Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds

Niall O'Murchadha

Niall ‘O Murchadha is an Editorial Board Member for Classical and Quantum Gravity and a Professor of Physics at University College Cork, Ireland

This is a very nice article which deserves to be studied carefully by anyone interested in finding solutions to the constraints. In particular, they show how to construct a solution which is far from maximal, and, at the same time, is asymptotically flat. Readers should be aware that the first theorem, Theorem 1.1, covers a much broader range of data than the second theorem, Theorem 1.2. Further, they should be aware that the titles of the theorems ‘Far-from-CMC’ (Theorem 1.1), and ‘Near-CMC’ (Theorem 1.2), especially the second one, are not particularly illuminating.

There are conditions which are surprising. No restriction is placed on Τ2 (other than the AF condition), but we are asked Continue reading

Welcome to CQG+

Clifford Will

Clifford Will is the Editor-in-Chief of Classical and Quantum Gravity, Distinguished Professor of Physics at the University of Florida, Chercheur Associé at the Institut d’Astrophysique de Paris, and James McDonnell Professor of Space Sciences Emeritus at Washington University in St. Louis. His research interests are the observational consequences of general relativity and alternative theories of gravity, dynamics of systems containing compact bodies, and gravitational radiation.

Who would ever have imagined that perusing papers on gravitational physics would be like  trying to get a sip from a fire hose?  When I was starting my career 45 years ago, we used to receive by snail mail three or four times a year some mimeographed pages from the GR society listing the 20 or so recent preprints or published papers in the field that had been received at the offices in Bern, Switzerland.  Today, the gr-qc branch of the arXiv alone features 70 – 100 articles per week, and that doesn’t even include related articles in particle physics, astrophysics or mathematics.  We all learn, of course, how to narrow our focus to those papers that directly impact our own specific research, but what if we want to read a paper in some different area?  How do we identify a really good paper in that subtopic?

Today we launch CQG+, which we hope will help.  With CQG+ we will notify you of papers of exceptional quality, as identified by our referees.  We will ask authors or referees of such papers to write short commentaries explaining what the paper is about in accessible terms.  The entries will also include information about the author(s).  We will announce focus issues, where we have invited leading researchers in a specific topic to contribute papers on their latest research.   Our CQG “highlights’’, in which our editorial board selects the best articles from the previous year, will be featured in CQG+.  There may be an occasional editorial or commentary on a topic of interest to the readers of CQG+.  In fact the content of CQG+ may evolve with time, and to that end, we invite your feedback.   What would you find most useful in CQG+?

All you have to do is enter your email address at the foot of this page, and you will receive email alerts when there is something new in CQG+.

On a personal note, I want to thank the CQG Editorial Board and the CQG publishing team, headed by Adam Day, for their support of the journal during the last five years.  That stalwart support went a long way toward convincing me to “re-up’’ for another five-year term as Editor.  I also want to thank our CQG authors and referees – no journal can thrive without first-rate authors publishing great research or good referees holding authors’ feet to the fire to ensure that their papers are of the highest quality.  Our only goal is to publish the best work in gravitational physics, and I encourage you all to submit your next great paper to CQG.  Continue reading

CQG is 30

Adam Day

Adam Day is the Publisher of Classical and Quantum Gravity and CQG+

Time contracts when you are enjoying yourself! It doesn’t seem like 5 whole years have passed since we were celebrating CQG’s quarter-century – and we certainly have had a lot to celebrate over that short time – including a substantial rise in the number of high quality papers published by CQG.

In recognition of this excellent research, we are launching this new companion website, CQG+. Readers of CQG+ can look forward to notifications of high quality papers published in CQG and unique insights into those papers from authors and referees. Additionally, CQG+ will feature the latest news from CQG including notifications of new focus issues, the famous CQG highlights and more. Sign up for email alerts using the box at the foot of this page. Continue reading

Black holes dual to exotic superconductors

 

Figure 2c

Each point under the blue curve corresponds to a superconducting p-wave black hole with a helical structure at temperature T and with helical pitch 2πk. The red line denotes the thermodynamically preferred black holes which have the smallest free energy at a given temperature. The black holes exhibit a reversal of the direction of the helical pitch at T~ 0.04.

The gauge-gravity correspondence provides a fascinating theoretical framework for investigating non-perturbative features of strongly coupled quantum systems using weakly coupled dual gravitational descriptions in one lower space-time dimension. In particular, the thermodynamic phase structure of the quantum system is obtained by finding the black hole solutions with the smallest free energy. Such studies have led to the discovery of fundamentally new classes of black hole solutions and it is hoped that these endeavours will lead to new insights into exotic materials which are observed in nature. Continue reading

Non-orientability constrains couplings in 2+1 quantum gravity

Jorma Louko

Jorma Louko is an Associate Professor in Applied Mathematics at the School of Mathematical Sciences, University of Nottingham

2+1 gravity is topological even without spacetime orientability, and quantisable for selected couplings

General relativity in four and more spacetime dimensions has local dynamical degrees of  freedom, as manifested for example in gravitational waves. In three spacetime dimensions,  by contrast, Einstein’s equations preclude local dynamics but allow still dynamics in the  global properties. This makes (2+1)-dimensional general relativity a dynamically simple but geometrically interesting arena for quantising gravity. Continue reading

Quantum gravity on a Klein bottle

Figure 1a

(A) Klein bottle, or the non-orientable surface of genus 2; The fundamental polygon representation of the Klein bottle is shown in the inset.

Figure 1b

(B) The orientable double cover of the Klein bottle is the orientable surface of genus 1, or the toroid. Closed loops on the double cover that traverse the non-orientable boundary— red/blue line in (B)— wind around the non-orientable surface in panel (A) twice.

In this work we study a model of quantum gravity on two-dimensional, non-orientable manifolds, for example a Klein bottle. We find that for a simplified version of quantum gravity called U(1) BF theory, a generalization of U(1) Chern-Simons theory, the fact that the manifold is non-orientable induces severe constraints on the values allowed for the coupling constant appearing in the action; in fact it can only take values of ½, 1, or 2. This comes about because the coupling constant appears in the commutation relation (or uncertainty relation) for the fields, and because the fields in the effective gauge theory must be consistent with the discrete symmetry groups for homeomorphisms on manifold. These discrete symmetry groups include the large gauge transformation group, the holonomy group, and the mapping class group. Continue reading

Boundary states in higher-dimensional loop quantum gravity

Higher-dimensional Chern-Simons theory appears in the description of isolated horizon boundaries in higher-dimensional General Relativity.

It is a well-known fact that the presence of boundaries (“edges”) leads to the concept of boundary states, which e.g. ensure gauge invariance for parallel transporters ending on the boundary. Most famously, the quantum Hall effect can be explained using such states. In the context of black hole (quantum) physics, boundary states are important since they are microscopic states associated to the horizon of the black hole. Counting such boundary states in agreement with the macroscopic properties of a black hole is thus a good candidate for a microscopic explanation of the Bekenstein-Hawking entropy. This paradigm has been successfully employed in 3+1 dimension in the context of loop quantum gravity, a canonical quantisation of General Relativity. Continue reading