Singularity Theorems and Their Consequences

Abstract

This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains wrong headers and footers in its 1st page. This has led to many wrong citations, and to some confusion. The pdf file here contains the right information. ORIGINAL ABSTRACT: A detailed study of the singularity theorems is presented. I discuss the plausibility and reasonability of their hypotheses, the applicability and implications of the theorems, as well as the theorems themselves. The consequences usually extracted from them, some of them without the necessary rigour, are widely and carefully analysed with many clarifying examples and alternative views.

PDF file correcting an error in the bibliographical information that appears in the journal's online version. 148 pages, 17 figures, 247 references. Review on singularities that was published in the GRG journal in 1998

References in corpus (20)

• Eternal inflation and the initial singularity
• Regular Black Holes and Topology Change
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• Open and Closed Universes, Initial Singularities and Inflation
• Singularities in Inflationary Cosmology: A Review
• Axial symmetry and conformal Killing vectors
• Violations of the Weak Energy Condition in Inflating Spacetimes
• Theorems on shear-free perfect fluids with their Newtonian analogues
• Generalised Functions and Distributional Curvature of Cosmic Strings
• The Cosmological Time Function
• The abstract boundary---a new approach to singularities of manifolds
• A singularity-free space-time
• The 2m <= r property of spherically symmetric static spacetimes
• Homothetic perfect fluid space-times
• New Non-Diagonal Singularity-Free Cosmological Perfect-Fluid Solution
• Singularity-Free Cylindrical Cosmological Model
• Singularity Free Inhomogeneous Models with Heat Flow
• New Non-Separable Diagonal Cosmologies
• Causality violation and singularities
• The Total Space-Time of a Point-Mass When the Cosmological Constant is Nonzero and Its Consequences for the Lake-Roeder Black Hole

Cited by in corpus (159)

• The Bardeen Model as a Nonlinear Magnetic Monopole
• New Regular Black Hole Solution from Nonlinear Electrodynamics
• The 1965 Penrose singularity theorem
• A Primer on Energy Conditions
• Super-energy tensors
• Scalar fields, energy conditions, and traversable wormholes
• Energy conditions in general relativity and quantum field theory
• Geodesically complete black holes
• Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity
• Globally hyperbolic spacetimes can be defined as "causal" instead of "strongly causal"
• Marginally trapped tubes and dynamical horizons
• Present status of the Penrose inequality
• Causality theory for closed cone structures with applications
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Trapped surfaces and symmetries
• Convex neighborhoods for Lipschitz connections and sprays
• Trapped surfaces, horizons and exact solutions in higher dimensions
• Causal Relationship: a new tool for the causal characterization of Lorentzian manifolds
• Effects of Thermal Fluctuations on Non-minimal Regular Magnetic Black Hole
• Causal structures and causal boundaries
• Trapped surfaces
• Singularity theorems from weakened energy conditions
• Singularity theorems based on trapped submanifolds of arbitrary co-dimension
• Signature Change on the Brane
• Quasinormal modes-shadow correspondence for rotating regular black holes
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity
• Non-polynomial Lagrangian approach to Regular Black Holes
• Hidden past of dark energy cosmological models
• A Reformulation of the Hoop Conjecture
• Einstein-Cartan Cosmologies
• On the existence of horizons in spacetimes with vanishing curvature invariants
• Hawking's singularity theorem for $C^{1,1}$-metrics
• Bouncing Unitary Cosmology I: Mini-Superspace General Solution
• The Penrose singularity theorem in regularity $C^{1,1}$
• K-causality coincides with stable causality
• Chronological spacetimes without lightlike lines are stably causal
• The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
• Raychaudhuri equation and singularity theorems in Finsler spacetimes
• Complete conformal classification of the Friedmann-Lemaitre-Robertson-Walker solutions with a linear equation of state
• Lorentzian and signature changing branes
• Phantom singularities and their quantum fate: general relativity and beyond
• Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence
• A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
• Non-Singular Black Holes, the Cosmological Constant and Asymptotic Safety
• Observations in Quantum Cosmology
• Nonlinear electrodynamics in Bianchi spacetimes
• Classification of spacelike surfaces in spacetime
• Accretion onto Some Well-Known Regular Black Holes
• Geometric inequivalence of metric and Palatini formulations of General Relativity
• Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship
• Is the accelerated expansion evidence of a forthcoming change of signature on the brane?
• Plausible scenario for a generic violation of the weak cosmic censorship conjecture in asymptotically flat four dimensions
• Accreting Fluids onto Regular Black Holes Via Hamiltonian Approach
• Inner-extremal regular black holes from pure gravity
• Hayward black hole in scalar-Einstein-Gauss-Bonnet gravity in four dimensions
• Cylindrically symmetric dust spacetime
• From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect
• Turning big bang into big bounce: II. Quantum dynamics
• Asymptotic singular behavior of Gowdy spacetimes in string theory
• Accelerated observers and the notion of singular spacetime
• The singularity theorems of General Relativity and their low regularity extensions
• Geometry and topology of singularities in spherical dust collapse
• A singularity theorem based on spatial averages
• The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics
• A semiclassical singularity theorem
• Exterior Differential System for Cosmological G2 Perfect Fluids and Geodesic Completeness
• A singularity theorem for Einstein-Klein-Gordon theory
• New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Some global, analytical and topological properties of regular black holes
• Some Result on Cosmological and Astrophysical Horizons and Trapped Surfaces
• Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples
• Oscillating non-singular relativistic spherical model
• A critical appraisal of the singularity theorems
• A new derivation of singularity theorems with weakened energy hypotheses
• Smooth transitions from Schwarzschild vacuum to de Sitter space
• Equatorial periodic orbits and gravitational waveforms in a black hole free of Cauchy horizon
• Gauss-Bonnet braneworld redux: A novel scenario for the bouncing universe
• Einstein-Rosen waves and the self-similarity hypothesis in cylindrical symmetry
• Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes
• Singularities and n-dimensional black holes in torsion theories
• Cosmological singularity
• New non-singular cosmological solution of non-local gravity
• Big Bang Singularity Resolution In Quantum Cosmology
• Singularity free dilaton-driven cosmologies and pre-little-bang
• The Geometry of Black Hole singularities
• Would Two Dimensions be World Enough for Spacetime?
• Spherical collapse of inhomogeneous dust cloud in the Lovelock theory
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Gravitational signatures of a nonlinear electrodynamics in $f(R,T)$ gravity
• On the nature of inner light-rings
• Varying c cosmology and Planck value constraints
• A stellar constraint on Eddington-inspired Born-Infeld gravity from cataclysmic variable binaries
• Volume comparison for $C^{1,1}$ metrics
• Motion of particles around a magnetically charged Euler-Heisenberg black hole with scalar hair and the Event Horizon Telescope
• Quantization and spacetime topology
• Complete classification of Friedmann-Lemaître-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics
• Singularity theorems and the inclusion of torsion in affine theories of gravity
• Quantum creation and inflationary universes: a critical appraisal
• Generalizations of the Abstract Boundary singularity theorem
• From fundamental physics to tests with compact objects in metric-affine theories of gravity
• Non-geodesic incompleteness in Poincaré gauge gravity
• On the causal properties of warped product spacetimes
• The Interiors of Singularity-Free Rotating Black Holes
• Can Quantum Particles Cross a Horizon?
• Marginally trapped and anti-trapped surfaces for matter evolution in D-dimensions
• Geodesic Completeness of Orthogonally Transitive Cylindrical Spacetimes
• On the existence of marginally trapped tubes in spacetimes with local rotational symmetry
• Curvature invariants for the Bianchi IX spacetime filled with tilted dust
• Cosmic tangle: Loop quantum cosmology and CMB anomalies
• Charged superradiant instability in a spherical regular black hole
• Spacetime singularities and curvature blow-ups
• A covariant Hamiltonian tetrad approach to numerical relativity
• On the causal characterization of singularities in spherically symmetric spacetimes
• New family of inhomogeneous $\gamma$-law cosmologies: example of gravitational waves in a homogeneous $p=\varrho /3$ background
• Geodesically complete nondiagonal inhomogeneous cosmological solutions in dilatonic gravity with a stiff perfect fluid
• Are Causality Violations Undesirable?
• A new singularity theorem for black holes which allows chronology violation in the interior
• Singularity theorems for warped products and the stability of spatial extra dimensions
• Geodesic completeness of a ring wormhole
• Energy emission from high curvature region and its backreation
• Non-singular G2 stiff fluid cosmologies
• Depletion of energy from Naked Singular regions during gravitational collapse
• Regularity of curve integrable spacetimes
• From disformal electrodynamics to exotic spacetime singularities
• Bel-Robinson tensor and dominant energy property in the Bianchi type I Universe
• Cosmological Singularity and Power-Law Solutions in Modified Gravity
• A New Type of Singularity Theorem
• Tipler Naked Singularities in $N$ Dimensions
• The Endpoint Theorem
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• Constraints on the Scale Parameter of Regular Black Hole in Asymptotically Safe Gravity from Extreme Mass Ratio Inspirals
• Exact results in a punctured neighborhood of a strong curvature singularity
• A Scale-Dependent Distance Functional between Past Light Cones in Cosmology
• Spacetime Singularities in (2+1)-Dimensional Quantum Gravity
• Singular spacetime and quantum probe
• Widening the light cones on subsets of spacetime: some variations to stable causality
• A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary
• On the hypotheses of Penrose's singularity theorem under disformal transformations
• Testing the null energy condition with precise distance measurements
• Radial kinks in the boson stars
• Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
• Spin effects on particle creation and evaporation in $f(R,T)$ gravity
• Singularity free cosmological solutions of Einstein-Maxwell equations
• Traversable ghost wormholes
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• Charged Superradiant Instability of Spherically Symmetric Regular Black Holes in de Sitter Spacetime: Time- and Frequency-Domain Analysis
• Ultra-massive spacetimes in 2+1 dimensions with positive Λ
• Non-singular radiation cosmological models
• Classification of quantum states based on the null energy condition
• Role of equation of states and thermodynamic potentials in avoidance of trapped surfaces in gravitational collapse
• Geodesics near a curvature singularity of stationary and axially symmetric space-times
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory
• Casimir traversable wormholes in Gauss-Bonnet gravity
• Black Hole Singularities from Holographic Complexity
• Hypersurface Anchored Variational Principle for General Relativity
• Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences
• Can Light Cross a Singularity? Exact Solutions from Analogue Gravity