Recent content by ikjyotsingh

I think we have to be a bit careful here. The big crunch leading to a black hole singularity is a bit misnomer, since the geometries from a dynamic evolution sense don't match. Our current universe is FLRW which admits a six-dimensional isometry group. Black hole solutions given by the...

I really wish that everyone could see the truth about Gandhi. He wasn't the great saint that he is made out to be.

The great Guru Gobind Singh and Guru Granth Sahib

Geodesics You can do this because the geodesics are planar (as this problem represents a central force problem), so I don't have a problem with that. I had a problem with the incorrect statement you made, "and the method is completely general", which as I just showed is not true.

Nope So, when you defind E = (1 - rS/r)(dt/dτ) [energy], you are saying that this is completely general?? You can define "Energy" in ALL spacetimes? Indeed, this method is not general at all. The reason you can do this for the Schwarzschild metric is that you have 4 killing vectors, one...

You actually have given me the Christoffel symbols You actually find the Christoffel symbols from minimizing the action of geodesics. They are read off the Lagrangian you have provided. The Newtonian potential method you have alluded to is generally not a good idea, as it suggests that this...

A matter of geodesics It doesn't matter how big the black hole is, the solution is still that of the Schwarzschild metric. Standing still is a matter of context, as, how would you propose an observer stands still with respect to his/her 4-velocity in the vicinity of the black hole...

No. For these type of problems, and in reality in physics especially, closed-form solutions are extremely rare! Indeed, the integral as you posted it only has the elliptical function as a solution, which is a "special function" solution. There are others for other such problems for example...

The correct definition of a vacuum in terms of general relativity, is a system with an isolated mass. You can have an isolated mass, with an asymptotically flat spacetime, which implies that the stress-energy tensor in the Einstein field equations is zero. Just for your own information, there is...

Umm yeah Umm yeah, but visualizing it is such a feeble task. You can only visualize it where an appropriate embedding exists, which according to my memory only exists for Bianchi I, V, and IX models, in addition to Schwarzschild family of metrics. Why don't you talk about visualizing it...

I just want to know why everyone here is interested in visualizing spacetime?

The book by Kundu and Cohen is quite excellent, as it covers applications and theory. The book by Frank M. White is the most popular amongst pure engineers, but it's the ire of theorists! The best fluids book from a purely theoretical perspective is Landau and Lifgarbagez.

Rubber Sheet model How would you even model a spring supporting a mass in T_{ab}? I don't know what that has to do with anything. So, according to your wikipedia article, spacetime is being modeled by a physical rubber sheet, of course that's nonsense. In all my years of studying G.R...

Rubber shet Anything supporting a mass in G.R. necessarily deforms into Flamms' paraboloid. I have a challenge for you then, in this regard. Find a solution of the Einstein Field equations that supports a mass other than the S-metric!

It is about embedding diagrams This is a discussion about embedding diagrams, no one seems to realize it, that's why there is so much confusion! The rubber sheet analogy which is an Euclidean embedding of the Schwarzschild vacuum metric only applies in this metric. You cannot have the rubber...