Scientific Secrets of Jainism

Author(s): Nandighoshvijay
Publisher: Research Institute of Scientific Secrets from Indian Oriental Scriptures Ahmedabad

Page 241

THE EXTERNAL FIELD OF A RADIATING STAR IN
GENERAL RELATIVITY
(i) dm-0, (11) & (r3 e ̃à T1') = 0,
(iii)
Ir is well known that the generalization of It is found that the field equations amount to Schwarzschild's solution corresponding to the external field of a radiating star has not yet been obtained. The internal field describes a mixture of matter and radiation. In the outer field there is the expanding inner zone of pure radiation, with radius r, at time t, beyond which the mpty space is described by Schwarzschild's static solution. The zone of pure radiation is given by
ds1 =
· − (1 − 2)* dr3 — ‚1 (de2 + sin" 9d4")
+ m2 (1-2m) de3,
(1)
f(m) = m'
(1-2m).
(2)
[As usual an overhead dot denotes a differentiation with regard to t and an overhead dash a differentiation with regard to r. f(m) is an arbitrary function of m.]
with
so that
Since the lines of flow of radiation must be null geordesics the radiation tensor has to be Tur = por o Spot = 3 (pv)μ= 0 and (v); v = 0. The surviving components of the tensor given by -T'=T1=
m' Am T.
m'2 4mm
T1=
For differentiation along a line of how have the operator
d=ex2+e
in 4nr*
(3)
(4)
(5)
are
(6)
we
(7)
(r' p) = 0, (iv) do
dr
-=0. (8) The equation that is most difficult to handle corresponds to T, 0. But it can be shown to be equivalent to (ii). The equation of continuity then leads to (iii) and (iv) readily. Thus, along the lines of flow of radiation m, vl and rp are all conserved. It is worthy of notice that m' is positive while is negative. This as well as the results (6) and (8) are suggested by the Newtonian analogue.
The total energy of matter and radiation is conserved. m is the affective mass of the whole system at a point. The value of mat the boundary rr, at t=t, is a constant, M. At time t,, for all values of r exceeding r,, the field is given by Schwarzschild's line-element corresponding to the value M Also-f(M) wher TT, and t=t,.
Th: new results are (1), (2), (6), (8). Further details and astronomical applications are considered in a paper to be published elsewhere.
My thanks are due to Prof. V. V. Narlikar under whose guidance this work was done and who showed me the result 8 (i).
Benares Hindu University, March 22, 1943.
P. C. VAIDYA
Einstein, Infeld and Hoffmann, Annals of Mathematics, 1938, p. 65; Narlikar, V. V., Bombay Univ. J.. 1939, 8, 37.
Reprinted from "Current Science", Vol. XII, No. 6, June 1943, page 183
Vaidya. His research contribution is therefore very important in astrophysics. necessary to make calculations according to the solution suggested by Dr
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