An Exploration of the Singularities in General Relativity
arXiv:1207.5303
Abstract
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which, under a set of conditions, allow us to define proper geometric invariants, and to write field equations, including equations which are equivalent to Einstein's at non-singular points, but remain well-defined and smooth at singularities. This class of singularities is large enough to contain isotropic singularities, warped-product singularities, including the Friedmann-Lemaitre-Robertson-Walker singularities, etc. Also a Big-Bang singularity of this type automatically satisfies Penrose's Weyl curvature hypothesis. The Schwarzschild, Reissner-Nordstrom, and Kerr-Newman singularities apparently are not of this benign type, but we can pass to coordinates in which they become benign. The charged black hole solutions Reissner-Nordstrom and Kerr-Newman can be used to model classical charged particles in General Relativity. Their electromagnetic potential and electromagnetic field are analytic in the new coordinates - they have finite values at r=0. There are hints from Quantum Field Theory and Quantum Gravity that a dimensional reduction is required at small scale. A possible explanation is provided by benign singularities, because some of their properties correspond to a reduction of dimensionality.
arXiv commentSeminar held at JINR, Dubna, May 15, 2012. 16 pages, 8 figures
References in corpus (22)
- Quantum Gravity at a Lifshitz Point
- Spectral Dimension of the Universe
- Emergence of a 4D World from Causal Quantum Gravity
- Reconstructing the Universe
- Fractal universe and quantum gravity
- A non-perturbative Lorentzian path integral for gravity
- Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?
- Gravity on a multifractal
- QCD at High Energies and Two-Dimensional Field Theory
- On Singular Semi-Riemannian Manifolds
- Schwarzschild Singularity is Semi-Regularizable
- Lectures in (2+1)-Dimensional Gravity
- Coupling running through the Looking-Glass of dimensional Reduction
- Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang singularity
- Analytic Reissner-Nordstrom Singularity
- Metric dimensional reduction at singularities with implications to Quantum Gravity
- On the Weyl Curvature Hypothesis
- Regge Regime in QCD and Asymmetric Lattice Gauge Theory
- The Friedmann-Lemaitre-Robertson-Walker Big Bang singularities are well behaved
- Kerr-Newman Solutions with Analytic Singularity and no Closed Timelike Curves
- Riemannian -Dim Space-Time Manifolds with Nonstandard Topology which Admit Dimensional Reduction to Any Lower Dimension and Transformation of the Klein-Gordon Equation to the -Dim Schrödinger Like Equation
- Tensor Operations on Degenerate Inner Product Spaces