An open question in experimental physics is the characterization of gravitational effects in quantum regimes. We propose an experimental set-up that uses well-tested techniques in cavity optomechanics to observe the effects of the gravitational interaction between two micro-mechanical oscillators on the interference of the cavity photons through the shifts in the visibility of interfering photons. The gravitational coupling leads to a shift in the period and magnitude of the visibility whose observability is within reach of current technology. We discuss the feasibility of the set-up as well as the effects on entanglement due to gravitational interaction. 1 c 1 (α + α * )) × [M ] =hγ(a † e iωat + ae −iωat + 2λ m c † 1 c 1 (1 − cos ω a t)) × [M ]which is Eq.16.

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For many purposes, a three-dimensional foliation of spacetime is more advantageous to understanding its light cone structure. We derive the equations describing such foliations for the Kerr geometry with non-zero cosmological constant, and show that they reduce to null hypersurfaces in vacuum (anti-)de Sitter spacetime in the limit of zero mass. Furthermore, we find that these null hypersurfaces are free of caustics everywhere for r > 0. Our construction has applications in numerical studies of rotating black holes, and in defining Kruskal coordinates for rotating black holes with non-zero cosmological constant.The discovery of the Kerr solution in 1963 [1] and its extension to the Kerr-Newman [2] family of solutions of Einstein equations have allowed accurate analytical studies of astrophysical black holes. These solutions furthermore have opened the door for theoretical studies of rotating black hole thermodynamics [3,4], and quantum gravity within the context of the AdS/CFT correspondence [5,6] and the Kerr/CFT correspondence [7].Null hypersurfaces of the Kerr geometry were first systematically studied in [8], where a three-dimensional null slicing of the spacetime was obtained and its properties studied. These hypersurfaces were found to possess no caustics, which make them ideal for studying initial-value problems and wave propagation in Kerr geometry.This type of analysis has never been extended to other rotating black holes, and it is the purpose of this paper to address this deficit by investigating null hypersurfaces for the Kerr-Anti de Sitter (Kerr-AdS) and Kerr-de Sitter (Kerr-dS) black holes. We find that a similar threedimensional null foliation of Kerr-(A)dS spacetimes can be obtained and prove that it also develops no caustics. * a2albalu@uwaterloo.ca † rbmann@uwaterloo.ca arXiv:1909.06419v1 [gr-qc]

Within the framework of the “complexity equals action” and “complexity equals volume” conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes for which considerable simplification occurs. We study the complexity of formation, uncovering a direct connection between complexity of formation and thermodynamic volume for large black holes. We consider also the growth-rate of complexity, finding that at late-times the rate of growth approaches a constant, but that Lloyd’s bound is generically violated.

In this work, we provide a UV safe Trinification theory in which the Standard Model is embedded. Using recently developed large number-of-flavor techniques, safety is achieved by adding to the theory gauged vector-like fermions. We find that all gauge, scalar quartic, and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. We find renormalization group flow solutions matching the Standard Model in the IR, indicating a truly UV completion of the Standard Model. Imposing constraints that realistic Higgs, top, bottom, tau and reasonable neutrino masses are recovered, we find the set of allowed solutions to be quite restrictive. Furthermore, the symmetry breaking scale is predicted to be around 10 TeV, making this model vulnerable to experiment.