2 00 6 A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I February 9 , 2008
نویسندگان
چکیده
Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system which are analogous to static black-hole models. These solutions exhibit a black-hole structure with a finite-time blowup on a characteristic line mimicking the null inner horizon of spinning or charged black holes. We conjecture that this behavior — namely black-hole formation with blow-up on a characteristic line — is a generic feature of our semi-linear system. Our simple system may provide insight into the formation of null sin-gularities inside spinning or charged black holes in the full system of Einstein equations.
منابع مشابه
A pr 2 00 7 A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I – Basic Formulation and a Conjecture February 7 , 2008
Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system wh...
متن کاملA Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes II
We study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system, which was introduced in [1], is a model for singularity formation inside black holes. We show for a particular case of the equations that the system demonstrates a finite time blowup. The singularity that is formed is a null singularity. Then we show that in this particular case the...
متن کاملOscillatory null singularity inside realistic spinning black holes
We calculate the asymptotic behavior of the curvature scalar (Riemann)2 near the null weak singularity at the inner horizon of a generic spinning black hole, and show that this scalar oscillates infinite number of times while diverging. The dominant parallelly-propagated Riemann components oscillate in a similar manner. This oscillatory behavior, which is in a remarkable contrast to the monoton...
متن کاملar X iv : g r - qc / 9 90 20 08 v 1 2 F eb 1 99 9 The Inner Structure of Black Holes
We study the gravitational collapse of a self-gravitating charged scalar-field. Starting with a regular spacetime, we follow the evolution through the formation of an apparent horizon, a Cauchy horizon and a final central singularity. We find a null, weak, mass-inflation singularity along the Cauchy horizon, which is a precursor of a strong, spacelike singularity along the r = 0 hypersurface. T...
متن کاملA pr 2 00 3 Developments in General Relativity : Black Hole Singularity and Beyond
At the 20-th Texas Symposium on Relativistic Astrophysics there was a plenary talk devoted to the recent developments in classical Relativity. In that talk the problems of gravitational collapse, collisions of black holes, and of black holes as celestial bodies were discussed. But probably the problems of the internal structure of black holes are a real great challenge. In my talk I want to out...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006