We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the ...We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the charged black hole by a new Tortoise coordinate transformation. Taking the reaction of the radiation of the particle to the spacetime into consideration, we not only derive the radiation spectrum that satisfies the unitary principle in quantum mechanics but also show that the contribution of ingoing particles is equal to the one of outgoing particles on the similar chemical potential term in radiation spectrum caused by charged particles.展开更多
After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the ...After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.展开更多
Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,t...Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.展开更多
In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters...In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.展开更多
Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition ...Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using Maxwell's equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T<T_(c))is related to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.展开更多
We study the Hawking radiation of the scalar field in the rotating Gdel black hole in minimal five-dimensional supergravity. We not only derive radiation spectra that satisfy the unitary principle but also obtain the ...We study the Hawking radiation of the scalar field in the rotating Gdel black hole in minimal five-dimensional supergravity. We not only derive radiation spectra that satisfy the unitary principle but also obtain the correction term of Bekenstein-Hawking entropy. The conclusion will help us learn more about the rotating Gdel black hole in minimal five-dimensional supergravity. This provides a greater understanding of the thermal radiation of black holes.展开更多
基金Supported by the Natural Science Foundation of Shanxi Province under Grant No. 2006011012the Shanxi Datong University Doctoral Sustentation Fund
文摘We extend the method that Banerjee and Majhi have used to discuss Hawking radiation. Under the condition that the total energy and electrical charge of spacetime are conserved, we investigate Hawking radiation of the charged black hole by a new Tortoise coordinate transformation. Taking the reaction of the radiation of the particle to the spacetime into consideration, we not only derive the radiation spectrum that satisfies the unitary principle in quantum mechanics but also show that the contribution of ingoing particles is equal to the one of outgoing particles on the similar chemical potential term in radiation spectrum caused by charged particles.
基金Project supported by the Natural Science Foundation of Shanxi Province, China (Grant No. 2006011012)the Shanxi Datong University Doctoral Sustentation Fund, China
文摘After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a fivedimensional Sehwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein-- Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein-Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a twoorder small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.
基金Supported by the Natural Science Foundation of China(11705106,12075143)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472)+2 种基金the Science Technology Plan Project of Datong City,China(2020153)the Science Foundation of Shanxi Datong University(2022Q1,2015Q6,2022Q2)the Teaching Reform Project of Shanxi Datong University(XJG2022234)。
文摘Recently,some meaningful results have been obtained by studying the phase transition,critical exponents,and other thermodynamical properties of different black holes.Especially for the Anti-de Sitter(AdS)black holes,their thermodynamical properties nearby the critical point have attracted considerable attention.However,there exists little work on the thermodynamic properties of the de Sitter(dS)spacetime with black holes.In this paper,based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law,we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence(i.e.,C-dSSQ spacetime).The boundaries of the two-phase coexistence region in both P_(eff)−T_(eff)and T_(eff)−S diagrams are obtained.The coexistent curve and the latent heat of phase transition for this system are also investigated.Furthermore,we analyze the effect of parameters(the state parameterωand the ratio of two horizon radii x=r+/r_(c))on the two-phase coexistence region boundary.The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid(vdw)system,which is determined by the electrical potential at the horizon.These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.
基金the National Natural Science Foundation of China(12075143)。
文摘In this study,we take the mass,electric charge,hair parameter,and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system,and when these state parameters satisfy the first law of thermodynamics,the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained.Then,we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes.It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position.We discuss the influence of the hair parameter and electric charge on the critical point.We also find that the isochoric heat capacity of the spacetime is not zero,which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes,which is zero.Using the Ehrenfest equations,we prove that the critical phase transition is a second order equilibrium phase transition.Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties.Our universe is an asymptotically dS spacetime,and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.
基金the Natural Science Foundation of China(11705106,11475108,12075143)the Natural Science Foundation of Shanxi Province,China(201901D111315)+2 种基金the Natural Science Foundation for Young Scientists of Shanxi Province,China(201901D211441)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(2020L0471,2020L0472)the Science Technology Plan Project of Datong City,China(2020153)。
文摘Understanding the thermodynamic phase transition of black holes can provide a deep insight into the fundamental properties of black hole gravity to establish the theory of quantum gravity.We investigate the condition and latent heat of phase transition for non-linear charged AdS black holes using Maxwell's equal-area law.In addition,we analyze the boundary and curve of the two-phase coexistence area in the expanded phase space.We suggest that the phase transition of the non-linear charged AdS black hole with the fixed temperature(T<T_(c))is related to the electric potential at the horizon,not only to the location of black hole horizon.Recently,the molecular number density was introduced to study the phase transition and microstructure of black holes.On this basis,we discuss the continuous phase transition of a non-linear charged AdS black hole to reveal the potential microstructure of a black hole by introducing the order parameter and using the scalar curvature.
基金Supported by National Natural Science Foundation of China (11075098)Shanxi Natural Science Foundation of China(2006011012)Doctoral Scientific Research Starting Foundation of Shanxi Datong University, China
文摘We study the Hawking radiation of the scalar field in the rotating Gdel black hole in minimal five-dimensional supergravity. We not only derive radiation spectra that satisfy the unitary principle but also obtain the correction term of Bekenstein-Hawking entropy. The conclusion will help us learn more about the rotating Gdel black hole in minimal five-dimensional supergravity. This provides a greater understanding of the thermal radiation of black holes.
