-17
Date Awarded
01/10/2025
License URL
Advisor
Wiseman, Toby
Publisher Department
Department of Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)