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  1. Abstract

    Unphysical equations of state result from the unrestricted use of the Synge G-trick of running the Einstein field equations backwards; in particular often this results inρ+p<0which implies negative inertial mass density, which does not occur in reality. This is the basis of some unphysical spacetime models including phantom energy in cosmology and traversable wormholes. The slogan ‘ER = EPR’ appears to have no basis in physics and is merely the result of vague and unbridled speculation. Wormholes (the ‘ER’ of the slogan) are a mathematical curiosity of general relativity that have little to no application to a description of our Universe. In contrast quantum correlations (the ‘EPR’ of the slogan) are a fundamental property of quantum mechanics that follows from the principle of superposition and is true regardless of the properties of gravity. The speculative line of thought that led to ‘ER = EPR’ is part of a current vogue for anti-geometrical thinking that runs counter to (and threatens to erase) the great geometrical insights of the global structure program of general relativity.

     
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    Free, publicly-accessible full text available March 15, 2025
  2. Free, publicly-accessible full text available October 1, 2024
  3. Free, publicly-accessible full text available May 31, 2024
  4. In this paper, a non-trivial system governed by a continuum PT-symmetric Hamiltonian is discussed. We show that this Hamiltonian is iso-spectral to the simple harmonic oscillator. We find its eigenfunctions and the path in the complex plane along which these functions form an orthonormal set. We also find the hidden symmetry operator, C, for this system. All calculations are performed analytically and without approximation.

     
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  5. Abstract Gravitational wave memory and its electromagnetic analog are shown to be straightforward consequences of the wave equation. From Maxwell’s equations one can derive a wave equation for the electric field, while from the Bianchi identity one can derive a wave equation for the Riemann tensor in linearized gravity. Memory in both cases is derived from the structure of the source of those wave equations. 
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  6. Abstract We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear σ model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann-Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant. 
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  7. Abstract We present a numerical study of the local stability of mean curvature flow (MCF) of rotationally symmetric, complete noncompact hypersurfaces with type-II curvature blowup. Our numerical analysis employs a novel overlap method that constructs ‘numerically global’ (i.e., with spatial domain arbitrarily large but finite) flow solutions with initial data covering analytically distinct regions. Our numerical results show that for certain prescribed families of perturbations, there are two classes of initial data that lead to distinct behaviours under MCF. Firstly, there is a ‘near’ class of initial data which lead to the same singular behaviour as an unperturbed solution; in particular, the curvature at the tip of the hypersurface blows up at a type-II rate no slower than ( T − t ) −1 . Secondly, there is a ‘far’ class of initial data which lead to solutions developing a local type-I nondegenerate neckpinch under MCF. These numerical findings further suggest the existence of a ‘critical’ class of initial data which conjecturally lead to MCF of noncompact hypersurfaces forming local type-II degenerate neckpinches with the highest curvature blowup rate strictly slower than ( T − t ) −1 . 
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