The C-metric black hole near the IR-brane in the AdS_4 space

Physics – High Energy Physics – High Energy Physics - Theory

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12 pages+ 2 figs

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We study the black hole shape using the C-metric solution for a matter trapped near the IR-brane in the ${AdS}_4$ space. In the AdS/CFT duality, the IR-brane is introduced by embedding a 2-brane at the ${AdS}_4$ radius $z=l$, while the UV-brane is defined by the ${AdS}_4$ boundary. We find the C-metric solution generates a negative tension IR-brane and a negative thermal energy gas of colliding particles. We analyze the momentum energy tensor at the ${AdS}_4$ boundary. We find that the negative energy black hole solution is entirely unstable even for a small perturbation in the Poincare coordinate space. However, such a black hole decays very rapidly due to the imaginary part emerges in the ADM mass. This imaginary part appears because of the orbifold constraints of the C-metric solution in the unusual coordinates. Moreover, this decay rate diverges at the UV-brane. This implies that the black hole evaporates instantaneously otherwise the boundary itself will collapse.

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