A modified thermodynamics method to generate exact solutions of the Einstein equations

Abstract

We modify the method to generate the exact solutions of the Einstein equations basing on the laws of thermodynamics. Firstly, the Komar mass is used to take the place of the Misner-Sharp energy which is used in the original methods, and then several exact solutions of Einstein equations are obtained, including the black hole solution which surrounded by quintessence. Moreover, the geometry surface gravity defined by Komar mass is obtained. Secondly, we use both the Komar mass and the ADM mass to modify such method, and the similar results are obtained. Moreover, with some generalize added to the definition of the ADM mass, our method can be generalized to global monopole sapcetime.

arXiv commentThis article raises a modified method to generate exact solutions of the Einstein equations according to thermodynamical relationships and some thermodynamical properties of the space-time with a global monopole charge is discussed

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• Thermodynamics of Spacetime: The Einstein Equation of State
• The Dynamics of General Relativity
• Quintessence and black holes
• Unified first law of black-hole dynamics and relativistic thermodynamics
• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Shear viscosity and instability from third order Lovelock gravity
• Misner-Sharp Mass in $N$-dimensional $f(R)$ Gravity
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Cited by in corpus (5)

• Thermodynamics and Shadows of GUP-corrected Black Holes with Topological Defects in Bumblebee Gravity
• Generalized Vaidya Solutions and Misner-Sharp mass for $n$-dimensional massive gravity
• The global monopole spacetime and its topological charge
• Non perturbative spherical gravitational waves
• Quasilocal Smarr relations for static black holes