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Andrew M. Steane

Print publication date: 2016

Print ISBN-13: 9780198788560

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780198788560.001.0001

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Self-gravitation and negative heat capacity

Self-gravitation and negative heat capacity

Chapter:
(p.375) 26 Self-gravitation and negative heat capacity
Source:
Thermodynamics
Author(s):

Andrew M. Steane

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198788560.003.0026

The basic thermodynamics of self-gravitating systems is explained. First the virial theorem is introduced, and it is shown that a gravitating cloud bound by its own gravity is unstable, and each region of such a cloud has a negative heat capacity. The Jean’s length is obtained by a simple argument. Black holes and Hawking radiation are discussed. The area theorem and Penrose process are sketched, and the formulae for temperature and entropy of a black hole are given. Black hole evaporation is described.

Keywords:   Self-gravitation, negative heat capacity, virial theorem, Jean’s length, area theorem, Penrose process, Hawking radiation, black hole temperature, black hole entropy

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