arXiv subjects

João Paulo M. Pitelli

Publications and source records attributed to João Paulo M. Pitelli.

18 recordsLinked to original sources

arXiv2026

Corrections to the Unruh Effect from Robin Boundary Conditions in Punctured Minkowski Spacetime

We consider a real massless scalar field in punctured Minkowski spacetime, endowed at the removed origin with the stable one-parameter family of Robin boundary conditions $G(0)-βG'(0)=0$, $β\geq0$. We obtain the boundary-induced part of the static ground-state Wightman function in closed form and study the response of a uniformly accelerated Unruh-DeWitt detector. The puncture breaks the boost symmetry underlying the stationary Unruh response, so the boundary-induced pullback is nonstationary in proper time. The corresponding subtracted detector contribution can either enhance or suppress the ordinary Minkowski response and depends on the Robin parameter, the detector gap, and the portion of the trajectory sampled. For the unshifted, radially aligned trajectory studied in detail, we prove that the boundary-induced pullback is absolutely integrable in the two proper-time variables. Consequently, as the smooth interaction is extended over the full detector history, this contribution approaches a finite limit and remains $O(1)$, producing no additional term linear in the interaction duration. The formal Neumann limit is singular: the boundary-induced two-point function grows logarithmically because of an infrared singularity in the $s$-wave sector, and the numerical response exhibits growth consistent with this asymptotic behavior.

hep-th↗

arXiv2026

Vacuum fluctuations and the renormalized stress-energy tensor on a cone with arbitrary boundary conditions

We analyze the vacuum fluctuations and the stress-energy tensor of a scalar field of mass $M$ in a conical spacetime, where the topological singularity at the apex requires boundary conditions for the field equation. The necessity of boundary conditions was established by Kay and Studer in the early 1990s, while for $M=0$ stability is achieved only under Dirichlet boundary conditions, and for $M>q$ the field is stable and a localized mode emerges. This mode admits a natural interpretation as a covariant model of an extended particle detector, which allows us to investigate whahow such detectors modify the local vacuum structure. In this framework, the renormalized stress-energy tensor offers a natural way to quantify the influence of the detector on the surrounding spacetime.

hep-th↗

arXiv2026

Vacuum polarization in the Schwarzschild black hole with a global monopole

We investigate vacuum polarization on the event horizon of a Schwarzschild black hole carrying a global monopole. For a massless scalar field $Ψ$ in the Hartle-Hawking state and with arbitrary curvature coupling, we compute the renormalized vacuum expectation value $\langle Ψ^2 \rangle_{\textrm{ren}}$. The monopole produces a solid-angle deficit and makes the spacetime non-Ricci-flat. Working perturbatively in the monopole parameter $η$ and retaining terms through $O(η^2)$, we find that $\langle Ψ^2 \rangle_{\textrm{ren}}$ on the horizon splits into two contributions: a genuinely monopole-induced term evaluated at the horizon and the usual Schwarzschild result--with the event horizon radius modified by the presence of $η$. We also investigate whether an analogous decomposition holds for $\langle T^μ_{\phantomμμ}\rangle_\textrm{ren}$ when it is determined by this method. Our result parallels earlier analyses of Schwarzschild black holes pierced by a cosmic string.

gr-qc↗

arXiv2026

Invisible extended Unruh-DeWitt detector

We develop a localized particle detector model formulated as a massive quantum field on Minkowski spacetime with the spatial origin excised. To render the problem well posed at the puncture, we impose boundary conditions at the excised point, which we take to be of Robin type. This setup yields a discrete sector, given by bound state solutions of the radial equation with real, positive frequencies, which characterizes the detector. We construct the full two-point function and show its decomposition into (i) the discrete radial bound state sector, (ii) the boundary condition modified continuous sector, and (iii) the unmodified Dirichlet sector. We then compute the detector field's stress-energy tensor and prove its covariant conservation. For the specific localized modes in this setup, the discrete sector contribution cancels in the complete stress-energy tensor, leaving only boundary condition induced terms. Notably, the discrete modes crucial to localized field based detectors emerge naturally from the boundary conditions, without ad hoc confining potentials, providing a covariant framework that extends the traditional Unruh-DeWitt paradigm. This mechanism is not restricted to Minkowski spacetime; the same construction can be applied to massive fields on backgrounds with naked singularities, such as conical and global monopole spacetimes, offering a unified route to detector localization in a broad class of geometries.

hep-th↗

arXiv2025

Quantum detection of boundary conditions

The quantum detection of spacetime conicity was investigated in reference [Phys. Lett. B 820, 136482 (2021)] through the analysis of the response function of an Unruh-deWitt detector coupled to a massless scalar field. In particular, it was shown that the detector can discern the presence of the deficit angle of a region of spacetime even when it is placed on a flat region with no conical deficit and (due to the rapid switching on and off) is classically isolated from the conical region. The scalar field was supposed to be continuous at the three dimensional timelike hypersurface connecting both regions and it was argued that the non-trivial effects on the response function were only due to the deficit angle of the outer conical region. In this paper, we study the response function of the Unruh-deWitt detector on the same classical framework, but exploring the effects of the choice of boundary conditions for the scalar field at the connecting hypersurface. These boundary conditions are extracted from the two-interval Sturm-Liouville theory and each one gives rise to a physically inequivalent sensible dynamics for the quantum field. We show that they play an important role on the response function of the detector, which effectively ``feels'' the combined effect of conicity + boundary condition.

hep-th↗

arXiv2024

Unruh-deWitt detector in impulsive plane wave spacetimes

We investigate the response function of an inertial Unruh-deWitt detector in an impulsive plane wave spacetime. Through symmetry considerations applied to the Wightman function, we demonstrate that the response function remains invariant for any inertial detector, even for those experiencing a discontinuous lightcone coordinate shift after interacting with the shockwave. This implies that the vacuum state in an impulsive plane wave spacetime is preserved under the associated spacetime symmetries. Additionally, we confirm that the quantum imprint of the shockwave, as discussed in [J. High Energ. Phys. 2021, 54 (2021)], is not an artifact and exhibits a distinct characteristic form. We identify this form by defining a "renormalized" response function for an eternally inertial detector, with Minkowski spacetime as a reference.

gr-qc↗

arXiv2023

Robin boundary conditions in acoustic BTZ black holes

We introduce an analog model for the conformally coupled scalar field on the BTZ black hole. The model is based on the propagation of acoustic waves in a Laval nozzle. Since the BTZ black hole is not a globally hyperbolic spacetime, the dynamics of the scalar field is not well defined until extra boundary conditions are prescribed at its spatial infinity. We show that quasinormal modes (QNMs) satisfying Dirichlet, Neumann, and Robin boundary conditions in the BTZ black hole can be interpreted in terms of ordinary QNMs defined with respect to an appropriately extended nozzle. We also discuss the stability of our model with respect to small perturbations.

gr-qc↗

arXiv2023

Quantum Mechanics on Sharply Bent Wires via Two-Interval Sturm-Liouville Theory

We study quantum mechanics on a curved wire by approximating the physics around the curved region by three parameters coming from the boundary conditions given by the two interval Sturm-Liouville theory. Since the geometric potential on a highly curved wire is strong an non-integrable, these parameters depend on the regularization of the curved wire. Hence, unless we know precisely the shape of the wire, the presented method becomes not only a useful approximation, but also a necessary scheme to deal with quantum mechanics on highly curved wires.

quant-ph↗

arXiv2022

Comment on "Analog Schwarzschild-like geometry in fluids with external pressure''

In Ref. [1], exact (not only conformally related) analogue models for the Schwarzschild and Reissner-Nordström spacetimes were found. The background non-relativistic fluid flow was sustained by an external body force which is not affected by the linearised fluctuations. Following a different route, by modelling the external force as the gradient of an external pressure, it was shown in~\cite{bilic} that the speed of sound is significantly modified. This effective speed of sound turns out to be inconsistent with the continuity equation. In this comment we analyse these two contradictory conclusions. We first show that the heuristic justification for the introduction of the external force via a variational principle given in Ref. [2] is conceptually incorrect. Then, by adding the external force appropriately, we show that the conclusions in [1] remain valid.

gr-qc↗

arXiv2022

Boundary conditions for isolated asymptotically anti-de Sitter spacetimes

We revisit the propagation of classical scalar fields in a spacetime which is asymptotically anti-de Sitter. The lack of global hyperbolicity of the underlying background gives rise to an ambiguity in the dynamical evolution of solutions of the wave equation, requiring the prescription of extra boundary conditions at the conformal infinity to be fixed. We show that the only boundary conditions tha are compatible with the hypothesis that the system is isolated, as defined by the (improved) energy-momentum tensor, are of Dirichlet and Neumann types.

gr-qc↗

arXiv2021

Thermal effects on a global monopole with Robin boundary conditions

Within quantum field theory on a global monopole spacetime, we study thermal effects on a naked singularity and its relation with boundary conditions. We first obtain the two-points functions for the ground state and for thermal states of a massive, arbitrarily-coupled, free scalar field compatible with Robin boundary conditions at the singularity. We then probe these states using a static Unruh-Dewitt particle detector. The transition rate is analyzed for the particular cases of massless minimally or conformally coupled fields at finite temperature. To interpret the detector's behavior, we compute the thermal contribution to the ground-state fluctuations and to the energy density. We verify that the behavior of the transition rate, the fluctuations and the energy density are closely intertwined. In addition, we find that these renormalized quantities remain finite at the singularity for, and only for, Dirichlet boundary condition.

hep-th↗

arXiv2021

Unruh-DeWitt detector in $\textrm{AdS}_2$

We find the response function and the transition rate for an Unruh-DeWitt detector interacting with a conformal scalar field in global two-dimensional anti--de Sitter (AdS) spacetime with different boundary conditions at its conformal infinities. We calculate the particle energy spectrum as seen by subcritical accelerated detectors and discuss how it depends on the choice of the boundary condition. We show that, despite this nontrivial dependence on the boundary conditions, the limit when the AdS length scale tends to zero is well defined and leads to the well-known results of 1+1 Minkowski space. One can thus interpret the AdS energy scale as a natural regulator for the well-known infrared ambiguity of massless scalar fields in 1+1 Minkowski spacetime.

gr-qc↗

arXiv2021

Analogue models for Schwarzschild and Reissner-Nordström spacetimes

We present analogue models for the Schwarzschild and Reissner-Nordström (RN) spacetimes based on unidirectional hydrodynamic flows. We show that, with appropriate coordinate transformations, sound waves in a moving fluid propagate as scalar fields at the equatorial sections of Schwarzschild and RN black holes. The coordinate associated with the direction of the flow plays the role of the radial coordinate in standard Schwarzschild/RN coordinates, while the transversal spatial coordinate is related to the angular coordinate on each equatorial slice. The magnitude of the flow velocity is related to the mass and charge of the analogue black hole. Physical quantities like pressure and density remain finite at the analogue horizon, thereby resulting in sound waves that are well defined almost everywhere, except possibly at the analogue black hole singularity.

gr-qc↗

arXiv2019

Boundary conditions and renormalized stress-energy tensor on a Poincaré patch of $\textrm{AdS}_2$

Quantum field theory on anti-de Sitter spacetime requires the introduction of boundary conditions at its conformal boundary, due essentially to the absence of global hyperbolicity. Here we calculate the renormalized stress-energy tensor $T_{μν}$ for a scalar field $ϕ$ on the Poincaré patch of $\text{AdS}_2$ and study how it depends on those boundary conditions. We show that, except for the Dirichlet and Neumann cases, the boundary conditions break the maximal $\textrm{AdS}$ invariance. As a result, $\langleϕ^2\rangle$ acquires a space dependence and $\langle T_{μν}\rangle$ is no longer proportional to the metric. When the physical quantities are expanded in a parameter $β$ which characterizes the boundary conditions (with $β=0$ corresponding to Dirichlet and $β=\infty$ corresponding to Neumann), the singularity of the Green's function is entirely subtracted at zeroth order in $β$. As a result, the contribution of nontrivial boundary conditions to the stress-energy tensor is free of singular terms.

gr-qc↗

arXiv2012

Quantum Singularities in Horava-Lifshitz Cosmology

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $ (t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary.

gr-qc↗

arXiv2010

Quantum singularities in FRW universe revisited

The components of the Riemann tensor in the tetrad basis are quantized and, through the Einstein equation, we find the local expectation value in the ontological interpretation of quantum mechanics of the energy density and pressure of a perfect fluid with equation of state $p=\frac{1}{3}ρ$ in the flat Friedmann-Robertson-Walker quantum cosmological model. The quantum behavior of the equation of state and energy conditions are then studied and it is shown that the later is violated since the singularity is removed with the introduction of quantum cosmology, but in the classical limit both the equation of state and the energy conditions behave as in the classical model. We also calculate the expectation value of the scale factor for several wave packets in the many-worlds interpretation in order to show the independence of the non singular character of the quantum cosmological model with respect to the wave packet representing the wave function of the Universe. It is also shown that, with the introduction of non-normalizable wave packets, solutions of the Wheeler-DeWitt equation, the singular character of the scale factor, can be recovered in the ontological interpretation.

gr-qc↗

arXiv2009

Quantum Singularities Around a Global Monopole

The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator are found and their importance to the quantum interpretation of singularities is emphasized.

gr-qc↗

arXiv2008

Quantum singularities in the BTZ spacetime

The spinless Bañados-Teiltelboim-Zanelli (BTZ) spacetime is considered in the quantum theory context. Specially, we study the case of negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need of additional information near the origin is confirmed for massive scalar particles and all the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ``healed'' and no extra boundary condition are needed. Near infinity, no boundary conditions are necessary.

gr-qc↗