Abstract
Following a recent approach, complete and analytic solutions (brane and bulk) of regular black holes are shown in a brane context. The metrics are regular both on the four-dimensional brane and in the five-dimensional bulk. Like many braneworld scenarios, the bulk spacetime is asymptotically anti--de Sitter. On the other hand, a de Sitter core on the brane avoids the singularity inside the event horizon, providing then well-known regular black holes on the brane. From the bulk perspective, the regular black holes are five-dimensional objects, with the event horizon extending to the extra dimension, but the de Sitter core is entirely on the four-dimensional brane.
Highlights
The Randall-Sundrum model I [1] was conceived of as an attempt to solve the hierarchy problem in particle physics by using a finite extra dimension and two branes embedded into a fivedimensional spacetime
The RandallSundrum II [2] adopts just one brane, with an infinite extra dimension and a warped factor in the bulk or fivedimensional spacetime that, in the second model version, confines gravity close to our universe. Since such models were studied in other contexts like gravitation and cosmology
Black hole and wormhole geometries are built from the four-dimensional brane, and equations in the five-dimensional bulk are ignored [6,7,8,9,10,11,12,13,14,15]
Summary
The Randall-Sundrum model I [1] was conceived of as an attempt to solve the hierarchy problem in particle physics by using a finite extra dimension and two branes (in which our universe is a brane) embedded into a fivedimensional spacetime. The RandallSundrum II [2] adopts just one brane, with an infinite extra dimension and a warped factor in the bulk or fivedimensional spacetime that, in the second model version, confines gravity close to our universe. Since such models were studied in other contexts like gravitation and cosmology.. Nakas and Kanti [17] presented an approach in which the geometry in the bulk is analytically obtained, and the brane spacetime metric (a known solution in general relativity) and the energy-momentum tensor (an effective tensor, for example) are fully calculated in a Randall-Sundrum II-type model. Capital Latin index runs from 0 to 4, and Greek index runs from 0 to 3
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