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## Main Question or Discussion Point

In recently closed thread titled Conservation of energy in GR, 4-velocity of popped up baseball along geodestic ##(u^0(r),u^1(r),0,0)## where ##x^1=r,x^2=\theta,x^3=\phi##, is derived.

In SR, 4-momentum of ball is ##m(u^0,u^1,0,0)## in contravariant component and ##m(u_0,u_1,0,0)## in covariant component. The two component may differ only in sigature.

In GR, the two componets differ in value also because ##g_{ik}\neq\eta_{ik}## anymore.

My questions are

1. In GR how can we derive energy of the ball using the two components ?

2. For energy-momentum, not 4-vector but two rank tensor ##T^{ik}## seems familiar in GR. Shall I move from 4-vector to 2 rank tensor in GR ? The two ways are compatible in SR/GR ?

Thanks in advance.

In SR, 4-momentum of ball is ##m(u^0,u^1,0,0)## in contravariant component and ##m(u_0,u_1,0,0)## in covariant component. The two component may differ only in sigature.

In GR, the two componets differ in value also because ##g_{ik}\neq\eta_{ik}## anymore.

My questions are

1. In GR how can we derive energy of the ball using the two components ?

2. For energy-momentum, not 4-vector but two rank tensor ##T^{ik}## seems familiar in GR. Shall I move from 4-vector to 2 rank tensor in GR ? The two ways are compatible in SR/GR ?

Thanks in advance.