Browsing by Author "Saeed, Mustafa"

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    Cosmological perturbation theory in a matter-time gauge
    (University of New Brunswick, 2019) Saeed, Mustafa; Husain, Viqar
    This work examines cosmological perturbations in a Hamiltonian framework with a matter-time gauge. Einstein's field equations are written in a matter-time gauge. The perturbed three-metric of cosmology, its conjugate momentum and the shift are substituted in these equations. The equations of motion of the perturbations to linear order are derived. These equations are expanded in terms of spatial Fourier modes and are then decomposed into scalar, vector and tensor components. After fixing gauges and solving constraints we find that the scalar mode is ultralocal and that the vector modes vanish. We also see that the traceless transverse tensor modes give the known propagation equation for gravitational waves in an expanding, spatially at, homogeneous and isotropic background.
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    Probing gravity-matter systems
    (University of New Brunswick, 2023-08) Saeed, Mustafa; Husain, Viqar
    This thesis explores gravity-matter systems within the context of cosmology and black holes. Two different studies are presented. First we study cosmological perturbation theory (CPT) with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a clock. The corresponding canonical action describes the dynamics of the scalar field and metric degrees of freedom with a non-vanishing physical Hamiltonian and spatial diffeomorphism constraint. We construct a momentum space Hamiltonian that describes linear perturbations, and show that the constraints to this order form a first class system. We then write the Hamiltonian as a function of certain gauge invariant canonical variables and show that it takes the form of an oscillator with time dependent mass and frequency coupled to an ultralocal field. We compare our analysis with other Hamiltonian approaches to CPT that do not use dust-time. Next we construct and study spin models on Euclidean black hole backgrounds. These resemble the Ising model, but are inhomogeneous with two parameters, the black hole mass M and the cosmological constant Λ. We use Monte-Carlo methods to study macroscopic properties of these systems for Schwarzschild and anti-deSitter black holes in four and five dimensions for spin-1/2 and spin-1. We find in every case that increasing M causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at sub-Planckian M.