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...AVoD is a long, short story ​full of pizzazz​ and physics​; perfect for the reader who can appreciate delusions of grandeur and stomach words such as tensors and geodesics....

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... on combinatorial manifold . . . . . . . . . . . . . . . 242 5.2.3 Exterior differentation. . . . . . . . . . . . . . . . . .244 5.3 Connections on tensors . . . . . . . . . . . . . . . . . . . . . 247 5.3.1 Connection on tensor . . . . . . . . . . . . . . . . . . .247 5.3.2 Torsion-free tensor . . . . . . . . . . . . . . . . . . . . . 250 5.3.3 Combinatorial Riemanni...

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...2.1.6 Field energy in the spatial continuum 2.1.7 Energy transport 2.2 Sinks and sources 2.2.1 Sink density 2.2.2 Moving sinks 2.3 Stress-energy tensors 2.3.1 Solenoidal stress-energy tensor 2.3.2 Irrotational stress-energy tensor 3 Electrodynamics vs Elastodynamics 3.1 Maxwell’s equations 3.1.1 From elastodynamics to Maxwell’s equations 3.1.2 The electromagneti...

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... , (19) where the four-dimensional completely antisymmetric dis- criminant tensorsE αβμν = e αβμν √ −g andE αβμν =e αβμν √ −g, transforming regular te... ...ikm F m . We also take Zelmanov’s identities for the chr.inv.-discriminant tensors [2] into account ∂ε imn ∂t =ε imn D, ∂ε imn ∂t =−ε imn D, (49) ... ...rue pressure of the medium . It is easy to see that the viscous strength tensorsα ik andβ ik are chr.inv.- quantities by their defnitions. By extrac... ...r.inv.- quantities by their defnitions. By extracting the viscous strength tensors α ik and β ik from the formula of the strength tensorU ik of a time... ..., (89) whereU ik =c 2 T ik andU ik =c 2 T ik are the chr.inv.-strength tensors in the falling wave and in the refected wave. So the three-dimensio... ...ant valencies are even; 2. Both covariant and contravariant indices of the tensors are split into pairs and inside each pair the tensor R αβγδ is anti... ...jk (2) , A iklj (3) are chronometrically invariant and spatially invariant tensors, which have no more than frst order derivatives of the wave functio... ...sor [37], we express the matrix R ab through components of the chr.inv.-tensors X ij andY ijk [66]. We obtain The 1st Kind R ab = x y y... ...D jl +A ij A kl + +A jk D il +A kl D ij +A li D jk (6.16) and contracted tensors H lk =H ∙∙∙ i lik∙ and C lk =C ∙∙∙ i lik∙ are re- lated as follows ...

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...The above Clifford-valued coordinates X M ,Σ A correspond to antisymmetric tensors of ranks r,s in the target spacetime background and in the world-ma... ... scalars (although in tensor calculus they are called scalars, vectors and tensors, respectively), whilst the objects γα,γα∧γ β ,..., are called vecto... ...αβρ δ −R αβγ ρ R μνρ δ , (112) which is the product of two usual curvature tensors. We can proceed in analogous way to calculate the other components ... ...ctive action in curved spacetimes given by sums of powers of the curvature tensors based on the quantization of non-linear sigma models [118]. If one ... ...mmetric spacetimes, like spheres and hyperboloids, where all the curvature tensors are proportional to suitable combinations of the metric tensor time... ...ion that the net combination of the sum of all the powers of the curvature tensors may cancel-out giving an overall zero value R=0. This possibility d...

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... the necessary property. We must also deal not in ordinary vectors, but in tensors, or relativistic 4-vectors. The specific 4-vectors needed are p...

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...ifferent phenomena observed, such as why the free particles in a gravitational field have the trajectories they have. And in this process, the metric tensors field helps explain the metric relations observed between material entities. Robert Weingard asserts that there is an ontological disagreement between the two metrics, the first being the relations between material en...