study a solution describing two static black holes in the presence of a cosmological

constant. We first analytically find an embedding diagram to visualize the geometry

outside the black holes. We then examine how the two black holes must be

interacting to remain static. Our main result is to show how the black holes behave

effectively like two electric charges. This charge model exhibits both attraction and

repulsion, which evidently balance and moreover are localized in different regions

of space. We also begin an investigation of the black holes’ interaction in terms of

the gravitational energy localized in a region (similar to a Gauss’s law approach).

One application of these static black holes is to construct a static wormhole, which

was started in a previous thesis. Here we finish this construction by verifying the

wormhole’s smoothness where the two black hole horizons are matched together.

]]>These nuances are apparent even in simplified two-dimensional models because of the depth of the relationship between a container's geometry and achieving balance. The purpose of such analysis is threefold: first, when considering a rectangular container, to determine the relationship between the angle at which it balances and the amount of fluid in the container; second, to consider a massless analogue to a standard twelve-ounce aluminum can which balances at a fixed angle and observe the interplay between the various parameters of that container's geometry and balance; and finally, to revisit the aluminum can model, this time considering its mass relative to the fluid's, and recover the familiar behavior observed when balancing real-world beverages in aluminum cans.

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