We discuss the geometry of timelike surfaces (two-dimensional submanifolds) in a Lorentzian manifold and its interpretation in terms of general relativity. A classification of such surfaces is presented which distinguishes four cases of special algebraic properties of the second fundamental form from the generic case. In the physical interpretation a timelike surface Σ can be viewed as the worl...

A bstract We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in boundary theory can be viewed as Wick rotation that changes spacelike subregion to one. An explicit definition EE 2d field theories is provided followed by numerical computations agree with analytic continuation replica method for CFTs. argue should correctly interpreted anothe...

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is never vanishing, then there are at least two distinct periodic geodesics; as ...

In conformally invariant quantum field theories one encounters besides the standard DHR superselection theory based on spacelike (Einsteincausal) commutation relations and their Haag duality another timelike (”Huygens”) based superselection structure. Whereas the DHR theory based on spacelike causality of observables confirmed the Lagrangian internal symmetry picture on the level of the physica...

Causality violating paths are known to exist in many spacetimes satisfying the Einstein field equations, especially those solutions associated with rotating matter or rotating singularities [1–3] (see also Bonnor [4], and references in [5]). However, examples of causality violating geodesics are sparse in the scientific literature. Chandrasekhar and Wright [6] showed that the Gödel spacetime [1...

Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalised energy density of the quantum field can be negative, when averaged along a timelike curve or over a more general timelike submanifold in spacetime. On globally hyperbolic spacetimes the minimally-coupled massive quantum Klein–Gordon field is known to obey a ‘difference’ QEI that depends on a ...

We employ the G-structure formalism to study supersymmetric solutions of minimal and SU(2) gauged supergravities in seven dimensions admitting Killing spinors with associated timelike Killing vector. The most general such Killing spinor defines an SU(3) structure. We deduce necessary and sufficient conditions for the existence of a timelike Killing spinor on the bosonic fields of the theories, ...

Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalised energy density of the quantum field can be negative, when averaged along a timelike curve or over a more general timelike submanifold in spacetime. On globally hyperbolic spacetimes the minimally-coupled massive quantum Klein–Gordon field is known to obey a ‘difference’ QEI that depends on a ...