On the thermodynamic origin of the Hawking entropy and a measurement of the Hawking temperature

TL;DR

This paper derives the Hawking entropy and temperature from a thermodynamic perspective using a holographic model of matter distribution, and verifies the Hawking temperature law with cosmological data to within 1%.

Contribution

It introduces a holographic solution with an interior string equation of state that reproduces Hawking's results and provides an experimental verification of the Hawking temperature law.

Findings

Hawking entropy and temperature can be derived from thermodynamics of a holographic matter distribution.

The holographic solution accurately models the universe and matches Hawking's temperature law within 1%.

The interior matter can be described as an ultra-relativistic gas consistent with black hole thermodynamics.

Abstract

In the spherically symmetric case the Einstein field equations take on their simplest form for a matter-density rho = 1 / (8 pi r^2), from which a radial metric coefficient g_{rr} \propto r follows. The boundary of an object with such an interior matter-density is situated slightly outside of its gravitational radius. Its surface-redshift scales with z \propto \sqrt{r}, so that any such large object is practically indistinguishable from a black hole, as seen from exterior space-time. The interior matter has a well defined temperature, T \propto 1 / \sqrt{r}. Under the assumption, that the interior matter can be described as an ultra-relativistic gas, the object's total entropy and its temperature at infinity can be calculated by microscopic statistical thermodynamics. They are equal to the Hawking result up to a possibly different constant factor. The simplest solution of the field equations with rho = 1 / (8 pi r^2) is the so called holographic solution, short "holostar". It has an interior string equation of state. The strings are densely packed, explaining why the solution does not collapse to a singularity. The holographic solution has been shown to be a very accurate model for the universe as we see it today in Ref[7]. The factor relating the holostar's temperature at infinity to the Hawking temperature can be expressed in terms the holostar's interior (local) radiation temperature and its (local) matter-density, allowing an experimental verification of the Hawking temperature law. Using the recent experimental data for the CMBR-temperature and the total matter-density in the universe measured by WMAP, the Hawking formula is verified to an accuracy of 1%.