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Adrian C. Ottewill

Publications and source records attributed to Adrian C. Ottewill.

50 records · Page 3Linked to original sources
arXiv2009

Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums

We present the first application of the Poisson-Wiseman-Anderson method of matched expansions, to compute the self-force acting on a point particle moving in a curved spacetime. The method uses two expansions for the Green function, valid in `quasilocal' and `distant past' regimes, which are matched within the normal neighbourhood. We perform our calculation in a static region of the spherically symmetric Nariai spacetime (dS_2 x S^2), on which scalar perturbations are governed by a radial equation with a Pöschl-Teller potential. We combine (i) a very high order quasilocal expansion, and (ii) an expansion in quasinormal modes, to determine the Green function globally. We show it is singular everywhere on the null wavefront (even outside the normal neighbourhood), and apply asymptotic methods to determine its singular structure. We find the Green function undergoes a transition every time the null wavefront passes through a caustic: the singular part follows a repeating four-fold sequence $δ(σ)$, $1/πσ$, $-δ(σ)$, $-1/πσ$ etc., where $σ$ is Synge's world function. The matched expansion method provides new insight into the non-local properties of the self-force; we find the contribution from the segment of the worldline lying outside the normal neighbourhood is significant. We compute the scalar self-force acting on a static particle, and validate against an alternative method. Finally, we discuss wave propagation on black hole spacetimes (where any expansion in quasinormal modes will be augmented by a branch cut integral) and predict that the Green function in Schwarzschild spacetime will inherit the four-fold singular structure found here.

gr-qc↗
arXiv2008

Quasi-local contribution to the scalar self-force: Geodesic Motion

We consider a scalar charge travelling in a curved background spacetime. We calculate the quasi-local contribution to the scalar self-force experienced by such a particle following a geodesic in a general spacetime. We also show that if we assume a massless field and a vacuum background spacetime, the expression for the self-force simplifies significantly. We consider some specific cases whose gravitational analog are of immediate physical interest for the calculation of radiation reaction corrected orbits of binary black hole systems. These systems are expected to be detectable by the LISA space based gravitational wave observatory. We also investigate how alternate techniques may be employed in some specific cases and use these as a check on our own results.

gr-qc↗
arXiv2005

The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum

We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that when the field is in this state, the expectation value of the energy-momentum stress tensor measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Hawking temperature rigidly rotating with the horizon.

gr-qc↗
arXiv2005

Canonical Quantization of the Electromagnetic Field on the Kerr Background

We investigate the canonical quantization of the electromagnetic field on the Kerr background. We give new expressions for the expectation value of the electromagnetic stress-energy tensor in various vacua states and give a physical interpretation of the separate terms appearing in them. We numerically calculate the luminosity in these states. We also study the form of the renormalized stress-energy tensor close to the horizon when the electromagnetic field is in the past Boulware state.

gr-qc↗
arXiv2004

Quasi-local contribution to the gravitational self-force

The gravitational self-force on a point particle moving in a vacuum background spacetime can be expressed as an integral over the past worldline of the particle, the so-called tail term. In this paper, we consider that piece of the self-force obtained by integrating over a portion of the past worldline that extends a proper time $Δτ$ into the past, provided that $Δτ$ does not extend beyond the normal neighborhood of the particle. We express this ``quasi-local'' piece as a power series in the proper time interval $Δτ$. We argue from symmetries and dimensional considerations that the $O(Δτ^0)$ and $O(Δτ)$ terms in this power series must vanish, and compute the first two non-vanishing terms which occur at $O(Δτ^2)$ and $O(Δτ^3)$. The coefficients in the expansion depend only on the particle's four velocity and on the Weyl tensor and its derivatives at the particle's location. The result may be useful as a foundation for a practical computational method for gravitational self-forces in the Kerr spacetime, in which the portion of the tail integral in the distant past is computed numerically from a mode sum decomposition.

gr-qc↗
arXiv2002

The Rotating Quantum Thermal Distribution

We show that the rigidly rotating quantum thermal distribution on flat space-time suffers from a global pathology which can be cured by introducing a cylindrical mirror if and only if it has a radius smaller than that of the speed-of-light cylinder. When this condition is met, we demonstrate numerically that the renormalized expectation value of the energy-momentum stress tensor corresponds to a rigidly rotating thermal bath up to a finite correction except on the mirror where there are the usual Casimir divergences.

hep-th↗
arXiv2002

Detection of negative energy: 4-dimensional examples

We study the response of switched particle detectors to static negative energy densities and negative energy fluxes. It is demonstrated how the switching leads to excitation even in the vacuum and how negative energy can lead to a suppression of this excitation. We obtain quantum inequalities on the detection similar to those obtained for the energy density by Ford and co-workers and in an `operational' context by Helfer. We revisit the question `Is there a quantum equivalence principle?' in terms of our model. Finally, we briefly address the issue of negative energy and the second law of thermodynamics.

gr-qc↗
arXiv2000

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.

gr-qc↗
arXiv2000

The renormalized stress tensor in Kerr space-time: general results

We derive constraints on the form of the renormalized stress tensor for states on Kerr space-time based on general physical principles: symmetry, the conservation equations, the trace anomaly and regularity on (sections of) the event horizon. This is then applied to the physical vacua of interest. We introduce the concept of past and future Boulware vacua and discuss the non-existence of a state empty at both scri- and scri+. By calculating the stress tensor for the Unruh vacuum at the event horizon and at infinity, we are able to check our earlier conditions. We also discuss the difficulties of defining a state equivalent to the Hartle-Hawking vacuum and comment on the properties of two candidates for this state.

gr-qc↗
arXiv2000

Divergence of a quantum thermal state on Kerr space-time

We present a simple proof, using the conservation equations, that any quantum stress tensor on Kerr space-time which is isotropic in a frame which rotates rigidly with the angular velocity of the event horizon must be divergent at the velocity of light surface. We comment on our result in the light of the absence of a `true Hartle-Hawking' vacuum for Kerr.

gr-qc↗
arXiv1996

Detection of Anisotropies in the Gravitational-Wave Stochastic Background

By correlating the signals from a pair of gravitational-wave detectors, one can undertake sensitive searches for a stochastic background of gravitational radiation. If the stochastic background is anisotropic, then this correlated signal varies harmonically with the earth's rotation. We calculate how the harmonics of this varying signal are related to the multipole moments which characterize the anisotropy, and give a formula for the signal-to-noise ratio of a given harmonic. The specific case of the two LIGO (Laser Interferometric Gravitational Observatory) detectors, which will begin operation around the year 2000, is analyzed in detail. We consider two possible examples of anisotropy. If the gravitational-wave stochastic background contains a dipole intensity anisotropy whose origin (like that of the Cosmic Background Radiation) is motion of our local system, then that anisotropy will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if Ω_{gw} > 5.3 \times 10^{-8} h_{100}^{-2}. We also study the signal produced by stochastic sources distributed in the same way as the luminous matter in the galactic disk, and in the same way as the galactic halo. The anisotropy due to sources distributed as the galactic disk or as the galactic halo will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if Ω_{gw} > 1.8 \times 10^{-10} h_{100}^{-2} or Ω_{gw} > 6.7 \times 10^{-8} h_{100}^{-2}, respectively.

gr-qc↗
arXiv1995

Long Range Effects of Cosmic String Structure

We combine and further develop ideas and techniques of Allen \& Ottewill, Phys. Rev.D, {\bf 42}, 2669 (1990) and Kay \& Studer Commun. Math. Phys., {\bf 139}, 103 (1991) for calculating the long range effects of cosmic string cores on classical and quantum field quantities far from an (infinitely long, straight) cosmic string. We find analytical approximations for (a) the gravity-induced ground state renormalized expectation values of $\hatφ^2$ and $\hat T_μ^ν$ for a non-minimally coupled quantum scalar field far from a cosmic string (b) the classical electrostatic self force on a test charge far from a superconducting cosmic string. Surprisingly -- even at cosmologically large distances -- all these quantities would be very badly approximated by idealizing the string as having zero thickness and imposing regular boundary conditions; instead they are well approximated by suitably fitted strengths of logarithmic divergence at the string core. Our formula for ${\langle {\hat φ}^2 \rangle}$ reproduces (with much less effort and much more generality) the earlier numerical results of Allen \& Ottewill. Both ${\langle {\hat φ}^2 \rangle}$ and ${\langle {\hat T}_μ{}^ν \rangle}$ turn out to be ``weak field topological invariants'' depending on the details of the string core only through the minimal coupling parameter ``$ξ$'' (and the deficit angle). Our formula for the self-force (leaving aside relatively tiny gravitational corrections) turns out to be attractive: We obtain, for the self-potential of a test charge $Q$ a distance $r$ from a (GUT scale) superconducting string, the formula $- Q^2/(16ε_0r\ln(qr))$ where $q$ is an (in principle, computable) constant of the order of the inverse string radius.

gr-qc↗
arXiv1994

One-loop Quantum Gravity in Schwarzschild Spacetime

The quantum theory of linearized perturbations of the gravitational field of a Schwarzschild black hole is presented. The fundamental operators are seen to be the perturbed Weyl scalars $\dotΨ_0$ and $\dotΨ_4$ associated with the Newman-Penrose description of the classical theory. Formulae are obtained for the expectation values of the modulus squared of these operators in the Boulware, Unruh and Hartle-Hawking quantum states. Differences between the renormalized expectation values of both $\bigl| \dotΨ_0 \bigr|^2$ and $\bigl| \dotΨ_4 \bigr|^2$ in the three quantum states are evaluated numerically.

gr-qc↗