This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with ...This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with Chaichian, Tureanu, Sun, Wang, Xie and Zhang.展开更多
We construct a family of d-dimensional Reissner–Nordstrom-AdS black holes inspired by noncommutative geometry. The density distribution of the gravitational source is determined by the dimension of space, the minimum...We construct a family of d-dimensional Reissner–Nordstrom-AdS black holes inspired by noncommutative geometry. The density distribution of the gravitational source is determined by the dimension of space, the minimum length of spacetime l, and other parameters（e.g., n relating to the central matter density）. The curvature of the center and some thermodynamic properties of these black holes are investigated. We find that the center of the source is nonsingular for n 0（under certain conditions it is also nonsingular for-2 n 〈 0）, and the properties at the event horizon, including the Hawking temperature, entropy, and heat capacity, are regular for n 〉-2. Due to the presence of l, there is an exponentially small correction to the usual entropy.展开更多
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
基金supported by National Natural Science Foundation of China (Grant Nos. 10725105, 10731080, 11021091)and Chinese Academy of Sciences
文摘This short paper is based on the talk on the conference Operator Algebras and Related Topics held on July 23-27, 2010, Beijing. The author surveys recent developments of the noncommutative gravity in joint works with Chaichian, Tureanu, Sun, Wang, Xie and Zhang.
文摘We construct a family of d-dimensional Reissner–Nordstrom-AdS black holes inspired by noncommutative geometry. The density distribution of the gravitational source is determined by the dimension of space, the minimum length of spacetime l, and other parameters（e.g., n relating to the central matter density）. The curvature of the center and some thermodynamic properties of these black holes are investigated. We find that the center of the source is nonsingular for n 0（under certain conditions it is also nonsingular for-2 n 〈 0）, and the properties at the event horizon, including the Hawking temperature, entropy, and heat capacity, are regular for n 〉-2. Due to the presence of l, there is an exponentially small correction to the usual entropy.
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.
