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.

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We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondary's orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in two different gauges. Using these results we demonstrate explicitly that our new balance law holds. I. INTRODUCTION Gravitational wave physics is now firmly established as an observational science. Ground-based detectors regularly observe the binary mergers of stellar-mass black holes and neutron stars [1]. Looking to the future, the construction of the space-based millihertz detector, LISA [2], will open a new window on binaries with a total mass in the range 10 4-10 7 M. One particularly interesting class of such systems are extreme mass-ratio inspirals (EMRIs) [3]. In these binaries, a compact object, such as a stellar mass black hole or neutron star, spirals into a massive black hole driven by the emission of gravitational waves. These systems have a (small) mass-ratio in the range of 10 −4 − 10 −7. In general EMRIs are not expected to completely circularize by the time of merger, resulting in a rich orbital and waveform structure that carries with it detailed information about the spacetime of the EMRI [4]. Additional complexity is added by the expectation that both the primary (larger) and secondary (smaller) compact object will be spinning, with no preferred alignment between the secondary's spin and the orbital angular momentum. Modelling the effects of the spin of the secondary is the focus of the present work. Extracting EMRI signals from the LISA data stream will require precise theoretical waveform models of these binaries. This is because the instantaneous signal-to-noise ratio of a typical EMRI will be very small, and so the waveforms can only be separated from the instrumental noise and the potentially many other competing sources by semi-coherent matched filtering techniques [3]. The small mass ratio in EMRIs naturally suggests black hole perturbation theory as a modelling approach. With this method, the spacetime of the binary is expanded around the analytically-known spacetime of the primary. The leading order contribution to the waveform phase comes from the orbit-averaged fluxes of gravitational radiation. These were calculated for a non-spinning secondary moving along a circular orbit about Kerr black hole in the 1970's [5]. These calculations were extended to eccentric [6] and fully generic (inclined) motion [7-9] in the 2000's. The waveforms that can be constructed from these results will likely be sufficient for detection of the very loudest EMRIs. In order to detect the many weaker signals, to perform...

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 µ in a radiation gauge, and the newer method of Frolov et al., yielding A µ 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 µν such that A µ lor = ∇ ν H µν . * s.dolan@sheffield.ac.ukRecent results from gravitational wave detectors and the Event Horizon Telescope support the hypothesis that the universe is replete with rotating (Kerr) black holes, across a range of mass scales (∼ 10-10 9 M ⊙ ). These experimental breakthroughs are underpinned by a solid theoretical understanding of how fields propagate on rotating black hole spacetimes, developed over several decades.This paper returns once more to the venerable topic of massless (test) fields on rotating black hole spacetimes. This area of enquiry blossomed in the 1970s, after Teukolsky [1][2][3][4] showed that certain components of the electromagnetic and gravitational fields on Kerr spacetime satisfy decoupled scalar equations that admit a full separation of variables. Shortly thereafter, Cohen & Kegeles [5,6], Chrzanowski [7], Chandrasekhar [8,9], Wald [10], Stewart [11], and others [12,13] developed methods for reconstructing, from scalar potentials, both the vector potential A µ of the electromagnetic field, and the metric perturbation h µν of the gravitational field. Several applications rely on these methods, from the scattering of gravitational waves [14] to gravitational self-force calculations [15][16][17].The classic Hertz potential method [5][6][7] of the 1970s generates fields in a radiation gauge: l µ A µ = l µ h µν = 0, where l µ is a principal null direction of the spacetime. However, for certain applications, it is preferable to work with a field in Lorenz gauge 1 : ∇ µ A µ = 0 and ∇ µ h µν = 0, 1 The gauge condition takes the name of L. V. Lorenz (1829-1891) rather than H. A. Lorentz (1853A. Lorentz ( -1928.2 Similarly, the statement δF = 0 implies that F = δC for some three-form C.