FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4211179018> ?p ?o ?g. }

• W4211179018 endingPage "290" @default.
• W4211179018 startingPage "225" @default.
• W4211179018 abstract "The chapter has as main objective to clarify some important concepts appearing in relativistic spacetime theories and which are necessary of a clear understanding of our view concerning the formulation and understanding of Maxwell, Dirac and Einstein theories. Using the definition of a Lorentzian spacetime structure $$(M,boldsymbol{g},D,tau _{boldsymbol{g}},uparrow )$$ presented in Chap. 4 we introduce the concept of a reference frame in that structure which is an object represented by a given unit timelike vector field $$boldsymbol{Z} in sec TU$$ ( $$U subseteq M$$ ). We give two classification schemes for these objects, one according to the decomposition of $$Dboldsymbol{Z}$$ and other according to the concept of synchronizability of ideal clocks (at rest in $$boldsymbol{Z}$$ ). The concept of a coordinate chart covering U and naturally adapted to the reference frame $$boldsymbol{Z}$$ is also introduced. We emphasize that the concept of a reference frame is different (but related) from the concept of a frame which is a section of the frame bundle. The concept of Fermi derivative is introduced and the physical meaning of Fermi transport is elucidated, in particular we show the relation between the Darboux biform $$Omega $$ of the theory of Frenet frames and its decomposition as an invariant sum of a Frenet biform $$Omega _{F}$$ (describing Fermi transport) and a rotation biform $$Omega _{mathbf{S}}$$ such that the contraction of $$star Omega _{mathbf{S}}$$ with the velocity field v of the spinning particle is directly associated with the so-called Pauli-Lubanski spin 1-form. We scrutinize the concept of diffeomorphism invariance of general spacetime theories and of General Relativity in particular, discuss what meaning can be given to the concept of physically equivalent reference frames and what one can understand by a principle of relativity. Examples are given and in particular, it is proved that in a general Lorentzian spacetime (modelling a gravitational field according to General Relativity) there is in general no reference frame with the properties (according to the scheme classifications) of the inertial referenced frames of special relativity theories. However there are in such a case reference frames called pseudo inertial reference frames (PIRFs) that have most of the properties of the inertial references frames of special relativity theories. We also discuss a formulation (that one can find in the literature) of a so-called principle of local Lorentz invariance and show that if it is interpreted as physical equivalence of PIRFs then it is not valid. The Chapter ends with a brief discussion of diffeormorphism invariance applied to Schwarzschild original solution and the Droste-Hilbert solution of Einstein equation which are shown to be not equivalent (the underlying manifolds have different topologies) and what these solutions have to do with the existence of blackholes in the “orthodox”interpretation of General Relativity." @default.
• W4211179018 created "2022-02-13" @default.
• W4211179018 creator A5029563034 @default.
• W4211179018 creator A5072574433 @default.
• W4211179018 date "2016-01-01" @default.
• W4211179018 modified "2023-10-17" @default.
• W4211179018 title "Some Issues in Relativistic Spacetime Theories" @default.
• W4211179018 cites W1485710077 @default.
• W4211179018 cites W1620889972 @default.
• W4211179018 cites W165787586 @default.
• W4211179018 cites W1963587789 @default.
• W4211179018 cites W1965548917 @default.
• W4211179018 cites W1968035388 @default.
• W4211179018 cites W1969930494 @default.
• W4211179018 cites W1970590942 @default.
• W4211179018 cites W1971871645 @default.
• W4211179018 cites W1974010651 @default.
• W4211179018 cites W1974228247 @default.
• W4211179018 cites W1974666760 @default.
• W4211179018 cites W1977980504 @default.
• W4211179018 cites W1979106006 @default.
• W4211179018 cites W1979381070 @default.
• W4211179018 cites W1982955648 @default.
• W4211179018 cites W1991990049 @default.
• W4211179018 cites W1994986908 @default.
• W4211179018 cites W1999105938 @default.
• W4211179018 cites W1999275326 @default.
• W4211179018 cites W2000549336 @default.
• W4211179018 cites W2002762157 @default.
• W4211179018 cites W2006199507 @default.
• W4211179018 cites W2013444691 @default.
• W4211179018 cites W2013918180 @default.
• W4211179018 cites W2015442843 @default.
• W4211179018 cites W2018370556 @default.
• W4211179018 cites W2018978561 @default.
• W4211179018 cites W2023407353 @default.
• W4211179018 cites W2025696836 @default.
• W4211179018 cites W2028257843 @default.
• W4211179018 cites W2029403139 @default.
• W4211179018 cites W2031813685 @default.
• W4211179018 cites W2032128790 @default.
• W4211179018 cites W2043085526 @default.
• W4211179018 cites W2044884914 @default.
• W4211179018 cites W2053348301 @default.
• W4211179018 cites W2059707786 @default.
• W4211179018 cites W2060729034 @default.
• W4211179018 cites W2060745302 @default.
• W4211179018 cites W2061225185 @default.
• W4211179018 cites W2061546949 @default.
• W4211179018 cites W2063732230 @default.
• W4211179018 cites W2065839833 @default.
• W4211179018 cites W2068880590 @default.
• W4211179018 cites W2069878724 @default.
• W4211179018 cites W2070272267 @default.
• W4211179018 cites W2081051184 @default.
• W4211179018 cites W2081418987 @default.
• W4211179018 cites W2082021896 @default.
• W4211179018 cites W2084274002 @default.
• W4211179018 cites W2086236442 @default.
• W4211179018 cites W2087945706 @default.
• W4211179018 cites W2090055503 @default.
• W4211179018 cites W2090196576 @default.
• W4211179018 cites W2091544442 @default.
• W4211179018 cites W2092384430 @default.
• W4211179018 cites W2092434381 @default.
• W4211179018 cites W2092798326 @default.
• W4211179018 cites W2094359492 @default.
• W4211179018 cites W2094420548 @default.
• W4211179018 cites W2095495107 @default.
• W4211179018 cites W2110216801 @default.
• W4211179018 cites W2120820458 @default.
• W4211179018 cites W2125169989 @default.
• W4211179018 cites W2127684545 @default.
• W4211179018 cites W2130246428 @default.
• W4211179018 cites W2145847827 @default.
• W4211179018 cites W2150547812 @default.
• W4211179018 cites W2226016876 @default.
• W4211179018 cites W2594720119 @default.
• W4211179018 cites W2951804731 @default.
• W4211179018 cites W2986325738 @default.
• W4211179018 cites W3100101815 @default.
• W4211179018 cites W3101214587 @default.
• W4211179018 cites W3106371340 @default.
• W4211179018 cites W4210370865 @default.
• W4211179018 cites W4229483602 @default.
• W4211179018 cites W4230133121 @default.
• W4211179018 cites W4233123182 @default.
• W4211179018 cites W4241733850 @default.
• W4211179018 cites W42515603 @default.
• W4211179018 cites W4251892848 @default.
• W4211179018 cites W4253715350 @default.
• W4211179018 cites W4300498648 @default.
• W4211179018 cites W4302795192 @default.
• W4211179018 cites W585438944 @default.
• W4211179018 cites W596136856 @default.
• W4211179018 cites W2051199013 @default.
• W4211179018 doi "https://doi.org/10.1007/978-3-319-27637-3_6" @default.
• W4211179018 hasPublicationYear "2016" @default.

• next