SEMICLASSICAL CONSISTENT CONSTRAINTS WITH MOMENTS IN SPHERICALLY SYMMETRIC QUANTUM GRAVITY
Open Access
- Author:
- Diaz, Manuel
- Graduate Program:
- Physics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- November 15, 2019
- Committee Members:
- Martin Bojowald, Thesis Advisor/Co-Advisor
Nitin Samarth, Program Head/Chair
Irina Mocioiu, Committee Member
Richard Wallace Robinett, Committee Member - Keywords:
- Canonical Quantum Gravity
Semiclassical Constraint Algebra
Canonical Effective Method
Dirac Algebra
Hypersurface Deformation Algebra
First-Class Algebra
First-Class Constraints
Constrained Hamiltonian System
Effective Theory - Abstract:
- A full theory of quantum gravity has eluded physicists for over 80 years. It is said by some to be the ``holy grail" of physics, but after all these years, there is both a lack of new insight from physical phenomena and, by and large, a lack of predictions that are falsifiable in all current candidates for a theory of quantum gravity. Therefore, extracting semiclassical quantum gravitational effects from an effective theory might be our best bet for giving us a way of doing meaningful phenomenology that is falsifiable. In this thesis, we applied a canonical effective method to derive semiclassical constraints for spherically symmetric space-times. The semiclassical quantum gravitational effects that we could extract from these constraints are suitable for situations where quantum effects are relevant, yet not dominant. Currently, there are two primary cases in which we know that quantum gravitational effects are relevant. First, black holes, as mathematical solutions to Einstein's field equations, provide environments in which quantum gravity becomes vital since singularities lead to the divergence of curvature and tidal forces. As astrophysical objects, black holes could potentially show properties not predicted by their mathematical counterparts in Einstein's theory of general relativity (GR). Moreover, some think that cosmological observations from the early universe are the most feasible way of detecting quantum gravitational effects. For these reasons, we used spherically symmetric space-time since it allows us to model both black holes and early-universe cosmologies where inhomogeneities are present. The canonical effective method mentioned above involves studying the dynamics due to the back-reaction, i.e., the average properties, of the moments of canonical variables. In this case, the canonical variables consist of real-valued densitized triads and extrinsic curvature components of a foliated general spherically symmetric space-time. Furthermore, a Hamiltonian formulation of GR involves constraints that generate a first-class algebra. This algebra of constraints leads directly to the diffeomorphism invariance of GR, and therefore its gauge symmetries. In order to constrain any arbitrariness and ambiguities associated with the method, we require that the gauge symmetries of GR generated by the classical constraints be preserved by the new semiclassical constraints that we derived using this method. Fortunately, the canonical effective method we used turned out to preserve the closure of the constraint algebra with respect to Poisson brackets such that the new semiclassical constraints still form a first-class algebra. Moreover, the new semiclassical constraints are consistent since they also have the correct classical limit. This means that the form of the constraint algebra itself is preserved in the new semiclassical constraint algebra. For this reason, we can say that we have a new semiclassical theory, which is entirely determined by the semiclassical constraints, that has the same gauge symmetries present in GR, and therefore is covariant. In addition, this new semiclassical theory could potentially help us find some new and unexpected physical phenomena, perhaps in black holes or cosmological scenarios, which could potentially lead, in the long term, to a full theory of quantum gravity.