The Kerr solution

Author(s):  
Valeria Ferrari ◽  
Leonardo Gualtieri ◽  
Paolo Pani
Keyword(s):  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.


1975 ◽  
Vol 29 (2) ◽  
pp. 322-339 ◽  
Author(s):  
P. A. Hogan

2004 ◽  
Vol 36 (4) ◽  
pp. 781-797 ◽  
Author(s):  
J. L. Hernández–Pastora ◽  
O. V. Manko ◽  
V. S. Manko ◽  
J. Martín ◽  
E. Ruiz

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Chandra B. Singh ◽  
David Garofalo ◽  
Benjamin Lang

The discovery of 3C 273 in 1963, and the emergence of the Kerr solution shortly thereafter, precipitated the current era in astrophysics focused on using black holes to explain active galactic nuclei (AGN). But while partial success was achieved in separately explaining the bright nuclei of some AGN via thin disks, as well as powerful jets with thick disks, the combination of both powerful jets in an AGN with a bright nucleus, such as in 3C 273, remained elusive. Although numerical simulations have taken center stage in the last 25 years, they have struggled to produce the conditions that explain them. This is because radiatively efficient disks have proved a challenge to simulate. Radio quasars have thus been the least understood objects in high energy astrophysics. But recent simulations have begun to change this. We explore this milestone in light of scale-invariance and show that transitory jets, possibly related to the jets seen in these recent simulations, as some have proposed, cannot explain radio quasars. We then provide a road map for a resolution.


2000 ◽  
Vol 61 (6) ◽  
Author(s):  
Chris Doran
Keyword(s):  

The equations appropriate for space-times with two space-like Killing-vectors are set up, ab initio , and explicit expressions for the components of the Riemann, the Ricci, and the Einstein tensors in a suitable tetrad-frame are written. The equations for the vacuum are reduced to a single equation of the Ernst type. It is then shown that the simplest linear solution of the Ernst equation leads directly to the Nutku-Halil solution for two colliding impulsive gravitational waves with uncorrelated polarizations. Thus, in some sense, the Nutku-Halil solution occupies the same place in space-times with two space-like Killing-vectors as the Kerr solution does in space—times with one time-like and one space-like Killing-vector. The Nutku-Halil solution is further described in a Newman-Penrose formalism; and the expressions for the Weyl scalars, in particular, make the development of curvature singularities manifest. Finally, a theorem analogous to Robinson’s theorem (but much less strong) is proved for space-times with two space-like Killing-vectors.


2000 ◽  
Vol 61 (4) ◽  
Author(s):  
Alexander Burinskii ◽  
Giulio Magli
Keyword(s):  

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