Perturbations and symmetry in gravitational theories : wormholes, wave dynamics, and quantum effects in rotating spacetimes.

This dissertation develops a symmetry-centered framework for gravitational perturbation theory, applying it to linearized gravity and horizonless rotating space-times. The central thesis is that gauge invariance and geometric symmetry provide a unifying language for identifying physical degrees of freedom, distinguishing observables from coordinate artifacts, and organizing wave dynamics in classical and quantum regimes. Part I establishes a gauge-invariant treatment of perturbations in flat, cosmological, and metric f(R) gravity backgrounds. Using plane gravitational waves, the Bardeen formalism is constructed and contrasted with curvature-based approaches like Newman–Penrose scalars and the Cartan–Karlhede algorithm. While curvature invariants fail to distinguish tensor polarization states, projections onto background Killing symmetries recover this physical content, clarifying the geometric origin of gauge-invariant observables. This framework is extended to f(R) gravity to isolate the additional scalar propagating mode and analyze its impact on polarization. Parallel cosmological treatments demonstrate how symmetry-based constructions systematically separate radiative and non-radiative sectors. Part II applies these methods to the Teo rotating wormhole and its asymptotically Anti–de Sitter (AdS) extension. Traversability, stability, and energy-condition violations are examined, emphasizing how effective geometric contributions support wormhole solutions without explicit exotic matter. Scalar perturbations serve as probes, reducing dynamics to a Schrödinger-type radial equation for quasinormal mode analysis via semiclassical WKB techniques. In near-throat regimes, the radial equation exhibits a conformal-type organization governed by local geometry. However, unlike black holes, the wormhole throat is a regular interior point that does not support ingoing boundary conditions. Instead, dynamics are controlled by throat regularity and AdS normalizability. This structure represents a local organizing principle rather than a global hidden conformal symmetry; when combined with global matching, it determines a discrete normal-mode spectrum and holographic boundary observables. Finally, a quantum field-theoretic treatment shows that horizonless rotating wormholes exhibit Bogoliubov mode mixing, superradiant amplification, and entanglement generation driven by rotational asymmetry. These results demonstrate how symmetry principles unify perturbative observables and quantum effects across gravitational systems without reliance on event horizons.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Doctoral

Grantor

Baylor University.

Year dc:date.issued

2026

Author dc:creator

• Radhakrishnan, Ramesh, 1966-

Advisor dc:contributor.advisor

• Cleaver, Gerald B.

• Holography.
• Analyticity.
• Anti–de Sitter (AdS) space-time.
• Holographic structure.
• Anti–de Sitter (AdS)-Teo space-time.
• Gauge invariance.
• Rotating wormhole.
• Teo wormhole.
• Gravitational wave polarization.
• Bardeen variables.
• Quantum entanglement.
• Quantum correlation.
• Monodromy.
• Hidden conformal symmetry.

Statement dc:rights

• Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2104/14839

OAI identifier oai:identifier

oai:baylor-ir.tdl.org:2104/14839