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In this paper we will be mathematically exploring low-dimensional gravitational physics and, more specifically, what it tells us about low-dimensional black holes and if there exists a Schwarzschild solution to Einstein's field equation in 2+1 dimensions. We will be starting with an existing solution in 3+1 dimensions, and then reconstructing the classical and relativistic arguments for 2+1 dimensions. Our conclusion is that in 2+1 dimensions, the Schwarzschild solution to Einstein's field equation is non-singular, and therefore it does not yield a black hole. While we still arrive at conic orbits, the relationship between Minkowski-like and Newtonian forces, energies, and geodesics in 2+1 dimensions is different than the relationship between Schwarzschild and Newtonian forces, energies, and geodesics in 3+1 dimensions.
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Stevens, Abigail Lauren, "A Mathematical Exploration of Low-Dimensional Black Holes" (2011). Senior Projects Spring 2011. 28.
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