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Title: Stable configuration of ultrarelativistic material spheres: The solution for an extremely hot gas

Abstract

During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a positive-valued energy to balance the decrease. We derive the internal-state properties of the ideal gas situated in an extremely strong, ultrarelativistic gravitational field and suggest the application of our result to a compact object with a radius that is slightly larger than or equal to the Schwarzschild gravitational radius. On the surface of the object, we find that the extreme attractivity of the gravity is accompanied with an extremely high internal heat energy. This internal energy implies a correspondingly high pressure, the gradient of which has such a behavior that it can compete with the gravity. In more detail, we find the equation of state in the case when the magnitude of the potential-type energy of constituting gas particles is much larger than their rest energy. This equation appears to be identical with the general relativity condition of the equilibrium between the gravity and pressure gradient. The consequences of the identity are discussed.

Authors:
 [1]
  1. Astronomical Institute of the Slovak Academy of Sciences, 05960 Tatranska Lomnica (Slovakia)
Publication Date:
OSTI Identifier:
21316238
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 80; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.80.024015; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BALANCES; CONFIGURATION; ENERGY CONSERVATION; EQUATIONS OF STATE; EQUILIBRIUM; GENERAL RELATIVITY THEORY; GRAVITATION; GRAVITATIONAL FIELDS; MATHEMATICAL SOLUTIONS; POTENTIAL ENERGY; POTENTIALS; PRESSURE GRADIENTS; RELATIVISTIC RANGE; SURFACES

Citation Formats

Neslusan, Lubos. Stable configuration of ultrarelativistic material spheres: The solution for an extremely hot gas. United States: N. p., 2009. Web. doi:10.1103/PHYSREVD.80.024015.
Neslusan, Lubos. Stable configuration of ultrarelativistic material spheres: The solution for an extremely hot gas. United States. https://doi.org/10.1103/PHYSREVD.80.024015
Neslusan, Lubos. 2009. "Stable configuration of ultrarelativistic material spheres: The solution for an extremely hot gas". United States. https://doi.org/10.1103/PHYSREVD.80.024015.
@article{osti_21316238,
title = {Stable configuration of ultrarelativistic material spheres: The solution for an extremely hot gas},
author = {Neslusan, Lubos},
abstractNote = {During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a positive-valued energy to balance the decrease. We derive the internal-state properties of the ideal gas situated in an extremely strong, ultrarelativistic gravitational field and suggest the application of our result to a compact object with a radius that is slightly larger than or equal to the Schwarzschild gravitational radius. On the surface of the object, we find that the extreme attractivity of the gravity is accompanied with an extremely high internal heat energy. This internal energy implies a correspondingly high pressure, the gradient of which has such a behavior that it can compete with the gravity. In more detail, we find the equation of state in the case when the magnitude of the potential-type energy of constituting gas particles is much larger than their rest energy. This equation appears to be identical with the general relativity condition of the equilibrium between the gravity and pressure gradient. The consequences of the identity are discussed.},
doi = {10.1103/PHYSREVD.80.024015},
url = {https://www.osti.gov/biblio/21316238}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 2,
volume = 80,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 2009},
month = {Wed Jul 15 00:00:00 EDT 2009}
}