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A Novel Derivation of Black Hole Entropy in all Dimensions from Truly Point Mass Sources

Journal of High Energy Physics, Gravitation and Cosmology 2024年第3期10卷 1017-1028页

作者： carlos castro perelman Bahamas Advanced Science Institute and Conferences Ocean Heights Stella Maris Long Island Bahamas Ronin Institute Haddon Place Montclair USA

It is explicitly shown how the Schwarzschild Black Hole Entropy (in all dimensions) emerges from truly point mass sources at r=0due to a non-vanishing scalar curvature involving the Dirac delta distribution. In order to achieve this, one is required to extend the domain of r to negative values −∞≤r≤+∞. It is the density and anisotropic pressure components associated with the point mass delta function source at the origin r=0which furnish the Schwarzschild black hole entropy in all dimensions D≥4after evaluating the Euclidean Einstein-Hilbert action. Two of the most salient results are i) that the observed spacetime dimension D=4is precisely singled out from all the other dimensions when the strong and weak energy conditions are met, and ii) the point mass source described in this work is not the result of a spherically symmetric gravitational collapse of a star as described by the Oppenheimer-Snyder model because we are not neglecting the pressure. As usual, it is required to take the inverse Hawking temperature βHas the length of the circle Sβ1obtained from a compactification of the Euclidean time in thermal field theory which results after a Wick rotation, it=τ, to imaginary time. This approach can be generalized to the Reissner-Nordstrom and Kerr-Newman metrics. The physical implications of this finding warrant further investigation since it suggests a profound connection between the notion of gravitational entropy and spacetime singularities.

关键词： General Relativity Black Holes Entropy Strings

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On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

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Journal of High Energy Physics, Gravitation and Cosmology 2024年第4期10卷 1699-1712页

作者： carlos castro perelman Bahamas Advanced Science Institute and Conferences Long Island Bahamas

A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.

关键词： Division Algebras Hopf Fibrations Barnes-Wall Lattice Leech Lattice Exceptional Lie Algebras Grand Unification Quasicrystals

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MRI射频能量与非MRI兼容植入性心脏装置功能的关系：前瞻性研究

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国际医学放射学杂志 2020年第4期 483-483页

作者： A.A.Rahsepar S.L.Zimmerman R.Hansford M.A.Guttman V.castro D.McVeigh 樊奇 Department of Medicine Division of Cardiology University of Pennsylvania Perelman School of Medicine

对于有植入性心脏装置的个体,通常认为MRI相关风险来自于植入装置与静态、梯度和射频磁场之间的相互作用。目的确定MRI检查时病人全身平均比吸收率(SAR)

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