redmosquito
Jun12-09, 05:27 PM
I've found a fairly concise review of the Kerr metric at http://www.physics.mcmaster.ca/phys3a03/The%20Kerr%20Metric.ppt
The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley.
On slide 6 they give the usual formulas for converting between Boyer-Lindquist and Cartesian coordinates.
On slide 12 they discuss the central singularity at r = 0, which when converted back to Cartesian coordinates is a ring of radius r_{{\it cartesian}} = a.
On slide 14 they discuss the outer event horizon at r = M + \sqrt{M^2 - a^2}, which when converted back to Cartesian coordinates is an oblate spheroid.
Is this correct? If so, wouldn't it be technically incorrect to draw a diagram of the Kerr spacetime where the central singularity is a ring (the Cartesian representation) but the outer event horizon is a sphere (the Boyer-Lindquist representation)? I see this a lot, and have always been confused by it.
The Kerr Metric for Rotating, Electrically Neutral Black Holes: The Most Common Case of Black Hole Geometry. Ben Criger and Chad Daley.
On slide 6 they give the usual formulas for converting between Boyer-Lindquist and Cartesian coordinates.
On slide 12 they discuss the central singularity at r = 0, which when converted back to Cartesian coordinates is a ring of radius r_{{\it cartesian}} = a.
On slide 14 they discuss the outer event horizon at r = M + \sqrt{M^2 - a^2}, which when converted back to Cartesian coordinates is an oblate spheroid.
Is this correct? If so, wouldn't it be technically incorrect to draw a diagram of the Kerr spacetime where the central singularity is a ring (the Cartesian representation) but the outer event horizon is a sphere (the Boyer-Lindquist representation)? I see this a lot, and have always been confused by it.