Abstract
We construct from first principles the geometry of an analytic, exponentially localized five-dimensional brane-world black hole. The black-hole singularity lies entirely on the 3-brane, while the event horizon is shown to have a pancake shape. The induced line-element on the brane assumes the form of the Schwarzschild solution while the bulk geometry is effectively AdS5 outside the horizon. The derived geometry is supported by an anisotropic fluid in the bulk described only by two independent components, the energy density and tangential pressure, whereas no matter needs to be introduced on the brane for its consistent embedding in the bulk.
Highlights
The warped brane-world model [1, 2] made its appearance more than twenty years ago and radically changed the way we thought about theories with extra spatial dimensions
We have demonstrated that the black-hole singularity lies entirely on the brane, while the event horizon extends into the bulk but is exponentially suppressed as we move along the extra dimension
This exponential localization alters the shape of the event horizon, making it appear as a five-dimensional pancake
Summary
The warped brane-world model [1, 2] made its appearance more than twenty years ago and radically changed the way we thought about theories with extra spatial dimensions. In [5], the four-dimensional Minkowski line-element was replaced by the Schwarzschild one in an attempt to construct a black hole localised on the brane, as a brane observer would witness. Each slice has a warp factor e−2k|y|, where k is the curvature of the five-dimensional Anti-de Sitter (AdS) spacetime supported by a negative bulk cosmological constant.
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