Abstract
Usually it is demanded that the metric and its 1st derivatives have to match at the boundary of two adjacent regions which are solutions to Einstein’s field equation. We propose a new linking condition concerning gravitational models based on surfaces which could be embedded into a higher dimensional flat space. We probe this condition for the Schwarzschild interior and exterior solution.
Highlights
The question of how spaces with different geometrical structures can be adapted to each other takes up a lot of space in gravity theory
It is demanded that the metric and its 1st derivatives have to match at the boundary of two adjacent regions which are solutions to Einstein’s field equation
We propose a new linking condition concerning gravitational models based on surfaces which could be embedded into a higher dimensional flat space
Summary
The question of how spaces with different geometrical structures can be adapted to each other takes up a lot of space in gravity theory. O’Brien and Synge [1] examined boundary conditions and jump conditions on surfaces where quantities and their derivatives can be discontinuous. Huber [17] considered adjacent regions with different structures He deformed the metrics of these regions in such a way that the linking conditions are satisfied at the boundary surface of these two regions. We want to go a third way and replace the condition that the 1st derivatives of the metrics have to match with another that is quite plausible and that connects the interior and exterior Schwarzschild solutions.
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