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1. The problem statement, all variables and given/known data
question attached
I am stuck on some of the reasoning as to why we set ##B(r=0)=0##
please not as described in the attempt I am interested in the concepts and have not posted my solution to A, nor any solutions not relevant to the concepts I am trying to understand
2. Relevant equations
below
3. The attempt at a solution
QUESTION 1
[
I understand ##r=0## and ##r=R## are going to be the 'critical ' points to look at to loose both integration constants. I am basically stuck on the concepts about the metric descrbing a cone etc.
So I understand that the tip of a cone is a singularity as it is 'geodesically incomplete'. However I am confused with the interpretation of what body\shape one claims that the metric describes, since the coordiantes have no physical meaning as they are just a way of parameterising the manifold.
So, if I can find some coordinates that take the metric to that of a cone, why do I interpret this as significant enough for me to decide that singularity is 'physical' enough for me to use it to impose constraints on ##B(r)## . i.e. there must be multiplie coordinate choices that will allow me to take it to a wide  range of shaped spacetimes as described by the metric, if these are all regular with no singularities I don't worry, but if there is just one such coordiante transformation that takes me to a body with a singularity I use it as a constraint so original coordiantes that the metric is in must be such that any possible coordinate transformation from that, yields a metric that has no singularities? Bit confused with this since we said coordiantes are not physically significant.
QUESTION 2
Also, I'm actually stuck as to why this describes a cone. I see the solution comments on the period of the cone,being less than a circle of 2pi, i can see that the new angle defined clearly has a period less than 2pi, however, I have no idea of what you define the period of a cone to be ?!
many thanks
question attached
I am stuck on some of the reasoning as to why we set ##B(r=0)=0##
please not as described in the attempt I am interested in the concepts and have not posted my solution to A, nor any solutions not relevant to the concepts I am trying to understand
2. Relevant equations
below
3. The attempt at a solution
QUESTION 1
[
I understand ##r=0## and ##r=R## are going to be the 'critical ' points to look at to loose both integration constants. I am basically stuck on the concepts about the metric descrbing a cone etc.
So I understand that the tip of a cone is a singularity as it is 'geodesically incomplete'. However I am confused with the interpretation of what body\shape one claims that the metric describes, since the coordiantes have no physical meaning as they are just a way of parameterising the manifold.
So, if I can find some coordinates that take the metric to that of a cone, why do I interpret this as significant enough for me to decide that singularity is 'physical' enough for me to use it to impose constraints on ##B(r)## . i.e. there must be multiplie coordinate choices that will allow me to take it to a wide  range of shaped spacetimes as described by the metric, if these are all regular with no singularities I don't worry, but if there is just one such coordiante transformation that takes me to a body with a singularity I use it as a constraint so original coordiantes that the metric is in must be such that any possible coordinate transformation from that, yields a metric that has no singularities? Bit confused with this since we said coordiantes are not physically significant.
QUESTION 2
Also, I'm actually stuck as to why this describes a cone. I see the solution comments on the period of the cone,being less than a circle of 2pi, i can see that the new angle defined clearly has a period less than 2pi, however, I have no idea of what you define the period of a cone to be ?!
many thanks
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