2020年11月25日 · For the Kerr metric I see we do not make such assumptions. It makes sense to me to not assume spherical symmetry, as a black hole (I think) cannot be always approximated to be a sphere. Besides, (I think) its shape can change over time so indeed it makes sense to not assume that the metric is time-independent. Let's now state the Kerr metric

2020年7月28日 · I have checked online and the Kerr metric never seems to be given in Cartesian coordinates (although there is a conversion factor from Cartesian to Boyer-Lindquist coordinates). Is there some reason for this, or would the metric become prohibitively complicated if one tried to switch to Cartesian coordinates?

2004年4月1日 · Its not simple. The most elegant way is by using the Kerr-Schild construction. Let the metric be of the form g=eta+k.k, where eta is the minkowski metric, and k is a null vector. There are various nice theorems that can be proven with this (even though it looks perturbative, the results are exact) that eventually lead to Kerr.

2021年6月14日 · The Time Dilation formula for the Kerr-Newman metric, in terms of a number of length parameters for a position ##(r,\theta)## away from center of mass and polar axis respectively of a gravitational body of mass ##M##, polar angular momentum ##J## and electrical charge ##Q##, is independent of azimuthal angle ##\phi## and expressed as: $$

The angular momentum of zero mass limit of Kerr metric. 0. Calculating the determinant of the Kerr metric. 2.

2019年3月11日 · Kerr Kerr metric Metric Tetrad In summary: The point then is the metric is just$$-e^0\otimes e^0+ e^1 \otimes e^1+ e^2 \otimes e^2+ e^3 \otimes e^3$$(I actually only verified the component for dt^2, but I think the others work out as well, but you should double check this).

2008年7月31日 · Kerr Kerr metric Metric In summary, the conversation discusses the possibility of diagonalizing the Kerr metric in Boyer-Lindquist coordinates. It is suggested that transforming to a co-rotating frame may make the calculations easier, but it is later discovered that this transformation does not diagonalize the metric.

2023年11月30日 · Penrose and Stephen Hawking then asserted that these must end in actual singularities. When they could not prove this they decreed it to be self evident. It is shown that there are counterexamples through every point in the Kerr metric. These are asymptotic to at least one event horizon and do not end in singularities.

2016年8月11日 · Leonardo Gualtieri and Valeria Ferrari, Black Holes in General Relativity, Chap. 3: The Kerr solution. I just noticed this: Leonardo Gualtieri and Valeria Ferrari, Black Holes in General Relativity, Chap. 4: Geodesics of the Kerr metric. You may know all this stuff, but it seems nice. Log in to Reply

2017年3月8日 · The Kerr metric describes the geometry of empty spacetime around a rotating uncharged axially-symmetric ...