Recent content by Sissy

Sorry, I made a mistake: The field equation for empty space with cosmical constant ist R_{ij} - \dfrac{1}{2} R g_{ij} + \Lambda g_{ij} = 0 And the exercise said, that R_{ij} + \Lambda g_{ij} = 0 So this means, that \dfrac{1}{2} R g_{ij} is 0 How this becomes zo zero? Is my...

In lecture we derived the Schwarzschild metric \mathrm{d} s^2 = \dfrac{\mathrm{d} r^2}{1 - (2m/r)} + r^2 ( \mathrm{d} \Theta ^2 + sin^2 \Theta \mathrm{d} \Phi^2 ) -c^2 \left( 1 - \dfrac{2m}{r} \right) \mathrm{d} t^2 and we derived b = 1 - \dfrac{2GM}{c^2 r} and called r_s =...

Hello, I don't understand how to solve this problem. I do not want a solution because I will calculate it by my own but I need some hints how to start. I don't know what to do :frown: Here is the exercise: Show that, if the cosmical constant term is retained in Einstein's equation...

We introduced \Gamma ^m_{kl} as \Gamma ^m_{kl} = g^{im} \Gamma_{ikl} with \Gamma_{ikl} = \dfrac{1}{2} \left( \dfrac{\partial g_{ik}}{\partial x^l} + \dfrac{\partial g_{li}}{\partial x^k} + \dfrac{\partial g_{kl}}{ \partial x^i} \right) and called \Gamma_{ikl} Christoffel symbols...

In the lecture we had this equation: \dfrac{\mathrm{d}^2 x^i }{ \mathrm{d} s^2 } + \Gamma ^i _{kl} \dfrac{ \mathrm{d} x^k}{ \mathrm{d} s} ~ \dfrac{\mathrm{d} x^l}{ \mathrm{d} s} = 0 But how to use this in my problem? greetings

Hello I have huge problems with the following exercise. Please give me some hints. No complete Solutions but a little bit help. Find the differential equations of the paths of test particles in the space-time of which the metric ist \mathrm{d}s^2 = e^{2kx} \left[- \left( \mathrm{d}x^2...