53 research outputs found
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.Comment: 15 pages, 9 figure
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.Comment: 18 pages, minor changes to introduction and conclusions, typos
correcte
Mode-Sum Prescription for Vacuum Polarization in Black Hole Spacetimes 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
Semiclassical 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 semiclassical 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 renormalized 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 semiclassical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in ℏ) 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 semiclassical 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 semiclassical equations
Mode-Sum Prescription for the 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 . 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
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
) 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.Comment: 25 pages, 4 figures. Significant edits to Section IV including the
addition of two new subsections. Accepted for publication in Physical Review
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 semiclassical backreaction
How Well Do Engineering Students Retain Core Mathematical Knowledge after a Series of High Threshold Online Mathematics Tests
In the Technological University Dublin, high threshold core skills assessments are run in mathematics for third year engineering students. Such tests require students to reach a threshold of 90% on a multiple-choice test based on a randomised question bank. The material covered by the test consists of the more important aspects of undergraduate engineering mathematics covered in the first two years of the Honours degree programme and/or the three years of the Ordinary degree programme . Students are allowed to re-sit the assessment as frequently as required until they pass. In order to measure the effectiveness of such an exercise a follow up assessment was given to students on their first day of fourth year. A comparison is made with the level of basic mathematical knowledge of these students on their first day in Third year, exactly a year previously. In addition students were surveyed on their view of, how much knowledge had been retained and how effective they felt that this approach had been
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.Comment: 18 pages, 4 figure
Renormalized stress-energy tensor for scalar fields in Hartle-Hawking, Boulware, and Unruh states in the Reissner-Nordström spacetime
In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström 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
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