Constructing AdS-like spacetimes

By Diego A. Carranza and Juan A. Valiente Kroon

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Maldacena’s AdS-CFT correspondence has brought the study of properties of anti de Sitter-like spacetimes (AdS spacetimes for short) to the centre of attention of a wide community of researchers. This class of spacetimes is characterised by a time-like conformal boundary similar to that of the anti-de Sitter spacetime. Maldacena’s correspondence relates AdS spacetimes to dual conformal field theories defined on the boundary of the spacetime. In particular, it allows to obtain information otherwise not easily accessible about the conformal field theories through the numerical computation of the dual spacetime. Thus, numerical simulations of these spacetimes have received a substantial amount of attention in recent years.  The existence of the time-like conformal boundary in these spacetimes also has implications of interest to mathematicians studying general properties of solutions to the Einstein equations. AdS spacetimes are examples of non-globally hyperbolic solutions to the Einstein field equations. Accordingly, if one wants to formulate a well-posed initial value problem for an AdS spacetime, in addition to the initial data, it is necessary to provide some information on the boundary. The prescription of boundary data is linked to the question of stability of this kind of solutions to the Einstein equations as, during the last years, numerical evidence has showed that under certain boundary conditions the anti-de Sitter spacetime is unstable under non-linear perturbations.

Diego A. Carranza is a PhD student at Queen Mary University of London, working under the supervision of Juan A. Valiente Kroon on conformal analysis of AdS-like spacetimes.

Juan A. Valiente Kroon is Reader in Applied Mathematics at Queen Mary University of London and author of a monograph on the use of conformal methods in General Relativity.

No go on spacetime reconstruction inside horizons

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Read the full article for free* in Classical and Quantum Gravity:
Covariant constraints on hole-ograhpy
Netta Engelhardt and Sebastian Fischetti 2015 Class. Quantum Grav. 32 195021
arXiv:1507.00354
*until 28/10/15

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Spacetime reconstruction in holography is limited in the presence of strong gravity.

Netta Engelhardt (left) and Sebastian Fischetti (right) practicing some of their less-developed skills at UCSB. Netta is a graduate student at UCSB. Sebastian was a graduate student at UCSB at the time of writing, and is now a postdoc at Imperial College London.

In recent years, it has become clear that there is a deep connection between quantum entanglement and geometry.  This mysterious connection has the potential to provide profound insights into the inner workings of a complete theory of quantum gravity.  Many concrete hints for how geometry and entanglement are related come from the so-called AdS/CFT duality conjectured by J.Maldacena, which relates certain types of quantum field theories (the “boundary”) to string theory on a negatively-curved spacetime called anti-de Sitter (AdS) space (the “bulk”) of one higher dimension.  In a certain limit, the string theory is

Holographic entanglement obeys strong subadditivity

Aron Wall is a member of the School of Natural Sciences at the Institute for Advanced Study. In his spare time he blogs at Undivided Looking. He was the 2013 recipient of the Bergmann-Wheeler thesis prize, which is sponsored by Classical and Quantum Gravity.

Gauge-gravity duality allows us to calculate properties of certain quantum field theories (QFT) from classical general relativity. One famous piece of this conjecture, due to Ryu and Takayanagi, relates the entanglement entropy in a QFT region to the area of a surface in the gravitational theory. In addition to being a clue about quantum gravity, this proposal is one of the few tools which allow us to calculate entanglement entropy analytically. Since the entanglement entropy is of increasing interest for field theory and condensed matter applications, it is important to check if the conjecture is true.

One important property of the entropy is strong subadditivity (SSA). This quantum inequality says that the sum of the entropies in two regions is always greater than the sum of the entropies of their union and intersection. My article uses proof

Three-dimensional massive gravity and AdS/CFT

Alasdair Routh (left) is a Ph.D. student in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Wout Merbis (right) is a Ph.D. student at the Centre for Theoretical Physics of the University of Groningen.

Einstein’s gravitational field equations, which relate the geometry of spacetime to the matter in it, can also be applied to a spacetime of three dimensions (3D) but in this case the matter completely determines the geometry, so there is no “room” for gravitational waves: gravitons in the quantum theory. However, in 3D there is a simple extension of Einstein’s second-order equations to the third-order equations of “Topologically-Massive Gravity” (TMG), which propagates a single massive spin-2 mode; i.e. a massive graviton.

In the context of asymptotically anti-de Sitter (AdS) space times, both 3D Einstein gravity and TMG are potentially semi-classical approximations to some consistent 3D quantum gravity theory defined, via the AdS/CFT correspondence, in terms of a 2D conformal field theory (CFT). However,