arXiv subjects

Finnian Gray

Publications and source records attributed to Finnian Gray.

32 records · Page 2Linked to original sources

arXiv2020

Thermodynamics of Rotating NUTty Dyons

We extend the work on thermodynamics of Lorentzian NUTty solutions, by including simultaneously the effect of rotation and electromagnetic charges. Due to the fact that Misner strings carry electric charge, and similar to the non-rotating case, we observe an interesting interplay between the horizon and asymptotic charges. Namely, upon employing the Euclidean action calculation we derive two alternative full cohomogeneity first laws, one that includes the variations of the horizon electric charge and the asymptotic magnetic charge and another that involves the horizon magnetic charge and the asymptotic electric charge. When one of the horizon charges vanishes, we obtain the corresponding "electric" and "magnetic" first laws that are connected by the electromagnetic duality. We also briefly study the free energy of the corresponding system.

hep-th↗

arXiv2020

Conformally Coupled Scalar in Rotating Black Hole Spacetimes

We demonstrate separability of conformally coupled scalar field equation in general (off-shell) Kerr-NUT-AdS spacetimes in all dimensions. The separability is intrinsically characterized by the existence of a complete set of mutually commuting conformal wave operators that can be constructed from a hidden symmetry of the principal Killing-Yano tensor. By token of conformal symmetry, the separability also works for any Weyl rescaled (off-shell) metrics. This is especially interesting in four dimensions where it guarantees separability of a conformally coupled scalar field in the general Plebanski-Demianski spacetime.

hep-th↗

arXiv2019

Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes

The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black hole) case.

hep-th↗

arXiv2019

Scalar and fermionic Unruh Otto engines

We investigate the behaviour of quantum heat engines, in which a qubit is put through the quantum equivalent of the Otto cycle and the heat reservoirs are due to the Unruh effect. The qubit is described by an Unruh--DeWitt detector model coupled quadratically to a scalar field and alternately to a fermion field. In the cycle, the qubit undergoes two stages of differing constant acceleration corresponding to thermal contact with a hot and cold reservoir. Explicit conditions are derived on the accelerations required for this cycle to have positive work output. By analytically calculating the detector response functions, we show that the dimensionality of the quadratic and fermionic coupling constants introduces qualitatively different behaviour of the work output from this cycle as compared to the case in which the qubit linearly couples to a scalar field.

quant-ph↗

arXiv2019

Principal Tensor Strikes Again: Separability of Vector Equations with Torsion

Many black hole spacetimes with a 3-form field exhibit a hidden symmetry encoded in a torsion generalization of the principal Killing--Yano tensor. This tensor determines basic properties of such black holes while also underlying the separability of the Hamilton--Jacobi, Klein--Gordon, and (torsion-modified) Dirac field equations in their background. As a specific example, we consider the Chong--Cvetič--Lü--Pope black hole of $D=5$ minimal gauged supergravity and show that the torsion-modified vector field equations can also be separated, with the principal tensor playing a key role in the separability ansatz. For comparison, separability of the Proca field in higher-dimensional Kerr--NUT--AdS spacetimes (including new explicit formulae in odd dimensions) is also presented.

hep-th↗

arXiv2019

The First Law for Rotating NUTs

We address a long-standing problem of describing the thermodynamics of rotating Taub--NUT solutions. The obtained first law is of full cohomogeneity and allows for asymmetric distributions of Misner strings as well as their potential variable strengths---encoded in the gravitational Misner charges. Notably, the angular momentum is no longer given by the Noether charge over the sphere at infinity and picks up non-trivial contributions from Misner strings.

hep-th↗

arXiv2019

Thermodynamics of Charged, Rotating, and Accelerating Black Holes

We show how to obtain a consistent thermodynamic description of accelerating asymptotically AdS black holes, extending our previous results by including charge and rotation. We find that the key ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the `string' tensions that are responsible for the acceleration of the black hole, yielding a first law of full cohomogeneity. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. In particular we compute the mass in two independent ways: through a Euclidean action calculation and by the method of conformal completion. The ambiguity in the choice of the normalization of the timelike Killing vector can be fixed by explicit coordinate transformation (in the case of rotation) to the standard AdS form or by holographic methods (in the case of charge). This resolves a long-standing problem of formulating the thermodynamics of accelerating black holes, opening the way to detailed studies of their phase behaviour.

hep-th↗

arXiv2019

Misner Gravitational Charges and Variable String Strengths

As shown recently (arXiv:1903.08668), consistent thermodynamics of the Lorentzian Taub-NUT solutions with Misner strings present can be formulated provided a new pair of conjugate quantities (related to the NUT parameter) $ψ-N$ is introduced. In (arXiv:1903.08668) this pair was calculated from the Euclidean action but no geometrical interpretation for the new quantities was provided. In this paper we propose that the potential $ψ$ should be identified with the surface gravity of the Misner string and the conjugate Misner charge $N$ can be obtained by a Komar-type integration over the tubes surrounding the string singularities. We show that similar tube contributions also modify the Komar formula for the thermodynamic volume. To render the integrals finite we employ the method of Killing co-potentials. By construction the new charges then satisfy the Smarr relation. Equipped with these geometrical notions, we generalize the first law for the (possibly charged) Taub-NUT spacetimes to account for asymmetric distributions of Misner strings and their potential variable strengths.

hep-th↗

arXiv2019

Thermodynamics and Phase Transitions of NUTty Dyons

Picking up the threads on a recent proposal [arXiv:1903.08668], we show how to formulate consistent thermodynamics of Lorentzian Taub-NUT spacetimes in the presence of electric and magnetic charges. Namely, with an entropy identified with a quarter of the horizon area and no Misner time periodicity condition imposed, we show that a new pair of conjugate quantities can be introduced so that the NUT parameter can be independently varied and the corresponding first law and Smarr relation can be consistently formulated. Moreover, we show that (contrary to the statements in the literature) the electric and magnetic parameters need not be proportional to one another and a full cohomogeneity first law including variations of both charges can be written down, provided one charge is considered on the horizon and the other at infinity. The corresponding phase transitions are also briefly discussed.

hep-th↗

arXiv2017

Electrostatic limit of the $T$-matrix for electromagnetic scattering: Exact results for spheroidal particles

The $T$-matrix, often obtained with Waterman's extended boundary condition method (EBCM), is a widely-used tool for fast calculations of electromagnetic scattering by particles. Here we investigate the quasistatic or long-wavelength limit of this approach, where it reduces to an electrostatics problem. We first present a fully electrostatic version of the EBCM/T-matrix method (dubbed ES-EBCM). Explicit expressions are then given to quantitatively express the long-wavelength limit of the EBCM matrix elements in terms of those of the ES-EBCM formalism. From this connection we deduce a number of symmetry properties of the ES-EBCM matrices. We then investigate the matrix elements of the ES-EBCM formalism in the special case of prolate spheroids. Using the general electrostatic solution in spheroidal coordinates, we derive fully analytic expressions (in the form of finite sums) for all matrix elements. Those can be used for example for studies of the convergence of the $T$-matrix formalism. We illustrate this by discussing the validity of the Rayleigh hypothesis, where analytical expressions highlight clearly the link with analytical continuation of series.

physics.class-ph↗

arXiv2016

"Twisted" black holes are unphysical

So-called "twisted" black holes have recently been proposed by Zhang (1609.09721 [gr-qc]), and further considered by Chen and Jing (1610.00886 [gr-qc]), and more recently by Ong (1610.05757 [gr-qc]). While these spacetimes are certainly Ricci-flat, and so mathematically satisfy the vacuum Einstein equations, they are also merely minor variants on Taub--NUT spacetimes. Consequently they exhibit several unphysical features that make them quite unreasonable as realistic astrophysical objects. Specifically, these "twisted" black holes are not (globally) asymptotically flat. Furthermore, they contain closed timelike curves that are not hidden behind any event horizon --- the most obvious of these closed timelike curves are small azimuthal circles around the rotation axis, but the effect is more general. The entire region outside the horizon is infested with closed timelike curves.

gr-qc↗

arXiv2015

Sparsity of the Hawking flux

It is (or should be) well-known that the Hawking flux that reaches spatial infinity is extremely sparse, and extremely thin, with the Hawking quanta, one-by-one, slowly dribbling out of the black hole. The typical time between quanta reaching infinity is much larger than the timescale set by the energy of the quanta. Among other things, this means that the Hawking evaporation of a black hole should be viewed as a sequential cascade of 2-body decays.

gr-qc↗

arXiv2015

Greybody factors for Schwarzschild black holes: Path-ordered exponentials and product integrals

In recent work concerning the sparsity of the Hawking flux [arXiv:1506.03975v2], we found it necessary to re-examine what is known regarding the greybody factors of black holes, with a view to extending and expanding on some old results from the 1970s. Focussing specifically on Schwarzschild black holes, we re-calculated and re-assessed the greybody factors using a path-ordered-exponential approach, a technique which has the virtue of providing a semi-explicit formula for the relevant Bogoliubov coefficients. These path-ordered-exponentials, (being based on a "transfer matrix" formalism), are closely related to so-called "product integrals", leading to quite straightforward and direct numerical evaluation, while avoiding any need for numerically solving differential equations. Furthermore, while considerable analytic information is already available regarding both the high-frequency and low-frequency asymptotics of these greybody factors, numerical approaches seem better adapted to finding suitable "global models" for these greybody factors in the intermediate frequency regime, where most of the Hawking flux is concentrated. Working in a more general context, these path-ordered-exponential techniques are also likely to be of interest for generic barrier-penetration problems.

gr-qc↗

arXiv2015

The Hawking cascade from a black hole is extremely sparse

The Hawking flux from a black hole, (at least as seen from asymptotic infinity), is extremely sparse and thin, with the average time between emission of the successive Hawking quanta being many times larger than the natural timescale set by the energies of the emitted quanta. While this result has been known for over 30 years, it has largely been forgotten. We shall focus on the early-stage low-temperature regime, and shall confront numerical estimates with semi-analytic approximations based on a naive Planck spectrum. First we shall identify several natural dimensionless figures of merit, and thereby compare the mean time between emission of successive Hawking quanta to several distinct but quite natural timescales that can be associated with the emitted quanta, demonstrating that very large ratios are typical for emission of massless quanta from a Schwarzschild black hole. Furthermore these ratios are independent of the mass of the black hole as it slowly evolves. We shall then show that the situation for the more general Reissner-Nordstrom and generic "dirty'' black holes is even worse, at least as long as the surrounding matter satisfies some suitable energy conditions. The situation for the Kerr and Kerr--Newman black holes (or even for charged particle emission from a Reissner--Nordstrom black hole) is considerably trickier, and depends on a careful accounting of the super-radiant modes. Overall, the Hawking quanta are seen to be dribbling out of the black hole one at a time, in an extremely slow cascade of 2-body decays. Among other things, this implies that the Hawking flux is subject to "shot noise''. Observationally, the Planck spectrum of the Hawking flux can only be determined by collecting and integrating data over a very long timescale. We conclude by connecting these points back to various kinematic aspects of the Hawking evaporation process.

gr-qc↗