The holographic solution – Why general relativity must be understood in terms of

Michael Petri

Table of contents :
Introduction:……Page 4
The holostar metric and fields……Page 7
Proper volume and radial distance……Page 10
Energy-conditions……Page 11
“Stress-energy content” of the membrane……Page 14
On the physical interpretation of the trace of the stress-energy tensor in the holographic space-time……Page 15
The equations of geodesic motion……Page 16
Bound versus unbound motion……Page 20
Bound motion of massive particles……Page 21
Unbound motion of photons……Page 23
An upper bound for the particle flux to infinity……Page 24
Geodesic motion of a spherical thin shell of photons……Page 27
Geodesic expansion of photons against the holostar pressure……Page 28
Geodesic expansion of photons against their radiation pressure……Page 30
Number of interior particles and holographic principle……Page 32
Local radiation temperature and the Hawking temperature……Page 34
Geodesically moving radiation preserves the Planck distribution……Page 36
A quick derivation of the Hawking temperature law……Page 37
Necessary conditions for nearly geodesic motion of massive particles……Page 38
Geodesic acceleration and pressure……Page 39
A case for a gravitational origin of the pressure with a Planck-sized cross-sectional area……Page 45
A possible origin of the negative radial pressure……Page 48
Is the pressure produced by ordinary matter?……Page 49
Or do we need some new form of matter?……Page 50
Geodesic motion of a thin spherical shell of massive particles……Page 53
Does the motion of massive particles conserve energy?……Page 55
On the relative number-densities of charged particles and photons……Page 56
The Hawking entropy-area law……Page 57
A holostar consisting predominantly out of ultra-relativistic particles……Page 58
A holostar consisting predominantly out of massive particles……Page 59
On the identity of local entropy density and geodesic acceleration……Page 60
On the interpretation of a compact self-gravitating body as a massive particle……Page 62
An upper limit for the mass of large black holes in the centers of galaxies……Page 66
Motion of massive particles in their own proper time……Page 67
A linear and a quadratic redshift-distance relation……Page 68
An isotropic Hubble flow of massive particles……Page 70
The angular diameter distance……Page 72
The luminosity distance……Page 75
Structure formation in the holostar space-time……Page 83
The evolution of density perturbations in the dust-case……Page 84
The evolution of density perturbations in the radiation dominated era……Page 87
Limits on the angular motion of massive particles……Page 89
The preon – a massive particle of roughly Planck mass?……Page 92
An independent estimate for the preon mass……Page 93
An estimate for the amplitude of the density perturbations……Page 95
Limits on the angular motion of photons – an estimate for the maximum angular correlation distance……Page 96
Applying the uncertainty principle to the holostar’s central region……Page 97
Estimating cosmological parameters from the radiation temperature……Page 98
A determination of the local entropy density……Page 101
On the relation between energy- and entropy-density and the free energy……Page 104
On the conservation of energy and entropy in the interior and exterior space-time……Page 106
Local matter distribution and self-similarity……Page 108
Some remarks about the frames of the asymptotic and the co-moving observer……Page 109
On the number- and energy-densities of massive particles……Page 110
On the number- and energy-densities of zero rest mass particles……Page 112
The assumption of constant rest mass……Page 115
A hypothesis of an r-dependent rest mass…….Page 121
Local geodesic acceleration and Unruh-temperature……Page 124
The Unruh-temperature at the membrane……Page 125
The Unruh temperature at the center and a determination of ri……Page 126
Unruh temperature due to the pressure-induced acceleration……Page 127
An alternative derivation of ri……Page 129
An argument for = S ’26-9muh at ri……Page 130
A relation between the string tension and length……Page 131
The holostar as a unified description for the fundamental building blocks of nature?……Page 132
The holostar as alternative to black holes?……Page 133
The holostar as a self-consistent model for the universe?……Page 134
The holostar as a simple model for a self gravitating particle with zero gravitational mass ?……Page 140
Discussion……Page 142