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Holostars: Black Holes Without Event Horizons

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Posted by Richard Ruquist on June 17, 2003 13:57:33 UTC

The Cornell archives had three very long papers on holostars today- 70, 43 and 40 pages. I just read the abstracts which are copied below.

Perhaps some physics student couls read the entire papers. My concern was mainly to know what a holostar was, as described in the abstracts below. Its name derives from the fact tht information is preserved in such a black hole, and must be a contraction of hologram and star. Not sure why a black hole should be called a star. Perhaps someone couls read and explain why to me.




The holostar - a self-consistent model for a compact self-gravitating object
Authors: Michael Petri (Bundesamt fuer Strahlenschutz, Salzgitter, Germany)
Comments: 70 pages
The holostar is an exact spherically symmetric solution to the field equations of general relativity with anisotropic interior pressure. Its properties are similar to a black hole. It has an internal temperature inverse proportional to the square root of the radial coordinate value, from which the Hawking temperature law follows. The number of particles within any concentric region of the holostar's interior is proportional to the proper area of its boundary. The holostar-metric is static throughout the whole space-time. There are no trapped surfaces, no singularity 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.
Geodesic motion of massive particles in a large holostar is similar to what is observed in the universe today: A material observer moving geodesically experiences an isotropic outward directed Hubble-flow of massive particles. The total matter-density decreases over proper time by an inverse square law. The local Hubble radius increases linearly over time. Geodesic motion of photons preserves the Planck-distribution. The local radiation temperature decreases over time by an inverse square law. The current radial position r of an observer can be determined by measurements of the total local mass-density, the local radiation temperature or the local Hubble-flow. The values of r determined from the CBMR-temperature, the Hubble constant and the total mass-density of the universe are equal within an error of a few percent to the radius of the observable universe.
The holographic solution also admits microscopic self-gravitating objects with a surface area of roughly the Planck-area and zero gravitating mass.

Charged holostars
Authors: Michael Petri (Bundesamt fuer Strahlenschutz, Salzgitter, Germany)
Comments: 43 pages
The so called holostar solution of general relativity is generalized to the charged case. The exterior metrics and fields of the charged holostar are equal to the Reissner-Nordstroem black hole solution. The holostar's gravitating mass, corrected by a quantity of roughly Planck-mass is always larger than its charge. Whereas Reissner Nordstroem solutions with larger charge are possible, but are excluded by the cosmic censorship hypothesis, a charged holostar with higher than the maximum charge doesn't exist.
The total interior energy density and principal pressures of the charged holostar - as well as the interior metric - are equal to the uncharged case. The holostar's exterior charge is proportional to the number of its interior (massive) particles. The membrane is uncharged. The interior energy density splits into an electromagnetic contribution and a "matter" contribution. An extremely charged holostar consists entirely out of electromagnetic energy. Its membrane vanishes and its metric derivatives are continuous at the boundary separating the sources of the electromagnetic field from the exterior electro-vac space-time.
A large charged/rotating holostar can be regarded as the classical analogue of a quantum gravity spin-network state. If the links of a large spin network state are identified with the interior relativistic particles of the holostar solution, the Immirzi parameter can be determined. Its value is roughly a factor of 4.8 higher than the result derived by Ashtekar by counting horizon surface states. An explanation for the discrepancy is given. An entropy conservation law for self gravitating systems is proposed.

Holostar thermodynamics
Authors: Michael Petri (Bundesamt fuer Strahlenschutz, Salzgitter, Germany)
Comments: 47 pages
A simple thermodynamic model for the final state of a collapsed, spherically symmetric star is presented. It is assumed, that the star's interior at the endpoint of the collapse consists of an ideal gas of ultra-relativistic fermions and bosons in thermal equilibrium and that the metric approaches the static metric of the so called holostar-solution of general relativity.
The final configuration has a radius slightly exceeding the gravitational radius of the star. The radial coordinate difference between gravitational and actual radius is of order of the Planck length. The total number of ultra-relativistic particles within the star is proportional its proper surface-area, measured in units of the Planck-area. This is first direct evidence for the microscopic-statistical nature of the Hawking entropy and indicates, that the holographic principle is valid for compact self gravitating objects of any size.
A "Stephan-Boltzmann-type" relation between the surface temperature and the surface area of the star is derived. This relation implies a well defined interior temperature proportional to the inverse square root of the radial coordinate. The Hawking temperature and -entropy are derived up to a constant factor. Interior temperature and Hawking temperature are related. Using the experimental values for the CMBR-temperature and the total matter-density of the universe the Hawking temperature law is verified to an accuracy of 1%.
The contribution of the holostar's membrane to its entropy and gravitating mass is discussed under the assumption, that the membrane consists of a gas of bosons whose number is roughly equal to the number of the interior particles. Some properties expected from a rotating holostar are discussed briefly.

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