טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGorbonos Dan
SubjectSingularity Formation in a Wave System Motivated by
Einstein Equations
DepartmentDepartment of Physics
Supervisors Professor Gershon Wolansky
Professor Amos Ori


Abstract

Einstein's equations are non-linear and hyperbolic in nature. These equations are known to lead to the formation of black holes and space-time singularities. This appears to be a demonstration of the mathematical phenomenon of finite time blowup: a formation of singularities from regular initial data.


In this work we study a simple system of two hyperbolic semi-linear equations, inspired by the Einstein equations. The system is a toy-model for singularity formation inside spherically-symmetric 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 singularity has features that are analogous to known features of models of spherical symmetric black-hole interiors - models that describe the inner-horizon instability. However, this investigation is not complete. Further research is needed to study the general case of  this system.


We use two methods in this study: the method of characteristic curves, and reduction to a system of ordinary differential equations. Only by combination of the two methods we can prove the existence of the null singularity and its features. This work may provide us with a better understanding of the formation of null singularities inside black holes.