Smooth Singularities Exposed: Chimeras of the Differential Spacetime Manifold
arXiv:gr-qc/0411121
Abstract
The smooth gravitational singularities of the differential spacetime manifold based General Relativity (GR) are viewed from the perspective of the background manifold independent and, in extenso, Calculus-free Abstract Differential Geometry (ADG). In particular, the inner Schwarzschild singularity is being `resolved' ADG-theoretically in two different ways. A plethora of important mathematical, physical and philosophical issues in current classical and quantum gravity research are addressed and tackled.
arXiv commentSize: 481 pages. The document is pretty much in its final form. We are still groping with quotations' referencing in the text. We shall rectify things duly
References in corpus (38)
- Thermodynamics of Spacetime: The Einstein Equation of State
- Complex Extension of Quantum Mechanics
- The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang
- Discreteness of area and volume in quantum gravity
- Quantum Theory of Gravity I: Area Operators
- Cosmic Evolution in a Cyclic Universe
- Absence of Singularity in Loop Quantum Cosmology
- The Spectral Action Principle
- Spin Networks and Quantum Gravity
- The Nature of Space and Time
- Weaving a classical geometry with quantum threads
- Projective Techniques and Functional Integration
- Spin Foam Models
- Partial observables
- A Classical Sequential Growth Dynamics for Causal Sets
- Representations of the holonomy algebras of gravity and non-Abelian gauge theories
- Differential Geometry on the Space of Connections via Graphs and Projective Limits
- A Universal Action Formula
- Forks in the Road, on the Way to Quantum Gravity
- Generalized Measures in Gauge Theory
- Gravitational Observables and Local Symmetries
- Loop Quantum Cosmology IV: Discrete Time Evolution
- Dynamical Initial Conditions in Quantum Cosmology
- Structural Issues in Quantum Gravity
- Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
- Spin foam model for Lorentzian General Relativity
- Discrete differential calculus, graphs, topologies and gauge theory
- Quantum Measure Theory and its Interpretation
- The geometry of quantum spin networks
- Differential Calculi on Commutative Algebras
- Remarks on "singularities"
- General Covariance and the "Problem of Time" in a Discrete Cosmology
- Discrete Differential Manifolds and Dynamics on Networks
- Quantising on a category
- Incidence algebras of simplicial complexes
- Finitary Cech-de Rham Cohomology: much ado without smoothness
- K-Theory of topological algebras and second quantization
- Scale invariant gravity and the quasi-static universe