By Dias, O J C
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Extra resources for Black Hole Solutions and Pair Creation of Black Holes in Three, Four and Higher Dimensional Spacetimes
2 Black holes in 3-dimensional spacetimes 2 we will analyze in detail the BTZ family of solutions, with a special focus on the topological construction leading to the rotating massive BTZ black hole, and on the magnetic BTZ solution. • Other 3-dimensional gravities and their black holes In order to turn the 3-dimensional dynamics more similar with the realistic 4-dimensional one, we can manage a way by which we introduce local degrees of freedom. This is done by coupling an extra field to the Einstein general relativity.
The A < 1/ℓ case was the one analyzed by Podolsk´ y , and the A = 1/ℓ case has been investigated by Emparan, Horowitz and Myers , which has acquired an important role since the authors have shown that, in the context of a lower dimensional Randall-Sundrum model, it describes the final state of gravitational collapse on the brane-world. The geodesic structure of this solution has been studied by Chamblin . Both cases, A < 1/ℓ and A = 1/ℓ, represent one single accelerated black hole.
However, physically we could in principle consider an external electromagnetic field that supplies the same energy and acceleration as our strings and, from the results of the Λ = 0 case Chapter 1. Overview (where the pair creation rates in the string and electromagnetic cases agree), we expect that the results found in [131, 132] do not depend on whether the energy is being provided by an external electromagnetic field or by strings. As an example of our results and to understand the physical interpretation that is associated with the process, we give the pair creation rates Γ of nonextreme black holes with m = q when a string breaks in the dS, flat and AdS backgrounds, respectively: C−metric ΓdS ∝ exp 3π 1 64Λ mA 1−4mA 1+4mA 1− 1 − (4mA)2 − 1+ 4m √ 3 √ Λ + 3A2 − √ 3π √1−4mA Λ 1+4mA , where the acceleration, A > 0, and the mass parameter m of the black holes must satisfy mA ≤ √ 3√ 1 , 4 Λ+3A2 C−metric π ∝ exp − 4A Γflat 2 −1+4mA+ √ √ 1−(4mA)2 , 1−(4mA)2 where the acceleration, A > 0, and the mass parameter m of the black holes must satisfy 0 < mA ≤ 1 4, C−metric ∝ exp − ω ΓAdS 4πm2 2 + (ω+ −1) − ω+ −ω− (ω+ +α)(ω− +α) + 1 ω+ −α 1 + 1+ 2 −1 3ω− 2 1− 8|Λ|m 3 ω 2 (1−ω 2 )2 − − 2 1−3ω− 2 ) ω− (1−ω− , where the acceleration A and the mass m of the black holes must satisfy the conditions A > |Λ| 3 √ 4m 1 2 and 0 < mA ≤ 4 , and we have ω± = 1 ± 4mA and α = 1 − √3 3A − |Λ|.
Black Hole Solutions and Pair Creation of Black Holes in Three, Four and Higher Dimensional Spacetimes by Dias, O J C