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Register a new userA simple traversable wormhole violating energy conditions only at the Planck scale
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Hideki Maeda
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We present a simple static spacetime which describes a spherically symmetric traversable wormhole characterized by a length parameter $l$ and reduces to Minkowski in the limit $lto 0$. The wormhole connects two distinct asymptotically flat regions with vanishing ADM mass and the areal radius of its throat is exactly $l$. All the standard energy conditions are respected outside the proper radial distance approximately $1.60l$ from the wormhole throat. If $l$ is identified as the Planck length $l_{rm p}$, the total amount of the negative energy supporting this wormhole is only $Esimeq -2.65m_{rm p}c^2$, which is the rest mass energy of about $-5.77times 10^{-5}{rm g}$.
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We explore the possibility that well known properties of the parity operator, such as its idempotency and unitarity, might break down at the Planck scale. Parity might then do more than just swap right and left polarized states and reverse the sign of spatial momentum ${bf k}$: it might generate superpositions of right and left handed states, as well as mix momenta of different magnitudes. We lay down the general formalism, but also consider the concrete case of the Planck scale kinematics governed by $kappa$-Poincare symmetries, where some of the general features highlighted appear explicitly. We explore some of the observational implications for cosmological fluctuations. Different power spectra for right handed and left handed tensor modes might actually be a manifestation of deformed parity symmetry at the Planck scale. Moreover, scale-invariance and parity symmetry appear deeply interconnected.
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