arXiv subjects

Cormac Breen

Publications and source records attributed to Cormac Breen.

14 recordsLinked to original sources

arXiv2026

Quantum effects of charged massive scalar fields on charged black hole space-times

We compute the renormalized expectation values of the scalar condensate, charge current and stress-energy tensor for a massive charged quantum scalar field on a Reissner-Nordstrom black hole. The mass of the scalar field is sufficiently large that classical superradiance is absent. We present results for the Boulware, Unruh and Hartle-Hawking states. Renormalized expectation values in the Hartle-Hawking state are computed using an efficient and accurate mode sum prescription, and for the other two states we employ state subtraction. The efficiency of our numerical method enables us to explore a large part of the parameter space, including near-extremal black hole charges and scalar field masses close to the superradiant limit.

hep-th↗

arXiv2026

Vacuum polarization and renormalized stress-energy tensor of spherical thin shells

We provide a thorough study of the properties of the Boulware vacuum in the spacetime of a spherical, static thin shell with a Minkowski interior. To this end, we calculate the renormalized vacuum polarization and stress-energy tensor of massless scalar fields via the extended-coordinate prescription, paying particular attention to their scaling as the shell approaches the black hole limit. Near the surface of the thin shell, we obtain the expected leading-order singular behavior of both quantities via two independent methods: a high-frequency approximation for the modes, and a weak-field approximation. At the center of the shell we find non-local, Casimir-like contributions that remain finite in the black hole limit, and whose backreaction effects we compute via the semiclassical Einstein equations. Away from these regions amenable to analytic treatment, we obtain numerical results for a wide range of shell compactnesses and field couplings. In the black hole limit, we show that the vacuum polarization and renormalized stress-energy tensor outside the shell quickly approach the ones generated by a Schwarzschild black hole, suggesting a possible universality in the vacuum outside highly compact horizonless objects. This work addresses the conceptual and technical aspects necessary for computing renormalized expectation values in matter configurations, laying the foundations for future explorations on the subject.

gr-qc↗

arXiv2024

Mode-sum prescription for renormalized expectation values for a charged quantum scalar field on a charged black hole

We present a new mode-sum prescription for the efficient computation of renormalized expectation values for a massive, charged, quantum scalar field propagating on a curved space-time background. Our method is applicable to any static, spherically-symmetric, four-dimensional space-time with a time-independent, background electrostatic potential and can be used to find the renormalized scalar condensate, current and stress-energy tensor. As an explicit example, we present a calculation of these quantities for a charged scalar field in the Hartle-Hawking state on a Reissner-Nordstrom black hole background.

hep-th↗

arXiv2024

The renormalized stress-energy tensor for scalar fields in the Boulware state with applications to extremal black holes

We provide a mode-sum prescription to directly compute the renormalized stress-energy tensor (RSET) for scalar fields in the Boulware vacuum. The method generalizes the recently developed extended coordinate method which was previously only applicable to Hartle-Hawking states. We exhibit the accuracy and efficiency of the method by calculating the RSET in sub-extremal and extremal Reissner-Nordstr\"om spacetimes. We find numerical evidence for the regularity of the RSET at the extremal horizon regardless of the field mass and its coupling. We employ our numerical results of the RSET to source the semi-classical Einstein equations, demonstrating that if the RSET is considered as a static perturbation, it will either de-extremalize the black hole, or convert it into a horizonless object.

gr-qc↗

arXiv2023

Renormalized stress-energy tensor for scalar fields in Hartle-Hawking, Boulware and Unruh states in the Reissner-Nordstr\"om spacetime

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordstr\"om black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed ``extended coordinate'' prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a range of coupling constants and masses for the field and a range of electric charge values for the black hole, including near-extreme values. Lastly, we compare these results with the analytic approximations available in the literature.

gr-qc↗

arXiv2022

A mode-sum prescription for the renormalized stress energy tensor on black hole spacetimes

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically-symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semi-classical backreaction.

gr-qc↗

arXiv2020

Semi-Classical Backreaction on Asymptotically Anti-de Sitter Black Holes

We consider a quantum scalar field on the classical background of an asymptotically anti-de Sitter black hole and the backreaction the field's stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semi-classical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page's approximation to the renormalised stress energy tensor while for massive fields, we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct renormalization freedom required to ensure the semi-classical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in $\hbar$) corrections to the metric are obtained. We also compute the corrections to the black hole event horizon, surface gravity and minimum temperature as well as corrections to the photon sphere and quadratic curvature invariants. We pay particular attention to the temperature profiles of the semi-classical black holes compared with their classical counterparts, pointing out some interesting qualitative features produced by the backreaction. These results ought to provide reasonable approximations to the first-order (one-loop) quantum backreaction on the geometry of asymptotically anti-de Sitter black holes when the exact numerical stress-energy tensor sources the semi-classical equations.

gr-qc↗

arXiv2018

Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime

Equipped with new powerful and efficient methods for computing quantum expectation values in static-spherically symmetric spacetimes in arbitrary dimensions, we perform an in-depth investigation of how the quantum vacuum polarization varies with the parameters in the theory. In particular, we compute and compare the vacuum polarization for a quantum scalar field in the Schwarzschild anti-de Sitter black hole spacetime for a range of values of the field mass and field coupling constant as well as the black hole mass and number of spacetime dimensions. In addition, a new approximation for the vacuum polarization in asymptotically anti-de Sitter black hole spacetimes is presented.

gr-qc↗

arXiv2017

A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function $f(r)$. As an explicit example of our method, we show plots for vacuum polarization of a massless scalar field in the Schwarzschild-Tangherlini spacetime for even $d=4,...,10$. However, the method presented applies straightforwardly to massive fields or to nonvacuum spacetimes.

gr-qc↗

arXiv2016

A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions

We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$. In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots for vacuum polarization in the Schwarzschild-Tangherlini spacetime for odd $d=5,...,11$.

gr-qc↗

arXiv2015

Vacuum polarization on the brane

We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD brane-world scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation value of the square of the quantum scalar field on the event horizon of the black hole. Outside the event horizon, this renormalized expectation value is computed numerically. The answer depends on the number of bulk space-time dimensions, with a magnitude which increases rapidly as the number of bulk space-time dimensions increases.

gr-qc↗

arXiv2011

Hadamard Renormalization of the Stress Energy Tensor in a Spherically Symmetric Black Hole Space-Time with an Application to Lukewarm Black Holes

We consider a quantum field which is in a Hartle-Hawking state propagating in a spherically symmetric black hole space-time. We calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, in the exterior region of this space-time. We then specialize these results to the case of the `lukewarm' Riessner-Nordstrom-de Sitter black hole.

gr-qc↗

arXiv2011

Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time

We consider a quantum field which is in a Hartle-Hawking state propagating in a general spherically symmetric black hole space-time. We make use of uniform approximations to the radial equation to calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, on the horizons of this space-time. We then specialize these results to the case of the `lukewarm' Reissner-Nordstrom-de Sitter black hole and derive some conditions on the stress tensor for the regularity of the Hartle-Hawking state.

gr-qc↗

arXiv2010

Extended Green-Liouville asymptotics and vacuum polarization for lukewarm black holes

We consider a quantum field on a lukewarm black hole spacetime. We introduce a new uniform approximation to the radial equation, constructed using an extension of Green-Liouville asymptotics. We then use this new approximation to construct the renormalized vacuum polarization in the Hartle-Hawking vacuum. Previous calculations of the vacuum polarization rely on the WKB approximation to the solutions of the radial equation, however the nonuniformity of the WKB approximations obscures the results of these calculations near both horizons. The use of our new approximation eliminates these obscurities, enabling us to obtain explicitly finite and easily calculable values of the vacuum polarization on the two horizons.

gr-qc↗