# T_NAKÄ[uO

## ɁuVvʂ̌ʁFCONSEQUENCES OF THE NEW METRICvǂށBiPj

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 "Remarks on the Equivalence of Inertial and Gravitational Masses and on the Accuracy of Einstein's Theory of Gravity." CONSEQUENCES OF THE NEW METRIC ǂ݂܂B [Vvʂ̌ʁFCONSEQUENCES OF THE NEW METRICiP-Pj]===================================== The new metric allows calculation of several important effects that are directly testable by comparing them with observations. Vvʂ́Aϑl𒼐ڔr邱Ƃɂ肢̏dvȌʂ̌vZ\ɂB The first one is the gravitational red shift. ŏ1́Ad͐ԕΈڂłB The recent discovery of the gravitational red shift of the Pulsar EXO 0748-676 allows an accurate determination of the pulsar mass to radius ratio. Pulsar EXO 0748-676̏d͐ԕΈڂ̍ŋ߂̔́ApT[ʔa䗦ɂ̐mȌB The observed value of Z was Z = 0.35, determined with a high precision. Z̊ϑl͍x Z = 0.35 ƌ肳ꂽB The gravitational red shift formulas are easily obtained directly from the corresponding metrics. d͐ԕΈڌ́AڑΉvʂȒPɓB For the Schwarzschild metric this becomes: (56)while for the new metric the formula, expressed as function of the coordinate distance, is as follows: (57)where the proper distance is evaluated as function the coordinate distance numerically using Eq.55. VcVgvʂ玟ƂȂF @$Z_{s}= \left ( 1-\frac{R_{s}}{r} \right )^{\frac{-1}{2}}-1\; \; \; \; \; \; (56)$ VvʂWŕ\킷Ǝ̒ʂF @$Z_{c}= e^{\frac{R_{s}}{2\rho (r)}}-1\; \; \; \; \; \; (57)$ ŁAŗL͐lIɁi55)gčW֐Ƃĕ]B The plots of the respective red shifts are shown for the neutron star of mass 1.4 times the mass of Sun in Fig.3. z1.4{̎ʂ̒q̐ԕΈڂ̃vbǵA}3ɂ̂߂ɎB =============================================================================================== S r ̈ʒǔŗL ƉW t W̊֌W @$\Delta \tau = (g_{00})^{1/2}\Delta t$ łAS狗r̒n_Ŕg em ̌˂Aꂽn_ɂāǍ̔g rec ƊϑꂽƂƁA @$\lambda _{em} = (g_{00})^{1/2}\lambda _{rec}$ łBŐԕΈڂ̎wW Z @$Z= \frac{\lambda _{rec}-\lambda _{em}}{\lambda _{em}}= \frac{\lambda _{rec}}{\lambda _{em}}-1=(g_{00})^{-1/2}-1$ łB [Vvʂ̌ʁFCONSEQUENCES OF THE NEW METRICiP-Qj]==================================== As can be seen from the graphs a reasonable and measurable difference between the predictions of respective theories is obtained. Ot番悤ɁAꂼ̗_̗\́A_IEϑIɂȂ̈ႢB If an independent and accurate determination of the pulsarfs radius or mass were found it would be possible to distinguish between these two metrics. ƗɃpT[̔a܂͎ʂ̐mȒl߂΁A2̌vʂ̗D邱Ƃłł낤B It might also be possible to collect statistical data from many pulsars and compare the corresponding statistical distributions of Z shifts. ̃pT[瓝vf[^W߂āAZ Έڂ̓vIzr邱Ƃo邩mȂB However, for more accuracy, it is necessary to replace the coordinate distance with the apparent distance,since the coordinate as well as the proper distance is not known. AȂ鐳m̂߂ɁAŗLĂȂWȂ̂ŁAWڂ̋Ɠւ邱ƂKvłB As shown in Fig.2 in the region close to the Schwarzschild radius there is a significant difference between the proper distance and the coordinate distance. }2Ŏ悤ɁAVcVga̋ߖTł͌ŗLƍWԂ̗LӍB The same is true for the apparent distance, the distance traveled by light, which is directly observable. Ƃ͌ڂ̋ɂƂĂ^łA͌̐isɂĎA͒ڊώ@\łB The coordinate distance can then be calculated from the apparent distance and the plot of Z shift versus the apparent distance made. ꂩAẂAڂ̂̂܂܂̋ɑ΂āAڂ̋ZΈڂ̃vbgvZ邱ƂłB It is interesting that in such a graph the Z shift saturates at approximately the observed value of Z. OtŁAZ Έڂق Z ̊ϑlŖOâ͋[B This is not shown in this paper. ́A{_ł͎ȂB }R. d͐ԕΈڂ́AVcVgvʂA܂[gŃvbgꂽpT[Wå֐ƂĂ̐Vvʂ\BpT[ʂ͑z 1.4 {Ɖ肵BZ ̊ϑn͐̔jŕ\킵B@ =============================================================================================== ͂̕ӂŁBB

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