Addendum to “Absorption of a massive scalar field by a charged black hole”

In [1] we studied the absorption cross section of a scalar field of mass m impinging on a static black hole of mass M and charge Q. We presented numerical results using the partial-wave method, and analytical results in the high- and low-frequency limit. Our low-frequency approximation was only valid if the (dimensionless) field velocity v exceeds vc=2πMm. In this addendum we give the complementary result for v≲vc, and we consider the possible physical relevance of this regime

Tidal invariants for compact binaries on quasicircular orbits

We extend the gravitational self-force approach to encompass "self-interaction" tidal effects for a compact body of mass μ on a quasicircular orbit around a black hole of mass M=μ. Specifically, we define and calculate at O(μ) (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at O(μ). We present accurate numerical results for the Schwarzschild case for orbital radii up to the light ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order post-Newtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves

Octupolar invariants for compact binaries on quasicircular orbits

We extend the gravitational self-force methodology to identify and compute new O(μ) tidal invariants for a compact body of mass μ on a quasicircular orbit about a black hole of mass Mμ. In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative 'electric' invariants and 3+1 'magnetic' invariants, satisfying 1+1 and 1+0 trace conditions. We express the new invariants for equatorial circular orbits on Kerr spacetime in terms of the regularized metric perturbation and its derivatives; and we evaluate the expressions in the Schwarzschild case. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytical results, and prior work. We explore the application of these invariants in effective one-body models and binary black hole initial-data formulations

Charge and mass effects on the evaporation of higher-dimensional rotating black holes

To study the dynamics of discharge of a brane black hole in TeV gravity scenarios, we obtain the approximate electromagnetic field due to the charged black hole, by solving Maxwell's equations perturbatively on the brane. In addition, arguments are given for brane metric corrections due to backreaction. We couple brane scalar and brane fermion fields with non-zero mass and charge to the background, and study the Hawking radiation process using well known low energy approximations as well as a WKB approximation in the high energy limit. We argue that contrary to common claims, the initial evaporation is not dominated by fast Schwinger discharge.Comment: Published version. Minor typos corrected. 29 pages, 5 figure

Large-N Collective Fields and Holography

We propose that the euclidean bilocal collective field theory of critical large-N vector models provides a complete definition of the proposed dual theory of higher spin fields in anti de-Sitter spaces. We show how this bilocal field can be decomposed into an infinite number of even spin fields in one more dimension. The collective field has a nontrivial classical solution which leads to a O(N) thermodynamic entropy characteristic of the lower dimensional theory, as required by general considerations of holography. A subtle cancellation of the entropy coming from the bulk fields in one higher dimension with O(1) contributions from the classical solution ensures that the subleading terms in thermodynamic quantities are of the expected form. While the spin components of the collective field transform properly under dilatational, translational and rotational isometries of $AdS$, special conformal transformations mix fields of different spins indicating a need for a nonlocal map between the two sets of fields. We discuss the nature of the propagating degrees of freedom through a hamiltonian form of collective field theory and argue that nonsinglet states which are present in an euclidean version are related to nontrivial backgrounds.Comment: 27 pages, harvmac. v2: references adde

Instability of the Proca field on Kerr spacetime

The field of a massive vector boson in the vicinity of a rotating black hole is known to suffer an instability, due to the exponential amplification of (co-rotating, low-frequency) bound state modes by black hole superradiance. Here we calculate the bound state spectrum by exploiting the separation of variables recently achieved by Frolov, Krtou, Kubiz'ak and Santos (FKKS) for the Proca field on Kerr-(A)dS-NUT spacetimes of arbitrary dimension. Restricting to the 4D Kerr case, we first establish the relationship between the FKKS and Teukolsky variables in the massless case; obtain exact results for the angular eigenvalues in the marginally-bound case; and present a spectral method for solving the angular equation in the general case. We then demonstrate that all three physical polarizations can be recovered from the FKKS ansatz, resolving an open question. We present numerical results for the instability growth rate for a selection of modes of all three polarizations, and discuss physical implications

Electromagnetic fields on Kerr spacetime, Hertz potentials, and Lorenz gauge

We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al., yielding $A^\mu$ in Lorenz gauge. We demonstrate that the vector potentials are related by straightforward gauge transformations, which we give in closed form. We obtain a new result for a separable Hertz potential $H^{\mu \nu}$ such that $A_{\text{lor}}^\mu = \nabla_\nu H^{\mu \nu}$.Comment: 19 pages, 0 figures. To match published versio

Scalar perturbation spectra from warm inflation

We present a numerical integration of the cosmological scalar perturbation equations in warm inflation. The initial conditions are provided by a discussion of the thermal fluctuations of an inflaton field and thermal radiation using a combination of thermal field theory and thermodynamics. The perturbation equations include the effects of a damping coefficient $\Gamma$ and a thermodynamic potential $V$. We give an analytic expression for the spectral index of scalar fluctuations in terms of a new slow-roll parameter constructed from $\Gamma$. A series of toy models, inspired by spontaneous symmetry breaking and a known form of the damping coefficient, lead to a spectrum with $n_s>1$ on large scales and $n_s<1$ on small scales.Comment: 12 pages, 5 figures, RevTeX 4, revised with extra figure

Angular profile of emission of non-zero spin fields from a higher-dimensional black hole

Recent works have included the effect of rotation on simulations of black hole events at the LHC, showing that the angular momentum of the black hole cannot be ignored and it makes a non-trivial contribution for most of the lifetime of the black hole. A key consequence of the rotation of the black hole is that the Hawking radiation is no longer isotropic, making it more difficult to infer space–time parameters from measurements of the emitted particles. In this Letter we study the angular distribution of the Hawking emission of non-zero spin particles with specific helicity on the brane. We argue that the shape of the distribution could be used as a measure of the angular momentum of the black hole

Quasinormal modes of massive vector fields on the Kerr spacetime

We study the spectrum of quasinormal mode frequencies for a Proca field on a rotating black hole spacetime. First, we review how the introduction of field mass modifies the spectrum in the scalar-field case, leading to evanescent modes and to quasiresonance. Next, we examine the three physical polarizations of the Proca field and their relation to the electromagnetic field modes in the massless limit. Exploiting a separation of variables, we obtain a five-term recurrence relation from an appropriate ansatz for the radial function. Gaussian elimination and the modified Lentz algorithm are applied, and the quasinormal frequencies are computed from the roots of a continued fraction. We validate our method by calculating quasibound state frequencies, which are complementary to quasinormal modes, and which can be calculated using the same method. We present a selection of results for the low-lying overtones of all three polarizations, across a range of black hole spins and field masses