A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli ...A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli （BTZ） black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS＋ Pr dA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 41πa is the entropy and T =κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS ＋ PrdA ＋Ω＋dJ, where Ω＋ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.展开更多
It is shown that the differential form of Friedmann equations of Friedman-Robertson-Walker （FRW） universe can be recast as a similar form of the first law ThdSh = dE＋ WdV of thermodynamics at the apparent horizon o...It is shown that the differential form of Friedmann equations of Friedman-Robertson-Walker （FRW） universe can be recast as a similar form of the first law ThdSh = dE＋ WdV of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that by employing the general expression of temperature Th=｜k｜/2π=1/2π~rA（1-2~rA/2H^rA）associated with the apparent horizon of an FRW universe and assumed that the temperature Tm of the energy inside the apparent horizon is proportional to the horizon temperature Tm=bTh, we are able to show that the generalized second law of thermodynamics holds in the Einstein gravity provided Th-Tm/~rA≤（ρ＋~P）.展开更多
It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown tha...It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature Th =｜κ｜/2π= 1/2πτA （1-τA/2HτA） associated with the apparent horizon of a Friedman Robertson-Walker （FRW） universe and assuming Tm = bTh, we are able to construct conditions for which the generalized second law holds in Gauss Bonnet and Lovelock gravities, where Tm and Th are the temperatures of the source and the horizon respectively.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10325525 and 90403029, and Chinese Academy of Sciences.
文摘A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In the case of static metric of Banados-Teitelboim-Zanelli （BTZ） black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS＋ Pr dA, where E = M is the mass of BTZ black hole, dA is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, Pr is the radial pressure provided by the source of Einstein equations, S = 41πa is the entropy and T =κ/2π is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole, showing that it is also possible to interpret the field equation near horizon as a thermodynamic identity dE = TdS ＋ PrdA ＋Ω＋dJ, where Ω＋ is the angular velocity and J is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near the horizon.
文摘It is shown that the differential form of Friedmann equations of Friedman-Robertson-Walker （FRW） universe can be recast as a similar form of the first law ThdSh = dE＋ WdV of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that by employing the general expression of temperature Th=｜k｜/2π=1/2π~rA（1-2~rA/2H^rA）associated with the apparent horizon of an FRW universe and assumed that the temperature Tm of the energy inside the apparent horizon is proportional to the horizon temperature Tm=bTh, we are able to show that the generalized second law of thermodynamics holds in the Einstein gravity provided Th-Tm/~rA≤（ρ＋~P）.
文摘It has been shown [Chin. Phys. Lett.25 （2008） 4199] that the generalized second law of thermodynamics holds in Einstein gravity. Here we extend this procedure for Gauss-Bonnet and Lovelock gravities. It is shown that by employing the general expression for temperature Th =｜κ｜/2π= 1/2πτA （1-τA/2HτA） associated with the apparent horizon of a Friedman Robertson-Walker （FRW） universe and assuming Tm = bTh, we are able to construct conditions for which the generalized second law holds in Gauss Bonnet and Lovelock gravities, where Tm and Th are the temperatures of the source and the horizon respectively.
