David Hochberg

Null Energy Condition in Dynamic Wormholes

We extend previous proofs that violations of the null energy condition are a generic and universal feature of traversable wormholes to completely nonsymmetric time-dependent wormholes. We show that the analysis can be phrased purely in terms of local geometry at and near the wormhole throat, and we do not have to make any technical assumptions about asymptotic flatness or other global properties. A key aspect of the analysis is the demonstration that time-dependent wormholes have {ital two} throats, one for each direction through the wormhole, and that the two throats coalesce only for the case of a static wormhole. {copyright} {ital 1998} {ital The American Physical Society}

Frank Model and Spontaneous Emergence of Chirality in Closed Systems

In a closed system an irreversible enantioselective autocatalysis coupled to a mutual inhibition reaction, corresponding to a fast and low exergonic formation of the heterochiral dimer which reverts to the monomers in the final reaction work-up, yields absolute asymmetric synthesis even in the absence of chiral polarizations. This is due to the very high chiral amplifications of the initial small statistical deviations from the ideal racemic composition. Moreover, this system is sensitive to very small chiral polarizations (energy differences between transition states below the mJ mol(-1) range). This behaviour can also be observed in reversible exergonic reactions, because the racemization time scale is substantially longer than that of the transformation of the initial reagents. The effect of the presence of other reactions likely to occur (i.e. non-catalytic transformations, non-enantioselective catalysis and homodimer formation) is discussed. Even if these decrease the sensitivity of the network in several chemical scenarios, the emergence of kinetically controlled spontaneous symmetry breaking is not hindered. These features, together with the response of the system to a sequential reaction procedure, suggest that a similar type of network is at the heart of the Soai reaction.

Absolute asymmetric synthesis in enantioselective autocatalytic reaction networks: theoretical games, speculations on chemical evolution and perhaps a synthetic option.

The Soai reaction and the Viedma deracemization of racemic conglomerate crystal mixtures are experimental pieces of evidence of the ability of enantioselective autocatalytic coupled networks to yield absolute asymmetric synthesis. Thermodynamically open systems or systems with non-uniform energy distributions may lead to chiral final states and, in systems able to come into thermodynamic equilibrium with their surroundings, to kinetically controlled absolute asymmetric synthesis. The understanding of network parameters and of the thermodynamic scenarios that may lead to spontaneous mirror symmetry breaking (SMSB) could assist in the development of new methods for asymmetric synthesis and enantioselective polymerizations (e.g., replicators), and to frame reasonable speculations on the origin of biological homochirality.

Self-Consistent Wormhole Solutions of Semiclassical Gravity

We present the first results of a self-consistent solution of the semiclassical Einstein field equations corresponding to a Lorentzian wormhole coupled to a quantum scalar field. The specific solution presented here represents a wormhole connecting two asymptotically spatially flat regions. In general, the diameter of the wormhole throat, in units of the Planck length, can be arbitrarily large, depending on the values of the scalar coupling

Stability of racemic and chiral steady states in open and closed chemical systems

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Lorentzian wormholes in higher order gravity theories

and the boundary values for the shape and redshift functions. In all cases we have considered, there is a fine structure in the form of Planck-scale oscillations or ripples superimposed on the solutions.

Lorentzian wormholes from the gravitationally squeezed vacuum

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.

Chiral polymerization: symmetry breaking and entropy production in closed systems

Abstract We present a method for constructing Minkowski-signature wormholes in higher-derivative gravity theories. This is accomplished by exploiting the dynamical equivalence between standard Einstein gravity (coupled to bosonic matter fields) and a large class of higher curvature gravity theories. Specific solutions of the former are grafted together using the connected sum, and this gives rise to a wormhole whose throat is identified with the boundary layer created by the surgery. We illustrate this procedure by constructing dynamic and static wormholes for pure R2 gravity.

Wormhole cosmology and the horizon problem

Abstract Minkowski-signature wormhole solutions of the Einstein field equations entail violations of the weak energy condition in the vicinity of the wormhole throat. Squeezed states of matter provide a natural source of violation for this condition. The matter vacuum is automatically squeezed as a result of the gravitational interaction, and gives rise to the negative energy densities required for supporting a wormhole structure in spacetime.

Spontaneous Emergence of Chirality in the Limited Enantioselectivity Model: Autocatalytic Cycle Driven by an External Reagent

We solve numerically a kinetic model of chiral polymerization in systems closed to matter and energy flow, paying special attention to its ability to amplify the small initial enantiomeric excesses due to the internal and unavoidable statistical fluctuations. The reaction steps are assumed to be reversible, implying a thermodynamic constraint among some of the rate constants. Absolute asymmetric synthesis is achieved in this scheme. The system can persist for long times in quasi-stationary chiral asymmetric states before racemizing. Strong inhibition leads to long-period chiral oscillations in the enantiomeric excesses of the longest homopolymer chains. We also calculate the entropy production σ per unit volume and show that σ increases to a peak value either before or in the vicinity of the chiral symmetry breaking transition.