Thermodynamics of quantum gravitational ensembles
Thermodynamics of quantum gravitational ensembles
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Date
2023
Authors
Banihashemi, Batoul
Advisor
Jacobson, Theodore A
Citation
Abstract
The discovery of black hole thermodynamics and its extension to cosmological horizonsdemonstrated a deep connection between thermodynamics and the nature of spacetime
as a quantum system. It is then of great importance to properly understand the statistical
mechanics of gravitational systems with horizon from first principles. While employing a
partition function and the gravitational “Euclidean path integral” produces the expected
physical result for entropy, a number of fundamental questions about the underlying analysis
persist. This dissertation sharpens and resolves some puzzles regarding statistical
mechanics of gravitational ensembles and the gravitational path integral, with a focus on
cosmological horizons and de Sitter space.
The main questions addressed in this dissertation are: how is the entropy of de Sitterspace derived in absence of any boundary on which the statistical ensemble can be properly
defined? What is the correct interpretation of the first law of de Sitter horizon, according
to which the horizon area shrinks upon adding matter in de Sitter static patch? And
finally, can entropy of horizon-bounded systems be derived from a Hamiltonian approach
and phase space path integral, without the trickery of the gravitational Euclidean path
integral? The first two questions are answered by introducing an artificial boundary in
the system on which a gravitational ensemble can be properly defined. Once the ensemble
is defined, the semiclassical approximation of the statistical partition function yields the
entropy, and the interpretation of the de Sitter first law becomes clear by identifying the
system energy as the quasilocal energy defined on the boundary. To tackle the last question,
the real-time phase space path integral is utilised in the Hamiltonian formulation which
maintains connection to the Hilbert space of the system, and it is found that the horizon
entropy is derived from a nearly Lorentzian configuration.