what is the metric of N-sheeted $AdS_3$?
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Answered by
1
About n-sheeted space, I do not know the precise defination. I will give some introductions.
consider a 3-dimensional space B_1 whose boundary is M_1. Then the manifold M_n is defined as n-folded cover of M_1: taking n copies of M_1, cutting each of them apart at a region A, and gluing them in cyclic order. Then the bulk solution B_n whose boundary is M_n is the n-sheeted space of B_1.
For example:
BTZ solution can be wriiten as :
d
s
2
=
r
2
d
τ
2
+
(
r
2
+
1
)
−
1
d
r
2
+
(
r
2
+
1
)
d
ϕ
2
ds2=r2dτ2+(r2+1)−1dr2+(r2+1)dϕ2
consider a 3-dimensional space B_1 whose boundary is M_1. Then the manifold M_n is defined as n-folded cover of M_1: taking n copies of M_1, cutting each of them apart at a region A, and gluing them in cyclic order. Then the bulk solution B_n whose boundary is M_n is the n-sheeted space of B_1.
For example:
BTZ solution can be wriiten as :
d
s
2
=
r
2
d
τ
2
+
(
r
2
+
1
)
−
1
d
r
2
+
(
r
2
+
1
)
d
ϕ
2
ds2=r2dτ2+(r2+1)−1dr2+(r2+1)dϕ2
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The answer of u r question is..✌️✌️
Is in the pic.
Thank you..⭐️⭐️
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