On the Kerr metric in a synchronous reference frame
TLDR
In this paper, the Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates.Abstract:
The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).read more
Citations
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On the discrete version of the Kerr geometry
TL;DR: In this article, the problem of solving the corresponding discrete Einstein equations (classical) with a length scale (having a quantum nature) arises as a problem of determining the optimal background metric for the perturbative expansion generated by the functional integral.
References
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Book
The Mathematical Theory of Black Holes
TL;DR: In a course of lectures on the underlying mathematical structures of classical gravitation theory given in 1978, Brandon Carter as discussed by the authors began with the statement ‘If I had been asked five years ago to prepare a course for recent developments in classical gravity theory, I would not have hesitated on the classical theory of black holes as a central topic of discussion. But I am grateful to them for their courtesy in assigning to me this privilege.
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Gravitational field of a spinning mass as an example of algebraically special metrics
Roy P. Kerr,Roy P. Kerr +1 more
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The Dynamics of General Relativity
TL;DR: This article appeared as Chapter 7 of an often cited compendium edited by L. Witten in 1962 as mentioned in this paper, which is now long out of print and is intended to provide contemporary accessibility to the flavor of the original ideas.
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Global structure of the Kerr family of gravitational fields
TL;DR: In this article, it was shown that in all except the spherically symmetric cases there is a nontrivial causality violation, i.e., there are closed timelike lines which are not removable by taking a covering space; moreover, when the charge or angular momentum is so large that there are no Killing horizons, this causal violation is of the most flagrant possible kind in that it is possible to connect any event to any other by a future-directed time line.
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Maximal analytic extension of the Kerr metric
TL;DR: Kruskal's transformation of the Schwarzschild metric is generalized to apply to the stationary, axially symmetric vacuum solution of Kerr, and is used to construct a maximal analytic extension of the latter.