Consider the static spherically symmetric metric ds² = 9abdxdxb = −e²A(r) dt² + e²B(r) dr² + r² (do² + sin² 0 do²). In addition, consider an anti-symmetric (0,2) tensor Fab = Fab], whose only non-vanishing components are Ftr , where Q is a positive constant. Then, the tt component of the energy-momentum tensor -Frt Q = Tab = FF - ac 9ab FF is given by: a. Ttt b. Ta tt ☐ c. Ttt d. Ttt Q² 27-4 = 0 = Q² 27-4 e Q² 27-4 -2B(r) -2A(r)
Consider the static spherically symmetric metric ds² = 9abdxdxb = −e²A(r) dt² + e²B(r) dr² + r² (do² + sin² 0 do²). In addition, consider an anti-symmetric (0,2) tensor Fab = Fab], whose only non-vanishing components are Ftr , where Q is a positive constant. Then, the tt component of the energy-momentum tensor -Frt Q = Tab = FF - ac 9ab FF is given by: a. Ttt b. Ta tt ☐ c. Ttt d. Ttt Q² 27-4 = 0 = Q² 27-4 e Q² 27-4 -2B(r) -2A(r)
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![Consider the static spherically symmetric metric ds² = 9abdxdxb = −e²A(r) dt² + e²B(r) dr² + r² (do² + sin² 0 do²). In addition, consider an anti-symmetric (0,2) tensor
Fab = Fab], whose only non-vanishing components are Ftr
, where Q is a positive constant. Then, the tt component of the energy-momentum tensor
-Frt
Q
=
Tab = FF
-
ac
9ab
FF is given by:
a. Ttt
b. Ta
tt
☐ c. Ttt
d. Ttt
Q²
27-4
= 0
=
Q²
27-4
e
Q²
27-4
-2B(r)
-2A(r)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59478137-42f5-43b0-8ccf-49f4a3475793%2Fb9394138-f88c-44cd-a729-1def8affb304%2Fkhkela_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the static spherically symmetric metric ds² = 9abdxdxb = −e²A(r) dt² + e²B(r) dr² + r² (do² + sin² 0 do²). In addition, consider an anti-symmetric (0,2) tensor
Fab = Fab], whose only non-vanishing components are Ftr
, where Q is a positive constant. Then, the tt component of the energy-momentum tensor
-Frt
Q
=
Tab = FF
-
ac
9ab
FF is given by:
a. Ttt
b. Ta
tt
☐ c. Ttt
d. Ttt
Q²
27-4
= 0
=
Q²
27-4
e
Q²
27-4
-2B(r)
-2A(r)
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