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

Cited by in corpus (77)

• The 1965 Penrose singularity theorem
• 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"
• Present status of the Penrose inequality
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Effects of Thermal Fluctuations on Non-minimal Regular Magnetic Black Hole
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Quasinormal modes-shadow correspondence for rotating regular black holes
• Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity
• Hidden past of dark energy cosmological models
• A Reformulation of the Hoop Conjecture
• Chronological spacetimes without lightlike lines are stably causal
• Lorentzian and signature changing branes
• Non-existence of self-similar solutions containing a black hole in a universe with a stiff fluid or scalar field or quintessence
• Observations in Quantum Cosmology
• Classification of spacelike surfaces in spacetime
• 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?
• Inner-extremal regular black holes from pure gravity
• Accreting Fluids onto Regular Black Holes Via Hamiltonian Approach
• Hayward black hole in scalar-Einstein-Gauss-Bonnet gravity in four dimensions
• The singularity theorems of General Relativity and their low regularity extensions
• A singularity theorem based on spatial averages
• The Hawking-Penrose singularity theorem for $C^1$-Lorentzian metrics
• A semiclassical singularity theorem
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• A critical appraisal of the singularity theorems
• Equatorial periodic orbits and gravitational waveforms in a black hole free of Cauchy horizon
• Nomen non est omen: Why it is too soon to identify ultra-compact objects as black holes
• New non-singular cosmological solution of non-local gravity
• Big Bang Singularity Resolution In Quantum Cosmology
• Gravitational signatures of a nonlinear electrodynamics in $f(R,T)$ gravity
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Spherical collapse of inhomogeneous dust cloud in the Lovelock theory
• On the nature of inner light-rings
• A stellar constraint on Eddington-inspired Born-Infeld gravity from cataclysmic variable binaries
• Complete classification of Friedmann-Lemaître-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics
• Motion of particles around a magnetically charged Euler-Heisenberg black hole with scalar hair and the Event Horizon Telescope
• Non-geodesic incompleteness in Poincaré gauge gravity
• The Interiors of Singularity-Free Rotating Black Holes
• On the existence of marginally trapped tubes in spacetimes with local rotational symmetry
• Marginally trapped and anti-trapped surfaces for matter evolution in D-dimensions
• On the causal characterization of singularities in spherically symmetric spacetimes
• Spacetime singularities and curvature blow-ups
• Charged superradiant instability in a spherical regular black hole
• Cosmic tangle: Loop quantum cosmology and CMB anomalies
• Geodesic completeness of a ring wormhole
• Depletion of energy from Naked Singular regions during gravitational collapse
• Regularity of curve integrable spacetimes
• Singularity theorems for warped products and the stability of spatial extra dimensions
• From disformal electrodynamics to exotic spacetime singularities
• The Endpoint Theorem
• A New Type of Singularity Theorem
• Cosmological Singularity and Power-Law Solutions in Modified Gravity
• Tipler Naked Singularities in $N$ Dimensions
• A Correspondence Between Distances and Embeddings for Manifolds: New Techniques for Applications of the Abstract Boundary
• Exact results in a punctured neighborhood of a strong curvature singularity
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• Widening the light cones on subsets of spacetime: some variations to stable causality
• A Scale-Dependent Distance Functional between Past Light Cones in Cosmology
• Constraints on the Scale Parameter of Regular Black Hole in Asymptotically Safe Gravity from Extreme Mass Ratio Inspirals
• Testing the null energy condition with precise distance measurements
• Traversable ghost wormholes
• Radial kinks in the boson stars
• Gravitational radiations from periodic orbits around a black hole in the effective field theory extension of general relativity
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• Spin effects on particle creation and evaporation in $f(R,T)$ gravity
• Classification of quantum states based on the null energy condition
• Gravitational Collapse of an Inhomogeneous Fluid in Rastall Theory
• Casimir traversable wormholes in Gauss-Bonnet gravity
• 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
• 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
• Geodesics near a curvature singularity of stationary and axially symmetric space-times
• Black Hole Singularities from Holographic Complexity