Boundary Quantum Mechanics

A reformulation of a physical theory in which measurements at the initial and final moments of time are treated independently is discussed, both on the classical and quantum levels. Methods of the standard quantum mechanics are used to quantize boundary phase space to obtain boundary quantum mechanics -- a theory that does not depend on the distinction between the initial and final moments of time, a theory that can be formulated without reference to the causal structure. As a supplementary material, the geometrical description of quantization of a general (e.g. curved) configuration space is presented.Comment: 35 pages, in Gravitation: Following the Prague Inspiration (To celebrate the 60th birthday of Jiri Bicak), O.Semerak, J.Podolsky, M.Zofka (eds.), World Scientific, Singapore, 2002, pp. 289--32

Minimal surfaces and entanglement entropy in anti-de Sitter space

According to Ryu and Takayanagi, the entanglement entropy in conformal field theory (CFT) is related through the AdS/CFT correspondence to the area of a minimal surface in the bulk. We study this holographic geometrical method of calculating the entanglement entropy in the vacuum case of a CFT which is holographically dual to empty anti-de Sitter (AdS) spacetime. Namely, we investigate the minimal surfaces spanned on boundaries of spherical domains at infinity of hyperbolic space, which represents a time-slice of AdS spacetime. We consider a generic position of two spherical domains: two disjoint domains, overlapping domains, and touching domains. In all these cases we find the explicit expressions for the minimal surfaces and the renormalized expression for the area. We study also the embedding of the minimal surfaces into full AdS spacetime and we find that for a proper choice of the static Killing vector we can model a dynamical situation of "tearing" of the minimal surface when the domains on which it is spanned are moved away from each other.Comment: 36 pages, 21 figures, for version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers

Radiative fields in spacetimes with Minkowski and de Sitter asymptotics

The classical Bondi-Penrose approach to the gravitational radiation theory in asymptotically flat spacetimes is recalled and recent advances in the proofs of the existence of such spacetimes are briefly reviewed. We then mention the unique role of the boost-rotation symmetric spacetimes, representing uniformly accelerated objects, as the only explicit radiative solutions known which are asymptotically flat; they are used as test beds in numerical relativity and approximation methods. The main part of the review is devoted to the examples of radiative fields in the vacuum spacetimes with positive cosmological constant. Type N solutions are analyzed by using the equation of geodesic deviation. Both these and Robinson-Trautman solutions of type II are shown to approach de Sitter universe asymptotically. Recent work on the the radiative fields due to uniformly accelerated charges in de Sitter spacetime ("cosmological Born's solutions") is reviewed and the properties of these fields are discussed with a perspective to characterize general features of radiative fields near a de Sitter-like infinity.Comment: 23 pages, invited talk, 10th Greek Relativity Meeting, Chalkidiki, May 200