Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity

Abstract

In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase transition in which case a locally stable small black hole tunnels into a globally stable large black hole as well as the standard Hawking-Page phase transition from a hot flat space to a black hole.

24 pages, 9 figures, references added, version to appear in EPJC

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• KG-particles in a cosmic string rainbow gravity spacetime in mixed magnetic fields
• Dark Energy Star in Gravity's Rainbow
• Stable three-dimensional (un)charged AdS gravastars in gravity's rainbow
• Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity
• Quantum corrections to the thermodynamics of rotating charged BTZ black hole in gravity's rainbow
• Geometrothermodynamic Analysis and $P$-$V$ criticality of Higher Dimensional Charged Gauss-Bonnet Black Holes With First Order Entropy Correction
• Quantum corrections to the thermodynamics and phase transition of a black hole surrounded by a cavity in the extended phase space
• Three-dimensional energy-dependent $C$-metric: black hole solutions
• Schwarzschild black hole surrounded by a cavity and phase transition in the non-commutative gauge theory of gravity
• Exploring black hole mechanics in cotangent bundle geometries
• Thermodynamics and Phase transition of Schwarzschild black hole in Gravity's Rainbow