Numerical relativity and high energy physics: Recent developments

We review recent progress in the application of numerical relativity techniques to astrophysics and high-energy physics. We focus on some developments that took place within the "Numerical Relativity and High Energy Physics" network, a Marie Curie IRSES action that we coordinated, namely: spin evolution in black hole binaries, high-energy black hole collisions, compact object solutions in scalar-tensor gravity, superradiant instabilities and hairy black hole solutions in Einstein's gravity coupled to fundamental fields, and the possibility to gain insight into these phenomena using analog gravity models.This is the final version of the article. It first appeared from World Scientific via https://doi.org/ 10.1142/S021827181641022

Uniformly Accelerated Observer in Moyal Spacetime

In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum of the inertial observer appears thermal to the accelerated observer, also known as the Unruh effect. We argue that an accelerating frame may be similarly defined (i.e. as a sequence of instantaneous Lorentz transformations) in noncommutative Moyal spacetime, and discuss the twisted quantum field theory appropriate for such an accelerated observer. Our analysis shows that there are several new features in the case of noncommutative spacetime: chiral massless fields in $(1+1)$ dimensions have a qualitatively different behavior compared to massive fields. In addition, the vacuum of the inertial observer is no longer an equilibrium thermal state of the accelerating observer, and the Bose-Einstein distribution acquires $\theta$-dependent corrections.Comment: 19 pages. Typos correcte

Tidal Forces in Reissner-Nordström Spacetimes

We analyze the tidal forces produced in the spacetime of Reissner-Nordstr\"om black holes. We point out that the radial component of the tidal force changes sign just outside the event horizon if the charge-to-mass ratio is close to $1$ unlike in Schwarzschild spacetime of uncharged black holes, and that the angular component changes sign between the outer and inner horizons. We solve the geodesic deviation equations for radially falling bodies towards the charged black hole. We find, for example, that the radial component of the geodesic deviation vector starts decreasing inside the event horizon unlike in the Schwarzschild case

Why should we care about quantum discord?

Entanglement is a central feature of quantum theory. Mathematical properties and physical applications of pure state entanglement make it a template to study quantum correlations. However, an extension of entanglement measures to mixed states in terms of separability does not always correspond to all the operational aspects. Quantum discord measures allow an alternative way to extend the idea of quantum correlations to mixed states. In many cases these extensions are motivated by physical scenarios and quantum information protocols. In this chapter we discuss several settings involving correlated quantum systems, ranging from distributed gates to detectors testing quantum fields. In each setting we show how entanglement fails to capture the relevant features of the correlated system, and discuss the role of discord as a possible alternative.Comment: Written for "Lectures on general quantum correlations and their applications

Entangled wavepackets in the vacuum

Motivated by the black hole firewall problem, we find highly entangled pairs of spatially localized modes in quantum field theory. We demonstrate that appropriately chosen wavepackets localized outside the horizon are nearly purified by 'mirror' modes behind the horizon. In addition, we calculate the entanglement entropy of a single localized wavepacket in the Minkowski vacuum. In all cases we study, the quantum state of the system becomes pure in the limit that the wavepackets delocalize; we quantify the trade-off between localization and purity.Comment: 33 pages, 4 figures. v3: typos correcte

Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories

Through the AdS/CFT correspondence, we study a uniformly accelerated quark in the vacuum of strongly-coupled conformal field theories in various dimensions, and determine the resulting stochastic fluctuations of the quark trajectory. From the perspective of an inertial observer, these are quantum fluctuations induced by the gluonic radiation emitted by the accelerated quark. From the point of view of the quark itself, they originate from the thermal medium predicted by the Unruh effect. We scrutinize the relation between these two descriptions in the gravity side of the correspondence, and show in particular that upon transforming the conformal field theory from Rindler space to the open Einstein universe, the acceleration horizon disappears from the boundary theory but is preserved in the bulk. This transformation allows us to directly connect our calculation of radiation-induced fluctuations in vacuum with the analysis by de Boer et al. of the Brownian motion of a quark that is on average static within a thermal medium. Combining this same bulk transformation with previous results of Emparan, we are also able to compute the stress-energy tensor of the Unruh thermal medium.Comment: 1+31 pages; v2: reference adde

Quantum fields and local measurements

The process of quantum measurement is considered in the algebraic framework of quantum field theory on curved spacetimes. Measurements are carried out on one quantum field theory, the "system", using another, the "probe". The measurement process involves a dynamical coupling of "system" and "probe" within a bounded spacetime region. The resulting "coupled theory" determines a scattering map on the uncoupled combination of the "system" and "probe" by reference to natural "in" and "out" spacetime regions. No specific interaction is assumed and all constructions are local and covariant. Given any initial state of the probe in the "in" region, the scattering map determines a completely positive map from "probe" observables in the "out" region to "induced system observables", thus providing a measurement scheme for the latter. It is shown that the induced system observables may be localized in the causal hull of the interaction coupling region and are typically less sharp than the probe observable, but more sharp than the actual measurement on the coupled theory. Post-selected states conditioned on measurement outcomes are obtained using Davies-Lewis instruments that depend on the initial probe state. Composite measurements involving causally ordered coupling regions are also considered. Provided that the scattering map obeys a causal factorization property, the causally ordered composition of the individual instruments coincides with the composite instrument; in particular, the instruments may be combined in either order if the coupling regions are causally disjoint. This is the central consistency property of the proposed framework. The general concepts and results are illustrated by an example in which both "system" and "probe" are quantized linear scalar fields, coupled by a quadratic interaction term with compact spacetime support. System observables induced by simple probe observables are calculated exactly, for sufficiently weak coupling, and compared with first order perturbation theory