The PP–v criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter （AdS） spacetime are studied. The cosmological constant is treat...The PP–v criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter （AdS） spacetime are studied. The cosmological constant is treated as a dynamical pressure and its conjugate quantity is thermodynamic volume of the noncommutative geometry-inspired Schwarzschild-AdS black hole. The noncommutative parameter is also treated as a variable, and as a consequence, a new thermodynamic quantity VθVθ conjugate to Pθ=-（8πθ）^-1 has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation. We find that the P–v criticality and the small black hole/large black hole phase transition appear for the noncommutative Schwarzschild-AdS black hole. Numerical calculations indicate that the noncommutative parameter θ affects the phase transition as well as the critical temperature Tc, horizon radius r＋cr＋c and pressure Pc. However, the critical ratio Pcr＋c/Tc is universal （independent of θ）, which is very similar to the result in the van de Waals liquid–gas system, but different from that in the noncommutative geometry-inspired Reissner–Nordstr？m-AdS black hole, where the critical ratio is no longer universal.展开更多
In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmol...In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmological constant.We prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes(the trivial black hole solutions of the EKG system for whichφ=0 identically)are asymptotically stable.Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes,with the metric on the black hole exterior approaching a SchwarzschildAdS spacetime.Bootstrap argument on the black hole exterior,with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis.Both integrated decay and pointwise decay estimates are obtained.展开更多
基金Supported by the Natural Science Foundation of Education Department of the Shaannxi Province under Grant No 15JK1077the Doctorial Scientific Research Starting Fund of Shaannxi University of Science and Technology under Grant No BJ12-02
文摘The PP–v criticality and phase transition in the extended phase space of a noncommutative geometry-inspired Schwarzschild black hole in anti-de Sitter （AdS） spacetime are studied. The cosmological constant is treated as a dynamical pressure and its conjugate quantity is thermodynamic volume of the noncommutative geometry-inspired Schwarzschild-AdS black hole. The noncommutative parameter is also treated as a variable, and as a consequence, a new thermodynamic quantity VθVθ conjugate to Pθ=-（8πθ）^-1 has to be defined further, which is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation. We find that the P–v criticality and the small black hole/large black hole phase transition appear for the noncommutative Schwarzschild-AdS black hole. Numerical calculations indicate that the noncommutative parameter θ affects the phase transition as well as the critical temperature Tc, horizon radius r＋cr＋c and pressure Pc. However, the critical ratio Pcr＋c/Tc is universal （independent of θ）, which is very similar to the result in the van de Waals liquid–gas system, but different from that in the noncommutative geometry-inspired Reissner–Nordstr？m-AdS black hole, where the critical ratio is no longer universal.
文摘In this paper,we study the global behavior of solutions to the spherically symmetric(it means that the problem is 2+2 framework)coupled Nonlinear-Einstein-Klein-Gordon(NLEKG)system in the presence of a negative cosmological constant.We prove the well posedness of the NLEKG system in the Schwarzschild-AdS spacetimes and that the Schwarzschild-AdS spacetimes(the trivial black hole solutions of the EKG system for whichφ=0 identically)are asymptotically stable.Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes,with the metric on the black hole exterior approaching a SchwarzschildAdS spacetime.Bootstrap argument on the black hole exterior,with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis.Both integrated decay and pointwise decay estimates are obtained.
