scholarly journals Constraint Equations for 3 + 1 Vacuum Einstein Equations with a Translational Space-Like Killing Field in the Asymptotically Flat Case

2014 ◽  
Vol 17 (2) ◽  
pp. 271-299 ◽  
Author(s):  
Cécile Huneau
Keyword(s):  
Einstein Equations ◽  
Killing Field ◽  
Asymptotically Flat ◽  
Constraint Equations ◽  
Vacuum Einstein Equations

scholarly journals “Twisted” black holes are unphysical

2017 ◽  
Vol 32 (18) ◽  
pp. 1771001 ◽  
Author(s):  
Finnian Gray ◽  
Jessica Santiago ◽  
Sebastian Schuster ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Rotation Axis ◽  
Einstein Equations ◽  
Entire Region ◽  
Asymptotically Flat ◽  
Ricci Flat ◽  
Vacuum Einstein Equations ◽  
Astrophysical Objects

So-called “twisted” black holes were recently proposed by [H. Zhang, arXiv:1609.09721 ], and were further considered by [S. Chen and J. Jing, arXiv:1610.00886 ]. More recently, they were severely criticized by [Y. C. Ong, J. Cosmol. Astropart. Phys. 1701, 001 (2017)]. While these spacetimes are certainly Ricci-flat, and so mathematically satisfy the vacuum Einstein equations, they are also merely minor variants on Taub–NUT spacetimes. Consequently, they exhibit several unphysical features that make them quite unreasonable as realistic astrophysical objects. Specifically, these “twisted” black holes are not (globally) asymptotically flat. Furthermore, they contain closed time-like curves that are not hidden behind any event horizon — the most obvious of these closed time-like curves are small azimuthal circles around the rotation axis, but the effect is more general. The entire region outside the horizon is infested with closed time-like curves.

Numerical methods for solving the planar vacuum Einstein equations

1991 ◽  
Vol 43 (6) ◽  
pp. 1808-1824 ◽  
Author(s):  
Peter Anninos ◽  
Joan Centrella ◽  
Richard A. Matzner
Keyword(s):  
Numerical Methods ◽  
Einstein Equations ◽  
Vacuum Einstein Equations

scholarly journals HOW TO BYPASS BIRKHOFF THROUGH EXTRA DIMENSIONS: A SIMPLE FRAMEWORK FOR INVESTIGATING THE GRAVITATIONAL COLLAPSE IN VACUUM

2006 ◽  
Vol 15 (12) ◽  
pp. 2217-2222 ◽  
Author(s):  
PIOTR BIZOŃ ◽  
BERND G. SCHMIDT
Keyword(s):  
Gravitational Collapse ◽  
Einstein Equations ◽  
Dimensional System ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Spherical Collapse ◽  
Geometric Setting ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem ◽  
Odd Dimensions

It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's equations become tractable only if they are reduced to a (1 + 1)-dimensional system of partial differential equations. Owing to this technical obstacle, very little is known about the collapse of pure gravitational waves because by Birkhoff's theorem there is no spherical collapse in vacuum. In this essay, we describe a new cohomogeneity-two symmetry reduction of the vacuum Einstein equations in five and higher odd dimensions which evades Birkhoff's theorem and admits time-dependent asymptotically flat solutions. We argue that this model provides an attractive (1 + 1)-dimensional geometric setting for investigating the dynamics of gravitational collapse in vacuum.

Diverging and twisting type N solutions of vacuum Einstein equations: an approximative approach

2006 ◽  
Vol 23 (3) ◽  
pp. 761-775 ◽  
Author(s):  
Maciej Przanowski ◽  
Miguel Ángel Rodríguez Segura
Keyword(s):  
Einstein Equations ◽  
Vacuum Einstein Equations ◽  
Approximative Approach
Sign in / Sign up

Export Citation Format

Share Document