This review is an introduction to causal properties of general relativity. Topics include the
Raychaudhuri equation, singularity theorems of Penrose and Hawking, the black hole area …

This review summarizes the current status of the energy conditions in general relativity and
quantum field theory. We provide a historical review and a summary of technical results and …

Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian
Penrose Inequality states that the area of an outermost minimal surface N in M is bounded …

All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum
spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture …

Supplementing earlier literature by eg Tipler et al.(1980), Israel (1987), Thorne (1994),
Earman (1999), Senovilla and Garfinkle (2015), Curiel (2019) and Landsman (2021), I …

An energy condition, in the context of a wide class of spacetime theories (including general
relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter …

In this paper, connections are uncovered between the averaged weak (AWEC) and
averaged null (ANEC) energy condtions, and quantum inequality restrictions (uncertainty …

We prove the quantum null energy condition (QNEC), a lower bound on the stress tensor in
terms of the second variation in a null direction of the entropy of a region. The QNEC arose …

The expectation value< T ab> of the renormalized stress-energy tensor of quantum fields
generically violates the classical, local positive energy conditions of general relativity …

Two theorems related to gravitational time delay are proven. Both theorems apply to
spacetimes satisfying the null energy condition and the null generic condition. The first …