UBC Theses and Dissertations
Merging black hole and cosmological horizons Prat, Alain
This thesis investigates the merging of horizons which occurs when a black hole crosses a cosmological horizon. We study the simplest spacetime which has both a black hole and cosmological horizon, namely Schwarzschild-deSitter (SdS) spacetime. First we develop a new coordinate system for SdS spacetime, which allows us to properly illustrate and analyze the merging of horizons. We then use a combination of numerical and analytical methods to study the structure of the merging horizons, including the null generators which make up the horizon, as well as the presence of caustic points on the horizon. We find an analytical formula for the location in spacetime where the black hole and cosmological horizon first touch. Next we study the area of the horizons. Using numerical methods, we find several intriguing results regarding the behavior of horizon area on time, and in the limit of small black hole mass. The first result is that the time at which the black hole first touches the cosmological horizon is also the time at which the rate of horizon area increase is maximal. The second and third results concern the horizon area in the limit of small black hole mass. The second result is that in this limit, all of the increase in horizon area occurs prior to horizon merger. The third and final result is that in the limit of small black hole mass, the increase in horizon area can be thought of as being due in equal parts to two effects: to the joining of new generators not previously on the horizon, and the expansion of generators on the horizon for all times. The first and third results just mentioned are both corroborated using analytical techniques. Finally, we conclude by discussing how the study of merging horizons in this thesis is a valuable first step to undertaking a similar study of the horizons which occur in merging black hole binaries.
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