arXiv subjects

Benito A. Juárez-Aubry

Publications and source records attributed to Benito A. Juárez-Aubry.

At least 19 recordsLinked to original sources

arXiv2025

A new class of semiclassical gravity solutions, gravitational quantum stealths and regular Cauchy horizons

We consider semiclassical gravity with a Klein-Gordon field with mass $m^2 \geq 0$ and curvature coupling $ξ= 1/2$. We identify a special class of Hadamard two-point functions for which the semiclassical system is quasi-linear hyperbolic and, within this class, provide the first well-posedness result for semiclassical gravity without spacetime symmetries. These two-point functions yield stress-energy expectation values proportional to the spacetime metric (modulo ambiguities). If the proportionality constant vanishes, one has a quantum version of gravitational `stealth' configurations. We discuss that some of these solutions have regular Cauchy horizons in the light of strong cosmic censorship.

gr-qc↗

arXiv2025

Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime

We obtain semiclassical gravity solutions in the Poincaré fundamental domain of $(3+1)$-dimensional Anti-de Sitter spacetime, PAdS$_4$, with a (massive or massless) Klein-Gordon field (with possibly non-trivial curvature coupling) with Dirichlet or Neumann boundary. Some results are explicitly and graphically presented for special values of the mass and curvature coupling (e.g. minimal or conformal coupling). In order to achieve this, we study in some generality how to perform the Hadamard renormalisation procedure for non-linear observables in maximally symmetric spacetimes in arbitrary dimensions, with emphasis on the stress-energy tensor. We show that, in this maximally symmetric setting, the Hadamard bi-distribution is invariant under the isometries of the spacetime, and can be seen as a `single-argument' distribution depending only on the geodesic distance, which significantly simplifies the Hadamard recursion relations and renormalisation computations.

gr-qc↗

arXiv2025

Recent developments in semiclassical gravity

Semiclassical gravity (SG) aims to describe the semiclassical regime of quantum gravity. In SG quantum fields curve classical spacetime in an effective way through the expectation value of their stress-energy tensor, while propagating in the spacetime they curve. I discuss some advances in SG in three directions: (i) in understanding structural properties or special solutions of SG in spacetimes with isometries or special Hadamard states (ii) in understanding the initial value formulation and (iii) in black hole evaporation and why information loss is not expected. Semiclassical frameworks beyond SG are briefly surveyed. The hope is that this short note will provide a good set of references and indicate interesting open problems and directions.

gr-qc↗

arXiv2024

Quantum strong cosmic censorship and black hole evaporation

It is common folklore that semiclassical arguments suggest that in black hole evaporation an initially pure state can become mixed. This is known as the \emph{information loss puzzle} (or {\it paradox}). Here we argue that, if taken at face value, semiclassical gravity suggests the formation of a final singularity instead of information loss. A quantum strong cosmic censorship conjecture, for which we give a rigorous statement, supports this conclusion. Thus, there are no reasons to expect a failure of unitarity in black hole evaporation or for any quantum gravity theory that can `cure' singularities.

gr-qc↗

arXiv2024

The Hadamard condition on a Cauchy surface and the renormalized stress-energy tensor

Given a Cauchy surface in a curved spacetime and a suitably defined quantum state on the CCR algebra of the Klein-Gordon quantum field on that surface, we show, by expanding the squared spacetime geodesic distance and the `$U$' and `$V$' Hadamard coefficients (and suitable derivatives thereof) in sufficiently accurate covariant Taylor expansions on the surface that the renormalized expectation value of the quantum stress-energy tensor on the surface is determined by the geometry of the surface and the first 4 time derivatives of the metric off the surface, in addition to the Cauchy data for the field's two-point function. This result has been anticipated in and is motivated by a previous investigation by the authors on the initial value problem in semiclassical gravity, for which the geometric initial data corresponds {\it a priori} to the metric on the surface and up to 3 time derivatives off the surface, but where it was argued that the fourth derivative can be obtained with aid of the field equations on the initial surface.

gr-qc↗

arXiv2023

On the initial value problem for semiclassical gravity without and with quantum state collapses

We explore how the initial value problem may be formulated for globally hyperbolic, Hadamard, solutions of the semiclassical Einstein-Klein-Gordon equations. Given a set of data on an initial 3-surface, consisting of the values on the surface of a spacetime metric and its first 3 time derivatives off the surface, we introduce a notion of 'surface Hadamard' state on the CCR algebra of the surface. We conjecture that, for a given such set of classical Cauchy data with a surface Hadamard state satisfying the semiclassical constraint equations, the initial value problem will be well posed. We present similar conjectures for a semiclassical scalars model and semiclassical electrodynamics. Moreover, partly inspired by work of Parker and Simon in 1993, we define semiclassical gravity `physical solutions' to be those that are (jointly smooth) functions of $\hbar$ and of coordinates continuous in $\hbar$ at $\hbar =0$. We conjecture that for such solutions the second and third time derivatives of the metric off the surface need not be specified, but rather will be determined by that continuity condition. Assuming the initial value conjecture for such physical solutions holds, and that a stochastic rule were available which leads to quantum state collapses occurring on (non-intersecting) random Cauchy surfaces, we discuss the well-posedness of semiclassical gravity with stochastic quantum state collapses. We also discuss two notions of approximate physical semiclassical solutions (both with and without collapses): Namely solutions to order $\hbar$ (first discussed by Parker and Simon in 1993) and solutions to order $\hbar^0$. We point out that the latter do not require higher derivative terms or Hadamard subtractions, but that nevertheless order $\hbar^0$ semiclassical gravity is a distinct theory from classical general relativity capable of incorporating quantum interference phenomena.

gr-qc↗

arXiv2023

Are inertial vacua equivalent in Lorentz-violating theories? Does it matter?

Several approaches to quantum gravity suggest violations of Lorentz symmetry as low-energy signatures. This article uses a concrete Lorentz-violating quantum field theory to study different inertial vacua. We show that they are unitarily inequivalent and that the vacuum in one inertial frame appears, in a different inertial frame, to be populated with particles of arbitrarily high momenta. At first sight, this poses a critical challenge to the physical validity of Lorentz-violating theories, since we do not witness vacuum excitations by changing inertial frames. Nevertheless, we demonstrate that inertial Unruh-De Witt detectors are insensitive to these effects. We also discuss the Hadamard condition for this Lorentz-violating theory.

hep-th↗

arXiv2022

What happens once an accelerating observer has detected a Rindler particle?

In a seminal paper, Unruh and Wald found that the detection of a right Rindler particle by a linearly uniformly accelerated detector coupled to a Klein-Gordon field in the Minkowski vacuum leads to the creation of a Minkowski particle from the inertial viewpoint. In this paper, we revisit the framework studied by Unruh and Wald, but now consider in addition what happens once the particle has been measured somewhere in the right Rindler wedge. From an orthodox point of view, the change in the field state induced by the measurement is non-local and occurs both in the left and right Rindler wedges. If one takes semiclassical gravity seriously in this context, this seems to open the possiblity for designing superluminal communication protocols between two spacelike separated observers confined to the right and left Rindler wedges respectively. We discuss the possible ways in which physics could prevent such measurement-induced, faster-than-light signaling protocols.

gr-qc↗

arXiv2022

Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes

We prove that semiclassical gravity in conformally static, globally hyperbolic spacetimes with a massless, conformally coupled Klein-Gordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the metric and the Klein-Gordon theory. Namely, it admits unique and stable solutions whenever constrained fourth-order initial data for the conformal factor and suitably defined Hadamard initial data for the Klein-Gordon state are provided on a spacelike Cauchy surface. As no spacetime symmetries are imposed on the conformal factor, the present result implies that, provided constrained initial data exists, there also exist exact solutions to the semiclassical gravity equations beyond the isotropic, homogeneous or static cases.

math-ph↗

arXiv2022

Ground State for the Klein-Gordon field in anti-de Sitter spacetime with dynamical Wentzell boundary conditions

We consider a real Klein-Gordon field in the Poincaré patch of $(d+1)$-dimensional anti-de Sitter spacetime, PAdS$_{d+1}$, and impose dynamical boundary condition on the asymptotic boundary of PAdS$_{d+1}$ that depend explicitly on the second time derivative of the field at the boundary. These boundary conditions are of generalized Wentzell type. We construct the Wightman two-point function for the ground state of the Klein-Gordon theory whenever the parameters of the theory (the field mass, curvature coupling and boundary condition parameters) render such ground state admissible. In the cases in which the mass of the Klein-Gordon field and the curvature coupling term yield an effectively massless theory, we can define a boundary field whose dynamics are ruled by the dynamical boundary condition and construct, in addition to the Wightman function for the Klein-Gordon field, boundary-to-boundary, boundary-to-bulk and bulk-to-boundary propagators.

hep-th↗

arXiv2022

A short review of the Casimir effect with emphasis on dynamical boundary conditions

We give a short review on the static and dynamical Casimir effects, recalling their historical prediction, as well as their more recent experimental verification. We emphasise on the central role played by so-called {\it dynamical boundary conditions} (for which the boundary condition depends on a second time derivative of the field) in the experimental verification of the dynamical Casimir effect by Wilson et al. We then go on to review our previous work on the static Casimir effect with dynamical boundary conditions, providing an overview on how to compute the so-called local Casimir energy, the total Casimir energy and the Casimir force. We give as a future perspective the direction in which this work should be generalised to put the theoretical predictions of the dynamical Casimir effect experiments on a rigorous footing.

hep-th↗

arXiv2022

Quantum kicks near a Cauchy horizon

We analyse a quantum observer who falls geodesically towards the Cauchy horizon of a $(1+1)$-dimensional eternal black hole spacetime with the global structure of the non-extremal Reissner-Nordström solution. The observer interacts with a massless scalar field, using an Unruh-DeWitt detector coupled linearly to the proper time derivative of the field, and by measuring the local energy density of the field. Taking the field to be initially prepared in the Hartle-Hawking-Israel (HHI) state or the Unruh state, we find that both the detector's transition rate and the local energy density generically diverge on approaching the Cauchy horizon, respectively proportionally to the inverse and the inverse square of the proper time to the horizon, and in the Unruh state the divergences on approaching one of the branches of the Cauchy horizon are independent of the surface gravities. When the outer and inner horizons have equal surface gravities, the divergences disappear altogether in the HHI state and for one of the Cauchy horizon branches in the Unruh state. We conjecture, on grounds of comparison with the Rindler state in $1+1$ and $3+1$ Minkowski spacetimes, that similar properties hold in $3+1$ dimensions for a detector coupled linearly to the quantum field, but with a logarithmic rather than inverse power-law divergence.

gr-qc↗

arXiv2021

Semiclassical gravity in static spacetimes as a constrained initial value problem

We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard singular structure can be characterised explicitly, which allows one to in principle give initial data for the Wightman function that has correct distributional singularities, such that the expectation value of the renormalised stress-energy tensor of the solution can be defined, and that hence the semiclassical Einstein equations make sense. Assuming a "positive energy" condition for the Klein-Gordon operator, we characterise the states for which, if the constraints hold for initial data, they hold everywhere in spacetime. These turn out to be time-translation invariant states. The static case is analysed by conformal techniques, effectively reducing the problem to an ultrastatic one.

gr-qc↗

arXiv2021

Quantum field theory with dynamical boundary conditions and the Casimir effect: Coherent states

We have studied in a previous work the quantization of a mixed bulk-boundary system describing the coupled dynamics between a bulk quantum field confined to a spacetime with finite space slice and with timelike boundary, and a boundary observable defined on the boundary. Our bulk system is a quantum field in a spacetime with timelike boundary and a dynamical boundary condition-the boundary observable's equation of motion. Owing to important physical motivations, in such previous work we have computed the renormalized local state polarization and local Casimir energy for both the bulk quantum field and the boundary observable in the ground state and in a Gibbs state at finite, positive temperature. In this work, we introduce an appropriate notion of coherent and thermal coherent states for this mixed bulk-boundary system, and extend our previous study of the renormalized local state polarization and local Casimir energy to coherent and thermal coherent states. We also present numerical results for the integrated Casimir energy and for the Casimir force.

hep-th↗

arXiv2020

Black Holes and the 2020 Nobel Prize in Physics

The 2020 Nobel Prize in Physics distinguished two research projects on black holes, which are one of the most striking predictions of General Relativity. The prize was divided in two parts. The first half was awarded to Roger Penrose in recognition of his singularity theorems that guarantee that black holes, which were mathematically found since an early stage of the study of General Relativity, are not mere highly-symmetric, curious gravitational configurations, but robust predictions of the theory. The second half was awarded to Andrea Ghez and Reinhard Genzel who led two independent groups that carried out sophisticated observations of the center of our galaxy, which suggest that therein is a supermassive black hole. In this note, the main ideas of the theory of general relativity are briefly described, as well as the main features of black holes. The two works awarded in the aforementioned Nobel prize are described.

physics.pop-ph↗

arXiv2020

Unruh-like effects: Effective temperatures along stationary worldlines

We study the detailed balance temperatures recorded along all classes of stationary, uniformly accelerated worldlines in four-dimensional Minkowski spacetime, namely along (i) linear uniform acceleration, (ii) cusped, (iii) circular, (iv) catenary, and (v) helix worldlines, among which the Unruh temperature is the particular case for linear uniform acceleration. As a measuring device, we employ an Unruh-DeWitt detector, modeled as a qubit that interacts for a long time with a massless Klein-Gordon field in the vacuum state. The temperatures in each case (i) - (v) are functions of up to three invariant quantities: curvature or proper acceleration, $κ$, torsion, $b$, and hypertorsion, $ν$, and except for the case (i), they depend on the transition frequency difference of the detector, $ω$. We investigate numerically the behavior of the frequency-dependent temperatures for different values of $κ$, $b$, and $ν$ along the stationary worldlines (ii) - (v) and evaluate analytically the regimes where the temperatures recorded along the different worldlines coincide with each other in terms of relevant asymptotic limits for $κ$, $b$, or $ν$, and discuss their physical meaning. We demonstrate that the temperatures in cases (ii) - (v) dip under the Unruh temperature at low frequencies and go above the Unruh temperature for large $|ω|$. It is our hope that this study will be relevant to the design of experiments seeking to verify the Unruh effect or generalizations thereof.

gr-qc↗

arXiv2020

Quantum field theory with dynamical boundary conditions and the Casimir effect

We study a coupled system that describes the interacting dynamics between a bulk field, confined to a finite region with timelike boundary, and a boundary observable. In our system the dynamics of the boundary observable prescribes dynamical boundary conditions for the bulk field. We cast our classical system in the form of an abstract linear Klein-Gordon equation, in an enlarged Hilbert space for the bulk field and the boundary observable. This makes it possible to apply to our coupled system the general methods of quantization. In particular, we implement the Fock quantization in full detail. Using this quantization we study the Casimir effect in our coupled system. Specifically, we compute the renormalized local state polarization and the local Casimir energy, which we can define for both the bulk field and the boundary observable of our system. Numerical examples in which the integrated Casimir energy is positive or negative are presented.

hep-th↗

arXiv2019

Semi-classical gravity in de Sitter spacetime and the cosmological constant

We show that there exist solutions to the semi-classical gravity equations in de Sitter spacetime sourced by the renormalised stress-energy tensor of a free Klein-Gordon field. For the massless scalar, solutions exist for every possible value of the cosmological constant, provided that the curvature coupling parameter is chosen appropriately. In the massive case, imposing Wald's axioms for the renormalised stress-energy tensor, the mass of the field and the curvature coupling constraint the allowed values of $Λ$. For a massive, minimally coupled field, a "small $Λ$" solution is found, fixed by the relation $m^2 \simeq 4.89707 \times 10^{12} Λ$. We emphasise that in this framework, the {\it old} cosmological constant problem in its standard formulation plays no rôle, in the sense that there are no bare-vs-physical values of $Λ$, for only the physical $Λ$ appears in the semi-classical equations, and the value that it is allowed to take is fixed or restricted by the equations themselves. We explain that there is an important relation between the cosmological constant problem and the violation of Wald's stress-energy renormalisation axioms.

gr-qc↗