The foundations of Minkowskian geometry

1950 ◽  
Vol 24 (1) ◽  
pp. 156-187 ◽  
Author(s):  
Herbert Busemann
Keyword(s):  
Minkowskian Geometry

Orbit propagation in Minkowskian geometry

2015 ◽  
Vol 123 (1) ◽  
pp. 13-43 ◽  
Author(s):  
Javier Roa ◽  
Jesús Peláez
Keyword(s):  
Orbit Propagation ◽  
Minkowskian Geometry

The Ptolemy Inequality and Minkowskian Geometry

1995 ◽  
Vol 68 (2) ◽  
pp. 98-109 ◽  
Author(s):  
John D. Smith
Keyword(s):  
Minkowskian Geometry

scholarly journals Cosmological Particle Production and Causal Thermodynamics

1999 ◽  
Vol 52 (4) ◽  
pp. 659 ◽  
Author(s):  
M. K. Mak ◽  
T. Harko
Keyword(s):  
Particle Production ◽  
Particle Creation ◽  
Phenomenological Theory ◽  
Physical Parameters ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Inflationary Phase ◽  
Bulk Viscous ◽  
Minkowskian Geometry ◽  
The Universe

The full linear causal Israel–Stewart–Hiscock theory of bulk viscous processes in relativistic cosmological fluids is reformulated as an effective phenomenological theory for describing particle production processes in the early universe. Explicit expressions for the particle balance law and particle production rates are obtained that relate the particle creation rate to the bulk viscous (creation) pressure. The general formalism is applied to the case of a full causal cosmological fluid with bulk viscosity coecient proportional to the Hubble function. In this case the general solution of the gravitational field equations can be expressed in an exact parametric form. For an appropriate choice of the physical parameters, the dynamics of the universe can be modelled as starting from a vacuum quasi-Minkowskian geometry, followed by an inflationary period but ending in a non-inflationary phase. The influence of the matter creation processes on the evolution of the universe and the behaviour of the energy density, temperature and entropy are investigated.

INDUCING CHARGES AND CURRENTS FROM EXTRA DIMENSIONS

2008 ◽  
Vol 23 (03) ◽  
pp. 197-203 ◽  
Author(s):  
M. A. S. CRUZ ◽  
F. DAHIA ◽  
C. ROMERO
Keyword(s):  
Extra Dimensions ◽  
Maxwell Equations ◽  
Dimensional Space ◽  
Einstein Equations ◽  
Matter Theory ◽  
Klein Theory ◽  
Fundamental Equations ◽  
Induced Matter ◽  
Minkowskian Geometry ◽  
Kaluza Klein

In a particular variant of Kaluza–Klein theory, the so-called induced-matter theory (IMT), it is shown that any configuration of matter may be geometrically induced from a five-dimensional vacuum space. By using a similar approach we show that any distribution of charges and currents may also be induced from a five-dimensional space. Although in the case of IMT the geometry is Riemannian and the fundamental equations are the five-dimensional Einstein equations in vacuum, here we consider a Minkowskian geometry and five-dimensional Maxwell equations in vacuum.

The Ptolemy Inequality and Minkowskian Geometry

1995 ◽  
Vol 68 (2) ◽  
pp. 98 ◽  
Author(s):  
John D. Smith
Keyword(s):  
Minkowskian Geometry

Minkowskian geometry, convexity conditions and the parallel axiom

1979 ◽  
Vol 12 (1) ◽  
pp. 17-33 ◽  
Author(s):  
H. Busemann ◽  
B. B. Phadke
Keyword(s):  
Minkowskian Geometry ◽  
Convexity Conditions
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