Abstract
We try to find out the nature of different thermodynamical parameters for a black hole solution drawn for a special case in Einstein-Scalar-Yang-Mills gravity. Whether a phase transition occurs for the solution or not is a matter of interest. The nature of the phase transition is tried to understand. Ruppeiner metric and the corresponding Ricci scalar is constructed. It is noticed that the metric is not of positive Ricci for all the parametric values and there exist(s) point(s) in thermodynamic space where the Ricci scalar becomes zero.
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Notes
Using quantum field theory Hawking was able to show that there is radiation from the BH similar to black body radiation, lately known as Hawking Radiation.
Observing the behavior of the thermodynamic free energy with respect to other thermodynamical quantities, the lowest derivative of the free energy, which is discontinuous will be the label of the phase transition. Though it must be remembered that this method has been found to be an inaccurate method of classifying phase transitions.
Afterwards we will verify it in F vs T H graphs.
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Acknowledgements
Author thanks ISRO grant “ISRO/RES/2/367/10-11” and CSIR project “Dark Energy Models and Accelerating Universe” (No. 03(1206)/12/EMR-II) for providing Research Associate Fellowship and Indian Institute of Science, Bangalore, India for different research facilities where a part of this work had been done.
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Biswas, R. Einstein-scalar-Yang-Mills black holes: a thermodynamical approach. Astrophys Space Sci 348, 459–465 (2013). https://doi.org/10.1007/s10509-013-1588-x
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DOI: https://doi.org/10.1007/s10509-013-1588-x