Spin-<i>s</i> Spherical Harmonics and ð

Goldberg, Joshua N.; Macfarlane, Alan; Newman, Ezra T.; Rohrlich, F.; Sudarshan, E. C. G.

doi:10.1063/1.1705135

Cited by 825 publications

(732 citation statements)

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“…Since q∂ z + sz raises the power of H by two units and q∂ z −sz lowers it by the same amount, we expect the former to be related to X + and the latter to X − . This relation was first noticed, using different notation and conventions from ours, in [14]. We now exhibit it in our notation.…”

Section: Jhep01(2014)114mentioning

confidence: 99%

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

Jante

Schroers

2014

J. High Energ. Phys.

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Abstract:We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently proposed geometric models of matter.

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Section: Jhep01(2014)114mentioning

confidence: 99%

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

Jante

Schroers

2014

J. High Energ. Phys.

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“…Let us briefly recall that in the case a = 0 the components S ± of the angular eigenfunctions can be expressed in terms of spin-weighted spherical harmonics [9,10] whereas for a = 0 they satisfy a generalized Heun equation [11]. We show now how to transform the radial equations for the components R ± of the radial functions in such a way that they are reduced to a GHE.…”

Section: The Dirac Equation In the Kerr-newman Metric And The Ghementioning

confidence: 99%

The generalized Heun equation in QFT in curved spacetimes

Batic

Schmid

Winklmeier

2006

J. Phys. A: Math. Gen.

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“…This mass term separates the KleinGordon equation with the ansatz ϕ = Ψ (r)S(θ)e −iωt+imφ . The angular eigenfunctions are the spin-weight-zero spheroidal wavefunctions [88,89], the eigenvalue is close to l(l+1) with l being an "angular quantum number". The superradiant amplification factors are shown in Table 1 for selected Table 1 The gain coefficient for scattering of scalar waves in a matter profile…”

Section: Generalized Scalar-tensor Theories and Superradiancementioning

confidence: 99%

Black hole bombs and explosions: from astrophysics to particle physics

Cardoso

2013

Gen Relativ Gravit

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Black holes are the elementary particles of gravity, the final state of sufficiently massive stars and of energetic collisions. With a forty-year long history, black hole physics is a fully-blossomed field which promises to embrace several branches of theoretical physics. Here I review the main developments in highly dynamical black holes with an emphasis on high energy black hole collisions and probes of particle physics via superradiance. This write-up, rather than being a collection of well known results, is intended to highlight open issues and the most intriguing results.Keywords Black holes · Superradiance · Cosmic Censorship · Transplanckian collisions IntroductionThe Kerr-Newman family of black holes in stationary four-dimensional, asymptotically flat spacetimes exhausts all possible electro-vacuum solutions in General Relativity. Theoretical aspects of black hole physics were fully developed decades ago, when the Kerr-Newman family was discovered and characterized. Most of the tools to understand black hole physics have been in place since that period and most processes involving black holes were controlled at the order-of-magnitude level for at least two decades. Perhaps due to these reasons, "black hole physics" conjures up images of horizons and time-warps and old-fashioned, frozen-in-time topics to lay audiences. However, in the last years the activity in the field is bubbling up Vitor Cardoso CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade Técnica de Lisboa -UTL, Av. Rovisco Pais 1, 1049 Lisboa, Portugal E-mail: vitor.cardoso@ist.utl.pt Present address: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9, Canada 2 Vitor Cardoso and the interest in these issues has widened, driven by several unrelated events at the observational/instrumental, technical and conceptual levels such as (i) our capacity to observationally scrutinize the region close to the horizon within a few Schwarzschild radii, with radio and deep infrared interferometry, of which we have seen but the first steps [1,2,3,4];(ii) the ability to measure black hole spins more accurately than ever before using X-ray spectroscopy [5,6] or "continuum-fitting" methods [7]. Measurement of black hole mass and spin is one necessary step in testing General Relativity [8]; (iii) huge technological progress in gravitational-wave observatories, some of which had been gathering data at design sensitivities for several years and are now being upgraded to sensitivities one order of magnitude higher (black hole binaries are thought to be among the first objects to ever be detected in the gravitational-wave spectrum);(iv) our ability to numerically evolve black hole binaries at the full nonlinear level [9,10,11] and its immediate importance for gravitational-wave searches and high-energy physics [12]; (v) improvement of perturbative schemes, either by an understanding of regularization schemes to handle the self-force [13,14], or by faster and more powerful methods to deal with the full ladder of pe...

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Spin-s Spherical Harmonics and ð

Cited by 825 publications

References 4 publications

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

Dirac operators on the Taub-NUT space, monopoles and SU(2) representations

The generalized Heun equation in QFT in curved spacetimes

Black hole bombs and explosions: from astrophysics to particle physics

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