Holostar thermodynamics

Abstract

The holostar is an exact solution of the Einstein field equations with a singularity free interior matter-density rho = 1 / (8 pi r^2) and a boundary membrane consisting out of tangential pressure. Although the interior matter has on overall string equation of state, part of the matter can be interpreted in terms of particles. A simple thermodynamic model is presented, treating the matter as an ideal gas of (ultrarelativistic) fermions and bosons. The number of ultra-relativistic particles within a holostar is proportional its surface-area, indicating that the holographic principle is valid in classical GR for self gravitating objects of any size. Using the grand canonical formalism we show, that the interior temperature is given by T \propto / \sqrt{r}. With a surface redshift z \propto \sqrt{r} the holostar's temperature at infinity is equal to the Hawking result, up to a constant factor. The factor depends on the number of particle degrees of freedom at the Planck energy, which is estimated as f ~ 7000. The holostar's total thermodynamic entropy is proportional to the area of its boundary membrane. The ultra-relativistic fermions in the interior space-time must acquire a non-zero chemical potential, which acts as a natural source for a profound matter-antimatter asymmetry at high temperatures. The local values of the interior temperature and matter-density are related to the holostar's temperature at infinity, enabling a "measurement" of the Hawking temperature from the interior space-time. Using the experimental values for the CMBR-temperature and the total matter-density of the universe determined by WMAP the Hawking result is verified to an accuracy of 1%.ior particles. Some properties expected from a rotating holostar are discussed briefly.

64 pages, 1 figure; revised v2: references and typos corrected, two minor errors on pages 34 and 38 of v1 corrected; v3: expanded thermodynamic model to include anti-fermions, added section on matter-antimatter asymmetry, replaced some numerical results with explicit formula

References in corpus (5)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Discreteness of area and volume in quantum gravity
• The holographic solution - Why general relativity must be understood in terms of strings
• Are we living in a string-dominated universe?
• On the origin of the matter-antimatter asymmetry in self-gravitating systems at ultra-high temperatures

Cited by in corpus (7)

• Charged Gravastar in a Dark Energy Universe
• The holographic solution - Why general relativity must be understood in terms of strings
• On the origin of the matter-antimatter asymmetry in self-gravitating systems at ultra-high temperatures
• Are we living in a string-dominated universe?
• Compact anisotropic stars with membrane - a new class of exact solutions to the Einstein field equations
• On the thermodynamic origin of the Hawking entropy and a measurement of the Hawking temperature
• The holostar - a self-consistent model for a compact self-gravitating object