Looking for Post on Uniform Acceleration in Relativity

qraal
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Hi Physics Forumites
I have tried to find a post which I didn't bookmark - foolish me. It discussed uniform accelerated motion in relativistic terms and, unusually, incorporated initial velocities, all in very nice LaTeX. I have scanned a bunch of threads on rocket motion, but can't find it again!
Does anyone know the thread I mean?
 
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'forumites'..is that a slur of somekind? if so, i have been called worse, even in these forums...

Do you know the date of the initial post? or the originator?
Someone also said go to your "MY PF" ...somehow you can locate threads that way...maybe if you posted in them...BenCrowell had made that suggestion to someone recnetly...
[It's pretty funny that I, who can never find the thread I want, is offering search suggestions!]
 
No slur.
If I knew the date...
Naty1 said:
'forumites'..is that a slur of somekind? if so, i have been called worse, even in these forums...

Do you know the date of the initial post? or the originator?
Someone also said go to your "MY PF" ...somehow you can locate threads that way...maybe if you posted in them...BenCrowell had made that suggestion to someone recnetly...
[It's pretty funny that I, who can never find the thread I want, is offering search suggestions!]
 

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
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Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
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Thread 'Hawking After 54 Years Confirmed: BH surfaces don't shrink'

Abstract The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses ## m_1=33.6_{-0.8}^{+1.2} M_{⊙} ## and ## m_2=32.2_{-1. 3}^{+0.8} M_{⊙}##, and small spins ##\chi_{1,2}\leq 0.26 ## (90% credibility) and negligible eccentricity ##e⁢\leq 0.03.## Postmerger data excluding the peak region are consistent with the dominant quadrupolar...
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