Question

general relativity question.

This problem is supposed to help one to understand deeper the notion of the event horizon and to learn other methods of how to find it for a given metric. In solving this problem one should find a normal vector to a class of surfaces and then, to find under what conditions this vector becomes light-like. The point is that at the moment when a particle is crossing a surface it has the velocity component along the surface's normal vector. If the latter vector is light-like, then to cross such a surface the particle should move with the speed of light. Solve the problems and prepare a report. The report should contain detailed solutions with justifications. The tasks can be done by hand or with a text(or Tex) editor. You must save the report in pdf format

Answer 1

there is all a always ov as so normal to horizon in any frame. Mence can be considered for vector has components (1,0,0,0) in Kerr - coordinates basis and T in components (0,0,0,1) Kerr - coordinate basis a label that thus ad has & leg u dx Ja=r7 a de we determine legu egu in kers- coordinates Therefore it is normal to surface fr = x +} {rort} ince dr (X) = 0 tangent surface. vector (1,00, 2H) in Kess basis X for every x Xi is the only t This 2 the term nonnal vector like the will vanish, and the surface r=rt to is right