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Full-Text Articles in Physical Sciences and Mathematics
An Extremum Principle For Charged Black Holes, Shaker Von Price Funkhouser
An Extremum Principle For Charged Black Holes, Shaker Von Price Funkhouser
Physics
There is a well known static condition that characterizes how two or more charged black holes stay in place: this condition is |qi |=mi , where a black hole (labeled by i) has electric charge qi and mass mi . For nearly half a century, this static condition has eluded a simple physical interpretation, without appealing to forces. I provide the first proof that the static condition, |qi |=mi , corresponds to an extremum of the black holes’ total energy. My approach uses geometry and calculus in the context of general relativity. For the non-specialist, this work draws upon one’s …
Aspects Of General Relativity In 1+1 Dimensions, Richard D. Mellinger Jr
Aspects Of General Relativity In 1+1 Dimensions, Richard D. Mellinger Jr
Physics
What would be the properties of a universe with only one spatial dimension and one time dimension? General relativity in 1+1 dimensions is unique since the two curvature terms in the Einstein field equations cancel. This makes the Einstein field equations algebraic rather than differential equations. This special feature can make 1+1 dimensionality attractive as an instructional tool to simplify the mathematics that many beginners find opaque. We explore the implications and features of the Einstein field equations in 1+1 dimensions and find they provide a surprisingly rich and interesting model. We then study an alternate theory and its implications …