This paper discusses the so called holographic solution , in short ” holostar ” .
The holostar is the simplest exact , spherically symmetric solution of the original Einstein field equations with zero cosmological constant , including matter .
The interior matter-distribution follows an inverse square law \rho = 1 / ( 8 \pi r ^ { 2 } ) .
The interior principal pressures are P _ { r } = - \rho and P _ { \perp } = 0 , which is the equation of state for a collection of radial strings with string tension \mu = - P _ { r } = 1 / ( 8 \pi r ^ { 2 } ) .
The interior space-time is separated from the exterior vacuum space-time by a spherical two-dimensional boundary membrane , consisting out of ( tangential ) pressure .
The membrane has zero mass-energy .
Its stress-energy content is equal to the holostar ’ s gravitational mass .
The total gravitational mass of a holostar can be determined by a proper integral over the Lorentz-invariant trace of the stress-energy tensor .

The holostar exhibits properties similar to the properties of black holes .
The exterior space-time of the holostar is identical to that of a Schwarzschild black hole , due to Birkhoff ’ s theorem .
The membrane has the same properties ( i.e .
the same pressure ) as the fictitious membrane attributed to a black hole according to the membrane paradigm .
This guarantees that the dynamical action of the holostar on the exterior space-time is identical to that of a black hole .
The holostar possesses an internal temperature proportional to 1 / \sqrt { r } and a surface redshift proportional to \sqrt { r } , from which the Hawking temperature and entropy formula for a spherically symmetric black hole are derived up to a constant factor .

The holostar ’ s interior matter-state is singularity-free .
It can be interpreted as the most compact spherically symmetric ( i.e .
radial ) arrangement of classical strings : The radially outlayed strings are densely packed , each string occupies exactly one Planck area in its transverse direction .
This maximally dense arrangement is the reason why the holostar does not collapse to a singularity and why the number of interior degrees of freedom scales with area .
Although the holostar ’ s total interior matter state has an overall string equation of state , part 
of the matter can be interpreted in terms of particles .
The number of zero rest-mass particles within any concentric region of the holostar ’ s interior is shown to be proportional to the proper area of its boundary , implying that the holostar is compatible with the holographic principle and the Bekenstein entropy-area bound , not only from a string but also from a particle perspective .

In contrast to a black hole , the holostar-metric is static throughout the whole space-time .
There are no trapped surfaces and no event horizon .
Information is not lost .
The weak and strong energy conditions are fulfilled everywhere , except for a Planck-size region at the center .
Therefore the holostar can serve as an alternative model for a compact self-gravitating object of any conceivable size .

The holostar is the prototype of a closed system in thermal equilibrium .
Its lifetime is several orders of magnitude higher than its interior relaxation time .
The thermodynamic properties of the interior space-time can be derived exclusively from the geometry .
The local entropy-density s in the interior space-time is exactly equal to the proper geodesic acceleration of a stationary observer , s = g / \hbar .
It is related to the local energy-density via sT = \rho .
The free energy in the interior space-time is minimized to zero , i.e . F = E - ST = 0 .
Disregarding the slow process of Hawking evaporation , energy and entropy are conserved locally and globally .

Although the holostar is a static solution , it behaves dynamically with respect to the interior motion of its constituent particles .
Geodesic motion of massive particles in a large holostar is nearly radial and exhibits properties very similar to what is found in the observable universe : Any material observer moving geodesically outward will observe an isotropic outward directed Hubble-flow of massive particles from his local frame of reference .
An inward moving observer experiences an inward directed Hubble-flow .
The outward motion is associated with an increase in entropy , the inward motion with a decrease .
The radial motion of the geodesically moving observer is accelerated , with the proper acceleration falling off over time ( for an outward moving observer ) .
The acceleration is due to the interior metric , there is no cosmological constant .

Geodesic motion of massive particles is highly relativistic , as viewed from the stationary coordinate system .
The \gamma -factor of an inward or outward moving observer is given by \gamma \approx \sqrt { r / r _ { 0 } } , where r _ { 0 } is a fundamental length parameter which can be determined experimentally and theoretically . r \approx 2 r _ { Pl } .
Inmoving and outmoving matter is essentially decoupled , as the collision cross-sections of ordinary matter must be divided by \gamma ^ { 2 } , which evaluates to \approx 10 ^ { 60 } at the radial position of an observer corresponding to the current radius of the universe .

The total matter-density \rho , viewed from the extended Lorentz-frame of a geodesically moving observer , decreases over proper time \tau with \rho \propto 1 / \tau ^ { 2 } .
The radial coordinate position r of the observer evolves proportional to \tau .
The local Hubble value is given by H = 1 / \tau .
Although the relation \rho \propto 1 / r ^ { 2 } seems to imply a highly non-homogeneous matter-distribution , the large-scale matter-distribution seen by a geodesically moving observer within his observable local Hubble-volume is homogeneous by all practical purposes .
The large-scale matter-density within the Hubble-volume differs at most by \delta \rho / \rho \approx 10 ^ { -60 } at radial position r \approx 10 ^ { 61 } , corresponding to the current Hubble-radius of the universe .
The high degree of homogeneity in the frame of the co-moving observer arises from the combined effect of radial ruler distance shrinkage due the radial metric coefficient ( \sqrt { g _ { rr } } \propto \sqrt { r / r _ { Pl } } and Lorentz-contraction in the radial direction because of the highly relativistic geodesic motion , which is nearly radial with \gamma \propto \sqrt { r / r _ { Pl } } .

The geodesically moving observer is immersed in a bath of zero rest-mass particles ( photons ) , whose temperature decreases with T \propto 1 / \sqrt { \tau } , i.e . \rho \propto T ^ { 4 } .
Geodesic motion of photons within the holostar preserves the Planck-distribution .
The radial position of an observer can be determined via the local mass-density , the local radiation-temperature , the local entropy-density or the local Hubble-flow .
Using the experimentally determined values for the matter-density of the universe , the Hubble-value and the CMBR-temperature , values of r between 8.06 and 9.18 \cdot 10 ^ { 60 } r _ { Pl } are calculated , i.e values very close to the current radius and age of the universe .
Therefore the holographic solution might serve as an alternative model for a universe with an overall negative ( string type ) equation of state , without need for a cosmological constant .

The holostar as a model for a black hole or the universe contains no free parameters : The holostar metric and fields , as well as the initial conditions for geodesic motion are completely fixed and arise naturally from the solution .
An analysis of the characteristic properties of geodesic motion in the interior space-time points to the possibility , that the holostar-solution might contribute substantially to the understanding of the phenomena in our universe .
The holostar model of the universe is free of most of the problems of the standard cosmological models , such as the ” cosmic-coincidence-problem ” , the ” flatness-problem ” , the ” horizon-problem ” , the ” cosmological-constant problem ” etc .
.
The cosmological constant is exactly zero .
There is no horizon-problem , as the co-moving distance r evolves exactly proportional to the Hubble-radius ( r \propto \tau for r \gg r _ { Pl } ) .
Inflation is not needed .
There is no initial singularity .
The expansion ( = radially outward directed geodesic motion ) starts out from a Plank-size region at the Planck-temperature , which contains at most one ” particle ” with roughly 1/8 to 1/5 of the Planck-mass .
The maximum angular separation of particles starting out from the center is limited to roughly 60 ^ { \circ } , which could explain the low quadrupole and octupole-moments in the CMBR-power spectrum .
The relation r \propto \tau for r \gg r _ { Pl } , whose fundamental origin can be traced to the zero active gravitational mass-density of the string-type matter in the interior space-time , can be interpreted in terms of a permanently unaccelerated expansion , from which H \tau = 1 follows .
This genuine prediction of the holostar model is very close to the observations , which give values between 0.98 and 1.04 .
Permanently undecelerated expansion is also compatible with the luminosity-redshift relation derived from the most recent supernova-measurements , although the experimental results favor the concordance \Lambda CDM-model over the holostar-model at roughly 1 \sigma confidence level .
The Hubble value in the holostar-model of the universe turns out lower than in the concordance model . H \simeq 1 / r = 62.35 ( km / s ) / MPc 
is predicted .
This puts H into the range of the other absolute measurements , which consistently give values H \approx 60 ( km / s ) / MPc and is compatible with the recent supernova-data , which favor values in the range H \approx 60 - 65 .
Geodesic motion of particles in the holostar space-time preserves the relative energy-densities of the different particle species ( not their number-densities !
) , from which a baryon-to photon ratio of roughly \eta \approx 10 ^ { -9 } at T _ { CMBR } = 2.725 K \approx 10 ^ { -9 } ( m _ { e } c ^ { 2 } / k ) is predicted .

The holographic solution also admits microscopic self-gravitating objects with a surface area of roughly the Planck-area and zero gravitating mass .