Sam R. Dolan

Instability of the massive Klein-Gordon field on the Kerr spacetime

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued-fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the l=1, m=1 state, for M{mu} < or approx. 0.5. For a fast rotating hole (a=0.99) we find a maximum growth rate of {tau}{sup -1}{approx_equal}1.5x10{sup -7}(GM/c{sup 3}){sup -1}, at M{mu}{approx_equal}0.42. The physical implications are discussed.

Superradiant instabilities of rotating black holes in the time domain

Bosonic fields on rotating black hole spacetimes are subject to amplification by superradiance, which induces exponentially-growing instabilities (the “black hole bomb”) in two scenarios: if the black hole is enclosed by a mirror, or if the bosonic field has rest mass. Here we present a time-domain study of the scalar field on Kerr spacetime which probes ultra-long timescales up to t≲5×106M, to reveal the growth of the instability. We describe a highly-efficient method for evolving the field, based on a spectral decomposition into a coupled set of 1+1D equations, and an absorbing boundary condition inspired by the “perfectly-matched layers” paradigm. First, we examine the mirror case to study how the instability timescale and mode structure depend on mirror radius. Next, we examine the massive-field, whose rich spectrum (revealed through Fourier analysis) generates “beating” effects which disguise the instability. We show that the instability is clearly revealed by tracking the stress-energy of the field in the exterior spacetime. We calculate the growth rate for a range of mass couplings, by applying a frequency-filter to isolate individual modal contributions to the time-domain signal. Our results are in accord with previous frequency-domain studies which put the maximum growth rate at τ-1≈1.72×10-7(GM/c3)-1 for the massive scalar field on Kerr spacetime.

Phenomenology of production and decay of spinning extra-dimensional black holes at hadron colliders

We present results of CHARYBDIS2, a new Monte Carlo simulation of black hole production and decay at hadron colliders in theories with large extra dimensions and TeV-scale gravity. The main new feature of CHARYBDIS2 is a full treatment of the spin-down phase of the decay process using the angular and energy distributions of the associated Hawking radiation. Also included are improved modelling of the loss of angular momentum and energy in the production process as well as a wider range of options for the Planck-scale termination of the decay. The new features allow us to study the effects of black hole spin and the feasibility of its observation in such theories. The code and documentation can be found at http://projects.hepforge.org/charybdis2/.

Brane decay of a (4+n)-dimensional rotating black hole: spin-0 particles

In this work, we study the ‘scalar channel’ of the emission of Hawking radiation from a (4+n)-dimensional, rotating black hole on the brane. We numerically solve both the radial and angular part of the equation of motion for the scalar field, and determine the exact values of the absorption probability and of the spheroidal harmonics, respectively. With these, we calculate the particle, energy and angular momentum emission rates, as well as the angular variation in the flux and power spectra – a distinctive feature of emission during the spin-down phase of the life of the produced black hole. Our analysis is free from any approximations, with our results being valid for arbitrarily large values of the energy of the emitted particle, angular momentum of the black hole and dimensionality of spacetime. We finally compute the total emissivities for the number of particles, energy and angular momentum and compare their relative behaviour for different values of the parameters of the theory.

Bound states and decay times of fermions in a Schwarzschild black hole background

We compute the spectrum of normalizable fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a hydrogen-like spectrum. The imaginary parts give decay times for the various states, due to the absorption properties of the hole, with states closer to the hole having shorter half-lives. As the coupling increases, the spectrum departs from that of the hydrogen atom, as states close to the horizon become unfavourable. Beyond a certain coupling the 1S1/2 state is no longer the ground state, which shifts to the 2P3/2 state, and then to states of successively greater angular momentum. For each positive energy state a negative energy counterpart exists, with opposite sign of its real energy, and the same decay factor. It follows that the Dirac sea of negative energy states is decaying, which may provide a physical contribution to Hawking radiation.

Fermion scattering by a Schwarzschild black hole

We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.

Scattering and absorption of gravitational plane waves by rotating black holes

This is a study of the scattering and absorption of planar gravitational waves by a Kerr black hole in vacuum. We apply the partial wave method to compute cross sections for the special case of radiation incident along the rotation axis. A catalogue of numerically-accurate cross sections is presented, for a range of incident wavelengths Mω ≤ 4 and rotation rates a ≤ 0.999M. Three effects are studied in detail: polarization, helicity-reversal and glory scattering. First, a new approximation to the polarization in the long-wavelength limit is derived. We show that black hole rotation distinguishes between co-rotating and counter-rotating wave helicities, leading to a term in the cross section proportional to aω. Second, we confirm that helicity is not conserved by the scattering process and show that superradiance amplifies the effect. For certain wavelengths, the back-scattered flux is enhanced by as much as ~35 times for a rapidly-rotating hole (e.g. for a = 0.999M at Mω = 0.945). Third, we observe regular glory and spiral scattering peaks in the numerically-determined cross sections. We show that the angular width and intensity of the peaks may be estimated via a semi-classical approximation. We conclude with a discussion of the observable implications of our results.

Fermion absorption cross section of a Schwarzschild black hole

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section {sigma} over a range of gravitational couplings Mm/m{sub P}{sup 2} and incident particle energies E. At high couplings, where the Schwarzschild radius R{sub S} is much greater than the particle wavelength {lambda}, we find that {sigma}(E) approaches the classical result for a point particle. At intermediate couplings, where R{sub S}{approx}{lambda}, we find oscillations around the classical limit whose precise form depends on the particle mass. At low couplings, where R{sub S}<<{lambda}, we demonstrate that the minimum-possible cross section approaches {pi}R{sub S}{sup 2}/2. For high incident particle energies, the cross section converges on the geometric-optics value of 27{pi}R{sub S}{sup 2}/4. At low particle energies we find agreement with an approximation derived by Unruh.

Massive vector fields on the Schwarzschild spacetime: quasi-normal modes and bound states

We study the propagation of a massive vector or Proca field on the Schwarzschild spacetime. The field equations are reduced to a one-dimensional wave equation for the odd-parity part of the field and two coupled equations for the even-parity part of the field. We use numerical techniques based on solving (scalar or matrix-valued) three-term recurrence relations to compute the spectra of both quasi-normal modes and quasi-bound states, which have no massless analogue, complemented in the latter case by a forward-integration method. We study the radial equations analytically in both the near-horizon and far-field regions and use a matching procedure to compute the associated spectra in the small-mass limit. Finally, we comment on extending our results to the Kerr geometry and its phenomenological relevance for hidden photons arising e.g. in string theory compactifications.

Scattering of massless scalar waves by Reissner-Nordström black holes

We present a study of scattering of massless planar scalar waves by a charged nonrotating black hole. Partial wave methods are applied to compute scattering and absorption cross sections, for a range of incident wavelengths. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. The glory in the backward direction is studied, and its properties are shown to be related to the properties of the photon orbit. The effects of the black hole charge upon scattering and absorption are examined in detail. As the charge of the black hole is increased, we find that the absorption cross section decreases, and the angular width of the interference fringes of the scattering cross section at large angles increases. In particular, the glory spot in the backward direction becomes wider. We interpret these effects under the light of our geodesic analysis.