Shock wave gives back reaction to spacetime and the information is stored in the memory of background. Quantum memory effect of localised shock wave on Minkowski metric is investigated here. We find that the Wightman function for massless scalar field, on both sides of the wave location, turns out to be the same for usual Minkowski spacetime. Therefore the observables obtained from this, for any kind of observer, do not show the signature of the shock. Moreover, the vacuum states of field on both sides are equivalent. On the contrary, the correlator for the non-vacuum state does memorise the classical shock wave and hence the effect of it is visible in the observables, even for any frame. We argue that rather than vacuum state, the non-vacuum ones are relevant to retrieve the quantum information of classical memory.
The interaction of two counter-propagating electromagnetic waves in a vacuum is analyzed within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. The nonlinear electromagnetic wave in the quantum vacuum is characterized by wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron{positron pair generation at the shock wave front.
We show that the vacuum expectation value of the stress-energy tensor of a scalar particle on the background of a spherical gravitational shock wave does not give a finite expression in second order perturbation theory, contrary to the case seen for the impulsive wave. No infrared divergences appear at this order. This result shows that there is a qualitative difference between the shock and impulsive wave solutions which is not exhibited in first order.
In Yang-Mills theory massless point sources lead naturally to shock-wave configurations. Their magnetic counterparts endow the vacuum of the four-dimensional compact abelian model with a Coulomb-gas behaviour whose physical implications are briefly discussed. (Contribution to ``Quark Confinement and the Hadron Spectrum'', Como 20-24 June 1994. Revised version.)
Usual uniformly accelerated frame, in Dray-'t Hooft spacetime, does not see the any quantum imprint on Unruh effect due to localised shock wave in Minkowski spacetime. Here we argue that such non-appearance of quantum memory is specific to those particular observers which do not incorporate the presence of wave in their trajectory. In fact a detector, associated with a frame which is affected by the shock, can not be trivial in terms of its response. We explicitly show that the later type of frame detects particle in the shock wave Minkowski vacuum which is the effect of shock. Therefore this …
Gravitational shockwaves are simple exact solutions of Einstein equations representing the fields of ultrarelativistic sources and idealized gravitational waves (shocks). Historically, much work has focused on shockwaves in the context of possible black hole formation in high energy particle collisions, yet they remain at the forefront of research even today. Representing hard modes in the bulk, shocks give rise to the gravitational memory effect at the classical level and implant supertranslation (BMS) hair onto a classical spacetime at the quantum level. The aim of this paper is to further o…
We study two counter-propagating electromagnetic waves in the vacuum within the framework of the Heisenberg-Euler formalism in quantum electrodynamics. We show that the non-linear field equations decouple for ordinary wave case and can be solved exactly. We solve the non-linear field equations assuming the solution in a form of a Riemann wave. We discuss the properties of the nonlinear electromagnetic wave propagating in the quantum vacuum, such as the wave steepening, subsequent generation of high order harmonics and electromagnetic shock wave formation with electron-positron pair generation …
We find a self-consistent pp-gravitational shock wave solution to the semiclassical Einstein equations resulting from the $1/N$ approach to the effective action. We model the renormalized matter stress-energy-momentum tensor by $N$ massless scalar fields in the Minkowski vacuum plus a classical particle. We show that quantum effects generate a milder singularity at the position of the particle than the classical solution, but the singularity does not disappear. At large distances from the particle, the quantum correction decreases slowly, as $1/ρ^2$ ($ρ$ being the distance to the particle in t…
In previous publications we have extensively studied spherically symmetric solutions of gravity coupled to a non-standard type of non-linear electrodynamics containing a square root of the ordinary Maxwell Lagrangian (the latter is known to yield QCD-like confinement in flat space-time). A class of these solutions describe non-standard black holes of Reissner-Nordstroem-(anti-)-de-Sitter type with an additional constant radial vacuum electric field, in particular, a non-asymptotically flat Reissner-Nordstroem-type black hole. Here we study the ultra-relativistic boost (Aichelburg-Sexl-type) li…
We study holographic thermalization of a strongly coupled theory inspired by two colliding shock waves in a vacuum confining background. Holographic thermalization means a black hole formation, in fact a trapped surface formation. As a vacuum confining background we considered a well know bottom-up AdS/QCD model that provides the Cornell potential as well as reproduces QCD beta-function. We perturb vacuum background by colliding domain shock waves, that are assumed to be holographically dual to heavy ions collisions. Our main physical assumption is that we can make a restriction on the time of…
Matter fields are supertranslated upon crossing a shock wave, which leads to entanglement of the quantum vacuum between the two regions on either side of the shock wave. We probe this entanglement for a scalar field in a planar shock wave background by computing the Bogoliubov transformation between the inertial and uniformly accelerated observer. The resulting Bogoliubov coefficients are shown to reproduce the standard Unruh effect without dependence on the form factor of the shock wave. In contrast, excited states lead to observables that depend upon the form factor. In the context of nonsph…
Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the $d$-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordström an…
We find an {\it exact} pp--gravitational wave solution of the fourth order gravity field equations. Outside the (delta--like) source this {\it not} a vacuum solution of General Relativity. It represents the contribution of the massive, $m=(-β)^{-1/2}$, spin--two field associated to the Ricci squared term in the gravitational Lagrangian. The fourth order terms tend to make milder the singularity of the curvature at the point where the particle is located. We generalize this analysis to $D$--dimensions, extended sources, and higher than fourth order theories. We also briefly discuss the scatteri…
We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lor…
We discuss some implications of recent progress in understanding the black hole information paradox for complementarity in de Sitter space. Extending recent work by two of the authors, we describe a bulk procedure that allows information expelled through the cosmological horizon to be received by an antipodal observer. Generically, this information transfer takes a scrambling time $t = H^{-1}\log(S_{\rm dS})$. We emphasize that this procedure relies crucially on selection of the Bunch-Davies vacuum state, interpreted as the thermofield double state that maximally entangles two antipodal static…
We reinvestigate the emission of Hawking radiation during gravitational collapse to a black hole. Both CGHS collapse of a shock wave in (1+1)-dimensional dilaton gravity and Schwarzschild collapse of a spherically symmetric thin shell in (3+1)-dimensional gravity are considered. Studying the dynamics of in-vacuum polarization, we find that a multi-parametric family of out-vacua exists. Initial conditions for the collapse lead dynamically to different vacua from this family as the final state. Therefore, the form of the out-vacuum encodes memory about the initial quantum state of the system. Wh…
Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equation and using the Levi-Civita solution for a seed, we construct a cylindrically symmetric single-soliton solution. Although the Levi-Civita spacetime generally includes singularities on its axis of symmetry, it is shown that for the obtained single-soliton solution, such singularities can be removed by choice of certain special parameters. This single-soliton solution describes propagation of nonlinear cylindrical gravitational shock wave pulses rather than solitonic waves. By analyzing wave amplitud…
It is shown that flat spacetime can be dressed with a real scalar field that satisfies the nonlinear Klein-Gordon equation without curving spacetime. Surprisingly, this possibility arises from the nonminimal coupling of the scalar field with the curvature, since a footprint of the coupling remains in the energy-momentum tensor even when gravity is switched off. Requiring the existence of solutions with vanishing energy-momentum tensor fixes the self-interaction potential as a local function of the scalar field depending on two coupling constants. The solutions describe shock waves and, in the …
Starting from a generic generally covariant classical theory we introduce the logarithmic correction to the quantum wave equation. We demonstrate the emergence of the evolution time from the group of automorphisms of the von Neumann algebra governed by this non-linear correction. It turns out that such time parametrization is essentially energy-dependent and becomes global only asymptotically - when the energies get very small comparing to the effective quantum gravity scale. Similar thing happens to the Lorentz invariance - in the resulting theory it becomes an asymptotic low-energy phenomeno…
This short review is intended as a colloquium-level summary, for the Snowmass 2021 process, on recent theoretical results on infrared observables in quantum gravity. We rely on simple physical arguments, most notably a random walk intuition, to show how effects of quantum gravity in the ultraviolet (at the Planck length $\ell_p \approx 10^{-35} \mbox{ m}$) may integrate into the infrared when the large measurement length scale $L$ enters into the observable. A quantum uncertainty at lightsheet horizons would give rise to an accumulated effect of size $δL^2 \simeq \ell_p L/4 π$. We discuss how …
We examine wave propagation and the formation of shocks in strongly magnetized plasmas by applying a variational technique and the method of characteristics to the coupled magnetohydrodynamic (MHD) and quantum-electrodynamic (QED) equations of motion. In sufficiently strong magnetic fields such as those found near neutron stars, not only is the plasma extremely relativistic but the effects of QED must be included to understand processes in the magnetosphere. As Thompson & Blaes [1] find, the fundamental modes in the extreme relativistic limit of MHD coupled with QED are two oppositely directed…
