Question

Please describe the black holes using the basic equations from Einsteins theory.

Answer 1

Black hole is described by singularity of Schwarzchild's equation.

`R_(Sch)=(2GM)/(c^2)`

Step-by-step explanation:

Einstein's field equations consists of 10 sets of equations describing general relativity: Space time curves in presence of mass and energy.

`R_(\mu\\u)-(1)/(2)Rg_(\mu\\u)+ \Lambda g_(\mu\\u)=(8\pi G)/(c^4)T_(\mu\\u)`

Condition of black-hole came from Schwarzchild's solution to Einstein's field equation:

`ds^2=(1-(2GM)/(c^2r))c^2dt^2-((1)/(1-(2GM)/(c^2r)))dr^2-r^2(d\theta^2+sin^2\theta d\phi^2)`

Black hole is described by singularity of Schwarzchild's equation.

`(1-(2GM)/(c^2r))=0`

`R_(Sch)=(2GM)/(c^2)`

It defines the event horizon of the Schwarzchild's black-hole.