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KEPLER PACKING. “Trapped surfaces form late in the collapse process, only when a certain threshold density is reached, analogous to the critical packing fraction required for jammed states in granular matter. In Fig. 2, untrapped and trapped surfaces are shown, with volume expansion of constant-time (spacelike hypersurface) slices of flat Minkowski spacetime, and volume con- traction occurring for a gravitationally collapsing body.” https://lnkd.in/dusKMKM View in LinkedIn

CONFLICTING STATES. “The laws appear to have firm underpinnings in out-of-equilibrium, nonlinear physical interactions, even though jamming per se appears to be a steady state feature.” https://lnkd.in/dusKMKM View in LinkedIn

ON BLACK HOLES AND JAMMED SAND. ‘In the gravity analogue, these states are proposed to map to untrapped and trapped surfaces which occur in general relativity, most spectacularly in gravitational collapse of a star to a black hole.” https://lnkd.in/dusKMKM View in LinkedIn

THE PROBLEM. “This dichotomic behaviour is at the heart of difficulties in the extensive ongoing and past assays in theoretical analyses of the laws that govern such materials.” https://lnkd.in/dusKMKM View in LinkedIn

THE ANALYSIS. “Isotropically Jammed states: A simple representative of an isotropically jammed state in a granular substance, in contrast to an unjammed state is depicted in Fig. 1, showing that for the same total number of grains, jamming clearly entails a contraction of the spatial volume.” https://lnkd.in/dusKMKM View in LinkedIn

DUAL STATES. “Thus, in each such alignment direction, these materials behave like a solid, while, in other directions, the material may indeed ‘flow’, akin to a fluid.” (Very quantum description in macroscopic material!) https://lnkd.in/dusKMKM View in LinkedIn

GEOMETRY IN NATURE. “But the formative faculty of the earth does not take to her heart only one shape; she knows and is practiced in the whole of geometry. I have seen… a panel inlaid with silver ore; from it, a dodecahedron, like a small hazelnut in size, projected to half its depth, as if in flower.” (Johannes Kepler, 1610, The Six-Cornered Snowflake) https://lnkd.in/duxTaRF View in LinkedIn

THE START. “The key idea is that we have a good empirical understanding of the overall galaxy number density, stellar ages and metallicities as a function of galaxy mass, and estimates of the initial mass function of stars that formed in these galaxies.” https://lnkd.in/d8Jh7TB View in LinkedIn

STRATEGY. “In this work, we outline a simple way to compute the BBH merger rate for stellar remnant black holes that allows one to assess the uncertainties in the various required ingredients in a transparent manner.” (BBH = binary black hole). https://lnkd.in/d8Jh7TB View in LinkedIn

ORIGINS. “As the field now pivots from gravitational wave discovery to gravitational wave astronomy, there are a number of questions we hope to explore in more detail. One basic question is the origin of these massive black holes. Heavy (≳30  M⊙) black holes are expected to exist as the result of stellar evolution, and have been predicted to dominate the LIGO signal.” (M⊙ = solar mass ~equivalent to mass of the sun; LIGO = The Laser Interferometer Gravitational-Wave Observatory). https://lnkd.in/d8Jh7TB View in LinkedIn