Jacobson and Sotiriou showed that rotating black holes could be spun-up past the extremal limit by the capture of non-spinning test bodies, if one neglects radiative and self-force effects. This would represent a violation of the Cosmic Censorship Conjecture in four-dimensional, asymptotically flat spacetimes. We show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities. The most general stationary vacuum black-hole (BH) solution of Einstein's equations in a four-dimensional, asymptotically flat spacetime is the Kerr geometry [1], characterized only by its mass M and angular momentum J. Solutions spinning below the Kerr bound cJ/GM 2 ≤ 1 possess an event horizon and are known as Kerr BHs. Solutions spinning faster than the Kerr bound describe a "naked singularity", where classical General Relativity breaks down and (unknown) quantum gravity effects take over. It was hypothesized by Penrose that classical General Relativity encodes in its equations a mechanism to save it from the breakdown of predictability. This is known as the Cosmic Censorship Conjecture (CCC) [2], which asserts that every singularity is cloaked behind an event horizon, from which no information can escape.There is no proof of the CCC. Indeed there are a few known counter-examples, but these require either extreme fine-tuning in the initial conditions or unphysical equations of state [2], or are staged in higher-dimensional spacetimes [3]. Moreover, all existing evidence indicates that Kerr BHs are perturbatively stable [4], while Kerr solutions with cJ/GM 2 > 1 are unstable [5]. Thus, naked singularities cannot form from BH instabilities.Because naked singularities appear when cJ/GM 2 > 1, it is conceivably possible to form them by throwing matter with sufficiently large angular momentum into a BH. With numerical-relativity simulations, Ref.[6] found no evidence of formation of naked singularities in a highenergy collision between two comparable-mass BHs: either the full nonlinear equations make the system radiate enough angular momentum to form a single BH, or the BHs simply scatter. The case of a test-particle plunging into an extremal Kerr BH was studied by Wald [7], who showed that naked singularities can never be produced, because particles carrying dangerously large angular momentum are just not captured. Recently, Jacobson and Sotiriou (JS) [8] (building onRefs. [9]) have shown that if one considers an almost extremal BH, non-spinning particles carrying enough angular momentum to create naked singularities are allowed to be captured. 1 As acknowledged by JS, however, their analysis neglects the conservative and dissipative selfforce (SF), and both effects may be important [10]. In this letter we will show that the dissipative SF (equivalent to radiation reaction, i.e. the energy and angular momentum losses through gravitational waves) ca...

A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is being refined during dynamical changes of the volume. In general, this leads to a new feature of dynamical difference equations which may not have constant step-size, posing new mathematical problems. It is discussed how such models can be evaluated and what lattice refinements imply for semiclassical behavior. Two detailed examples illustrate that stability conditions can put strong constraints on suitable refinement models, even in the absence of a fundamental Hamiltonian which defines changes of the underlying lattice. Thus, a large class of consistency tests of loop quantum gravity becomes available. In this context, it will also be seen that quantum corrections due to inverse powers of metric components in a constraint are much larger than they appeared recently in more special treatments of isotropic, free scalar models where they were artificially suppressed.

Using the effective-one-body (EOB) formalism and a time-domain Teukolsky code, we generate inspiral, merger, and ringdown waveforms in the small mass-ratio limit. We use EOB inspiral and plunge trajectories to build the Teukolsky equation source term, and compute full coalescence waveforms for a range of black hole spins. By comparing EOB waveforms that were recently developed for comparable mass binary black holes to these Teukolsky waveforms, we improve the EOB model for the (2, 2), (2, 1), (3, 3), and (4, 4) modes. Our results can be used to quickly and accurately extract useful information about merger waves for binaries with spin, and should be useful for improving analytic models of such binaries.

We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.