Locality in the Derivation of Cumulativity

It has been proposed that the part structures of denotations of plurals ‘project’ to the denotations of expressions including those plurals (e.g., Gawron & Kehler 2004, Kubota & Levine 2016, Schmitt 2019/2020). If such a plural projection is possible, not only plural DPs but also expressions including those plural DPs denote pluralities (e.g., saw the two recipes denotes a plurality {SAW(recipe1),SAW(recipe2)} instead of a singularity {SAW({recipe1,recipe2})}). One piece of support for plural projection comes from Schmitt’s (2020) observation about ‘non-local’ cumulativity. In this paper, I further examine when cumulativity is available non-locally, and show that a source of cumulativity in the literature (e.g., Krifka 1989, Kratzer 2007, Harada 2022b) can capture all the relevant non-local cumulativity data without plural projection while an analysis with plural projection can capture only a proper subset of those data. Therefore, this paper concludes that the relevant non-local cumulativity does not support the need of plural projection

Effect of a Weak Electromagnetic Field on Particle Acceleration by a Rotating Black Hole

We study high energy charged particle collisions near the horizon in an electromagnetic field around a rotating black hole and reveal the condition of the fine-tuning to obtain arbitrarily large center-of-mass (CM) energy. We demonstrate that the CM energy can be arbitrarily large as the uniformly magnetized rotating black hole arbitrarily approaches maximal rotation under the situation that a charged particle plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. Recently, Frolov [Phys. Rev. D 85, 024020 (2012)] proposed that the CM energy can be arbitrarily high if the magnetic field is arbitrarily strong, when a particle collides with a charged particle orbiting the ISCO with finite energy near the horizon of a uniformly magnetized Schwarzschild black hole. We show that the charged particle orbiting the ISCO around a spinning black hole needs arbitrarily high energy in the strong field limit. This suggests that Frolov's process is unstable against the black hole spin. Nevertheless, we see that magnetic fields may substantially promote the capability of rotating black holes as particle accelerators in astrophysical situations.Comment: 22 pages, 4 figure

Timescale for trans-Planckian collisions in Kerr spacetime

We make a critical comparison between ultra-high energy particle collisions around an extremal Kerr black hole and that around an over-spinning Kerr singularity, mainly focusing on the issue of the timescale of collisions. We show that the time required for two massive particles with the proton mass or two massless particles of GeV energies to collide around the Kerr black hole with Planck energy is several orders of magnitude longer than the age of the Universe for astro-physically relevant masses of black holes, whereas time required in the over-spinning case is of the order of ten million years which is much shorter than the age of the Universe. Thus from the point of view of observation of Planck scale collisions, the over-spinning Kerr geometry, subject to their occurrence, has distinct advantage over their black hole counterparts.Comment: 15 pages, v2: minor revisions, v3: minor revisions, to appear in EP