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Speaker |
MacLaurin, Colin |
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| Talk Title |
Time slicings of black holes |
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Abstract |
I present a family of foliations of Schwarzschild-Droste spacetime based on radially freefalling observers. These are contrasted with the usual "static" foliation based on hypersurfaces of Schwarzschild coordinate t=const. These different conventions result in different splittings of spacetime into "space" and "time". Hence those properties which depend on the splitting, such as spatial distance or simultaneity, are distinct between the two conventions. For instance, it is only observers at fixed r-coordinate who measure radial distance by the familiar expression (1-2M/r)^(1/2)dr, whereas the falling observers measure differently. The curvature of 3-space is commonly depicted by Flamm's paraboloid but this corresponds to static observers, whereas the 3-space of the falling observers has a cone shape. The statement that distant observers determine infinite time for an object to pass the horizon is valid under the static slicing plus redshift factor, but under the alternate slicing the far away time is only finite. My motivation is conceptual and pedagogical, and may have applications for quantum fields on curved spacetime. See current version here: http://colinscosmos.com/2017/08/04/time-slicings-of-black-holes-poster/ |
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