Category Archives: Author Insights

Author Insights are short informal articles written by authors of high quality CQG papers for the broad community served by the journal.

Non-CMC solutions to the constraints on AE manifolds

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Caleb Meier

Caleb Meier is a postdoctoral researcher in mathematics at the University of California, San Diego.

In the n+1 formalism of general relativity, the (n+1)-dimensional space-time is decomposed into n-dimensional space-like slices that are parametrized by a time function.  This is the basis for formulating Einstein’s equation as an initial value problem.  In an effort to understand which space-times are constructible, an important question is, “What is the admissible class of initial data for this problem?”  This question is addressed by analyzing the so-called Einstein constraint equations, which are an undetermined system of equations to be solved for a metric and an extrinsic curvature tensor.
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General-relativistic hydrodynamics: going beyond second-order convergence

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High accuracy in numerical relativity simulations is essential: now it can also be achieved for non-vacuum spacetimes.

Merging binary neutron stars are among the most promising sources of gravitational waves (GWs) for the next generation of interferometric detectors. Such waves carry valuable information about the masses, radii, and deformability of the two stars. Even a single detection would set stringent constraints on the equation of state of nuclear matter, which is still poorly known. Gravitational-wave observations, in combination with electromagnetic/neutrino counterparts, would also help to unravel the mystery behind gamma-ray bursts. Continue reading →

Black holes dual to exotic superconductors

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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 →

Quantum gravity on a Klein bottle

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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

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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 →