NDLI: Classical and quantum Reissner-Nordström black hole thermodynamics and first order phase transition

Content Provider	Springer Nature Link
Author	Ghaffarnejad, Hossein
Copyright Year	2015
Abstract	First we consider classical Reissner-Nordström black hole (CRNBH) metric which is obtained by solving Einstein-Maxwell metric equation for a point electric charge $e$ inside of a spherical static body with mass $M$ . It has 2 interior and exterior horizons. Using Bekenstein-Hawking entropy theorem we calculate interior and exterior entropy, temperature, Gibbs free energy and heat capacity at constant electric charge. We calculate first derivative of the Gibbs free energy with respect to temperature which become a singular function having a singularity at critical point $M_{c}=\frac{2\|e\|}{\sqrt{3}}$ with corresponding temperature $T_{c}=\frac{1}{24\pi\sqrt{3}\|e\|}$ . Hence we claim first order phase transition is happened there. Temperature same as Gibbs free energy takes absolutely positive (negative) values on the exterior (interior) horizon. The Gibbs free energy takes two different positive values synchronously for $0< T< T_{c}$ but not for negative values which means the system is made from two subsystem. For negative temperatures entropy reaches to zero value at $T\to-\infty$ and so takes Bose-Einstein condensation single state. Entropy increases monotonically in case $0< T< T_{c}$ . Regarding results of the work presented at Wang and Huang (Phys. Rev. D 63:124014, 2001) we calculate again the mentioned thermodynamical variables for remnant stable final state of evaporating quantum Reissner-Nordström black hole (QRNBH) and obtained results same as one in case of the CRNBH. Finally, we solve mass loss equation of QRNBH against advance Eddington-Finkelstein time coordinate and derive luminosity function. We obtain switching off of QRNBH evaporation before than the mass completely vanishes. It reaches to a could Lukewarm type of RN black hole which its final remnant mass is $m_{final}=\|e\|$ in geometrical units. Its temperature and luminosity vanish but not in Schwarzschild case of evaporation. Our calculations can be take some acceptable statements about information loss paradox (ILP).
Starting Page	1
Ending Page	13
Page Count	13
File Format	PDF
ISSN	0004640X
Journal	Astrophysics and Space Science
Volume Number	361
Issue Number	1
e-ISSN	1572946X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-12-04
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Reissner-Nordström black holes Negative temperatures Heat capacity Phase transition Dark matter Gibbs free energy Liquid helium Bose-Einstein condensation Quantum fields Backreaction Luminosity Mass loss Information loss paradox Astrophysics and Astroparticles Astronomy, Observations and Techniques Cosmology Extraterrestrial Physics, Space Sciences Astrobiology
Content Type	Text
Resource Type	Article
Subject	Astronomy and Astrophysics Space and Planetary Science

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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