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Astronomy, Volume 4, Issue 2 (June 2025) – 2 articles

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34 pages, 397 KiB  
Article
Hilbert Bundles and Holographic Space–Time Models
by Tom Banks
Astronomy 2025, 4(2), 7; https://doi.org/10.3390/astronomy4020007 - 22 Apr 2025
Viewed by 166
Abstract
We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensional Hilbert spaces. Following Jacobson, I view the background [...] Read more.
We reformulate holographic space–time models in terms of Hilbert bundles over the space of the time-like geodesics in a Lorentzian manifold. This reformulation resolves the issue of the action of non-compact isometry groups on finite-dimensional Hilbert spaces. Following Jacobson, I view the background geometry as a hydrodynamic flow, whose connection to an underlying quantum system follows from the Bekenstein–Hawking relation between area and entropy, generalized to arbitrary causal diamonds. The time-like geodesics are equivalent to the nested sequences of causal diamonds, and the area of the holoscreen (The holoscreen is the maximal d2 volume (“area”) leaf of a null foliation of the diamond boundary. I use the term area to refer to its volume.) encodes the entropy of a certain density matrix on a finite-dimensional Hilbert space. I review arguments that the modular Hamiltonian of a diamond is a cutoff version of the Virasoro generator L0 of a 1+1-dimensional CFT of a large central charge, living on an interval in the longitudinal coordinate on the diamond boundary. The cutoff is chosen so that the von Neumann entropy is lnD, up to subleading corrections, in the limit of a large-dimension diamond Hilbert space. I also connect those arguments to the derivation of the ’t Hooft commutation relations for horizon fluctuations. I present a tentative connection between the ’t Hooft relations and U(1) currents in the CFTs on the past and future diamond boundaries. The ’t Hooft relations are related to the Schwinger term in the commutator of the vector and axial currents. The paper in can be read as evidence that the near-horizon dynamics for causal diamonds much larger than the Planck scale is equivalent to a topological field theory of the ’t Hooft CR plus small fluctuations in the transverse geometry. Connes’ demonstration that the Riemannian geometry is encoded in the Dirac operator leads one to a completely finite theory of transverse geometry fluctuations, in which the variables are fermionic generators of a superalgebra, which are the expansion coefficients of the sections of the spinor bundle in Dirac eigenfunctions. A finite cutoff on the Dirac spectrum gives rise to the area law for entropy and makes the geometry both “fuzzy” and quantum. Following the analysis of Carlip and Solodukhin, I model the expansion coefficients as two-dimensional fermionic fields. I argue that the local excitations in the interior of a diamond are constrained states where the spinor variables vanish in the regions of small area on the holoscreen. This leads to an argument that the quantum gravity in asymptotically flat space must be exactly supersymmetric. Full article
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6 pages, 348 KiB  
Article
Distance to M87 as the Mode of the Modulus Distribution
by Mariusz Tarnopolski
Astronomy 2025, 4(2), 6; https://doi.org/10.3390/astronomy4020006 - 2 Apr 2025
Viewed by 181
Abstract
de Grijs and Bono (ApJS 2020, 246, 3) compiled a list of distances to M87 from the literature published in the last 100 years. They reported the arithmetic mean of the three most stable tracers (Cepheids, tip of the red giant branch, and [...] Read more.
de Grijs and Bono (ApJS 2020, 246, 3) compiled a list of distances to M87 from the literature published in the last 100 years. They reported the arithmetic mean of the three most stable tracers (Cepheids, tip of the red giant branch, and surface brightness fluctuations). The arithmetic mean is one of the measures of central tendency of a distribution; others are the median and mode. The three do not align for asymmetric distributions, which is the case for the distance moduli μ0 to M87. I construct a kernel density distribution of the set of μ0 and estimate the recommended distance to M87 as its mode, obtaining μ0=31.06±0.001(statistical)0.06+0.04(systematic) mag, corresponding to D=16.290.45+0.30 Mpc, which yields uncertainties smaller than those associated with the mean and median. Full article
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