Light rays, singularities, and all that

  title={Light rays, singularities, and all that},
  author={Edward Witten},
  journal={Reviews of Modern Physics},
  • E. Witten
  • Published 2020
  • Physics
  • Reviews of Modern Physics
This article is an introduction to causal properties of General Relativity. Topics include the Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area theorem, topological censorship, and the Gao-Wald theorem. The article is based on lectures at the 2018 summer program Prospects in Theoretical Physics that was held at the IAS as well as the New Zealand Mathematical Research Institute summer school held in Nelson in January, 2020. 
Raychaudhuri Equation in Kaluza Klein space time
We studied the Raychaudhuri equation in Kaluza-Klein space-time. We derived an additional term that is solely due to Kaluza-Klein's unification. This term affects the defocus of world lines near theExpand
A new derivation of singularity theorems with weakened energy hypotheses
The original singularity theorems of Penrose and Hawking were proved for matter obeying the Null Energy Condition or Strong Energy Condition respectively. Various authors have proved versions ofExpand
WdW-patches in AdS3 and complexity change under conformal transformations II
  • M. Flory
  • Physics
  • Journal of High Energy Physics
  • 2019
A bstractWe study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincaré-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting someExpand
Conformally invariant averaged null energy condition from AdS/CFT
We study the compatibility of the AdS/CFT duality with the bulk and boundary causality, and derive a conformally invariant averaged null energy condition (CANEC) for quantum field theories in 3 andExpand
Multiresolution quantum field theory in light-front coordinates
We analyse the use of wavelet transform in quantum field theory models written in light-front coordinates. In a recent paper W.N.Polyzou used x variable as ’time’, and applied wavelet transform toExpand
Classical Energy Conditions and Quantum Gravity
We propose a mechanism for restoring classical energy conditions in quantum gravity regime based on quantum inequalities and quantum interest conjecture. We assumed negative energy states to beExpand
Microscopic Description of the Multiverse
We propose a unification scheme based on quantum energy inequalities and quantum interest conjecture. By adopting this direction we were able to answer many outstanding questions related to the factExpand
Multiresolution quantum field theory in infinite-momentum frame
We analyse the use of wavelet transform in quantum field theory models written in infinite momentum frame. In a recent paper [1] the author used x variable as ’time’, and applied wavelet transform toExpand
Humanly traversable wormholes
We point out that there can be humanly traversable wormhole solutions in some previously considered theories for physics beyond the Standard Model, namely the Randall-Sundrum model.
Towards precision holography
A minimal requirement for any strongly coupled gauge field theory to have a classical dual bulk gravity description is that one should in principle be able to recover the full geometry as encoded onExpand


A Positive mass theorem based on the focusing and retardation of null geodesics
A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being thatExpand
The singularities of gravitational collapse and cosmology
  • S. Hawking, R. Penrose
  • Physics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected ifExpand
Energy conditions and spacetime singularities
In this paper, a number of theorems are proven which collectively show that singularities will occur in spacetime under weaker energy conditions than the strong energy condition. In particular, theExpand
Geodesic focusing, energy conditions and singularities
Standard work on geodesic focusing assumes that a pointwise inequality, known as an energy condition, holds. This pointwise condition has been weakened by Tipler (1978) to the requirement that aExpand
Gravitational collapse and spacetime singularities
The nature of gravitational collapse was the subject of debate and controversy for much of the last century. During the 1960’s and 1970’s our understanding of general relativity consolidated andExpand
The AdS/CFT correspondence and topological censorship
Abstract In this Letter we consider results on topological censorship, previously obtained by the authors in Phys. Rev. D 60 (1999) 104039, in the context of the AdS/CFT correspondence. These, andExpand
Gravitational waves in general relativity. VI. The outgoing radiation condition
  • R. Sachs
  • Physics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1961
A covariant formulation of the outgoing radiation condition for gravitational fields is proposed. The condition is based on a detailed examination of the geometry of null lines and of the algebraicExpand
Black holes in general relativity
It is assumed that the singularities which occur in gravitational collapse are not visible from outside but are hidden behind an event horizon. This means that one can still predict the futureExpand
Global aspects of the Cauchy problem in general relativity
It is shown that, given any set of initial data for Einstein's equations which satisfy the constraint conditions, there exists a development of that data which is maximal in the sense that it is anExpand
Averaged null energy condition from causality
A bstractUnitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, weExpand