Abstract
ABSTRACT We apply our tetrad-based approach for constructing spherically symmetric solutions in general relativity to modelling a void, and compare it with the standard Lemaître–Tolman–Bondi (LTB) formalism. In particular, we highlight the importance of considering the velocity as well as the density profile in constraining voids. We apply our approach to construct models for the void observed in the direction of Draco in the WISE–2MASS galaxy survey, and a corresponding cosmic microwave background (CMB) temperature decrement in the Planck data in the same direction. We find that the present-day density and velocity profiles of the void are not well constrained by the existing data, so that void models produced from the two approaches can differ substantially while remaining broadly consistent with the observations. We repeat our analysis to construct void models for the CMB Cold Spot, but show that although a single void can account for the WISE–2MASS galaxy survey data, it is not capable of producing a CMB temperature decrement sufficiently deep to be consistent with Planck CMB data.
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