Glassy phase transition and stability in black holes
S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, India
2 Narasinha Dutt College, 129, Belilious Road, Howrah, 711101, India
Revised: 25 August 2010
Published online: 6 October 2010
Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of a correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest’s scheme we further prove that this is a glassy phase transition with a Prigogine–Defay ratio close to 3. This value is well within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.
© Springer-Verlag / Società Italiana di Fisica, 2010