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FROM SAND TO GEODESICS. “An additional justification of this analogy of jammed states with trapped surfaces may be posited on the basis of the Raychaudhuri equation, for timelike geodesic congruence in the case of granular matter.” https://lnkd.in/dusKMKM View in LinkedIn

NOMENCLATURE. “In astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal physical matter in the Universe is either hydrogen or helium, and astronomers use the word "metals" as a convenient short term for "all elements except hydrogen and helium". (ie: a measure of nucleosynthesis in stars). https://lnkd.in/d8DupZu View in LinkedIn

METHOD. “Using these ingredients, together with the current generation of stellar evolution codes, we can provide a grounded estimate of the global distribution of black holes as a function of black hole mass and galaxy stellar mass. With this as a starting point, we are able to quantify the astrophysical parameters needed to produce the observed BBH merger signals observed.” (BBH = binary black hole). https://lnkd.in/d8Jh7TB View in LinkedIn

NON-COMPUTABILITY. “As we will see the argument also goes in the other direction: If the universal quantum computer produces greater than polynomial complexity in exponential time, then certain hard problems (PSPACE-complete) cannot be solved in polynomial time by a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

c(N). “Let us suppose that a universal quantum circuit, when run for exponential time failed to produce complexity greater than polynomial in the number of qubits. Consider some problem which is classically hard, i.e., it takes exponential time ∼ c(N) to solve it. It follows that there is a way to get to the answer in a polynomial number of steps running the computer as a quantum computer.” https://lnkd.in/dByfCJV View in LinkedIn

QUITE THE ANSWER. “The result was a theorem (mainly due to Aaronson) connecting the growth of complexity with certain plausible properties of complexity classes.” Originated from black hole quantum circuits. https://lnkd.in/dByfCJV View in LinkedIn

QUITE THE QUESTION. “Several years ago I asked Scott Aaronson a question: Can it be proved that the complexity of a universal quantum circuit, such as those that have been conjectured to describe black holes, grows at the fastest possible rate—linearly with time—until it saturates at the maximum complexity (exponential in the number of qubits)?” https://lnkd.in/dByfCJV View in LinkedIn

QUANTUM AND BLACK HOLES. “It is not known what the limitations are on using quantum computation to speed up classical computation. An example would be the power to speed up PSPACE-complete computations. It is also not known what the limitations are on the duration of time over which classical general relativity can describe the interior geometry of black holes. What is known is that these two questions are closely connected: the longer GR can describe black holes, the more limited are quantum computers.” (GR = general relativity). https://lnkd.in/dByfCJV View in LinkedIn

ROLE IN EVOLUTION. “Recently through a series of observations it has been shown that supermassive black holes (SMBH) residing at the center of galaxies play a significant role in cosmic evolution of structure in the Universe.” https://lnkd.in/dq-SEai View in LinkedIn