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Gravitation

PDF   The energy-momentum pseudo-tensor of the gravitational field is a mistake
Submitted to GRG 
Reviewer's comments:
The paper under consideration provides an explicit example of a well-known fact, namely that the energy-momentum pseudo-tensor does not provide an invariant means for calculating the energy-momentum contribution due to the gravitational field. It is dependent on the coordinate system, or more precisely on the reference frame used. So while I believe that the paper is correct I do not think that it contributes anything new and therefore, I suggest that it be rejected.

My reply:
Dear Abhay Ashtekar, Sorry, Your Reviewer is not correct when he writes “that the energy-momentum pseudo-tensor does not provide an invariant means for calculating the energy-mometum contribution due to the gravitational field. It is dependent on the coordinate system, or more precisely on the reference frame used”.
In reality, as is well known, the energy-momentum pseudo-tensor DOES provide an invariant means for calculating the energy-mometum contribution due to the gravitational field. It is INDEPENDENT on the coordinate system, or more precisely on the reference frame used. For example,
Tolman wrote:
“t_\mu^\nu is a quantity which is defined in all systems of coordinates by (87.12), and the equation is a covariant one valid in all systems of coordinates. Hence we may have no hesitation in using this very beautiful result of Einstein”.
Landau & Lifshitz wrote:
“The quantities P^i (the four-momentum of field plus matter) have a completely define meaning and are independent of the choice of reference system to just the extent that is necessary on the basis of physical considerations”.
Tolman wrote:
“It may be shown that the quantities J_\mu are independent of any changes that we may make in the coordinate system inside the tube, provided the changed coordinate system still coincides with the original Galilean system in regions outside the tube. To see this we merely have to note that a third auxiliary coordinate system could be introduced coinciding with the common Galilean coordinate system in regions outside the tube, and coinciding inside the tube for one value of the 'time' x^4 (as given outside the tube) with the original coordinate system and at a later 'time' x^4 with the changed coordinate system. Then, since in accordance with (88.5) the values of J_\mu would be independent of x^4 in all three coordinate systems, we can conclude that the values would have to be identical for the three coordinate systems”.
So you need to use another Reviewer.


Дата: 2013-10-17 08:19:57  Размер: 482.5 Кб  Скачано: 683 
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