We deal with the thermodynamic properties of the Bardeen regular black hole with reference to their respective horizons.It is argued here that the expression of the heat capacity at horizons is positive in one paramet...We deal with the thermodynamic properties of the Bardeen regular black hole with reference to their respective horizons.It is argued here that the expression of the heat capacity at horizons is positive in one parameter region and negative in the other,and between them the heat capacity diverges where the black hole undergoes the second-order phase transition.展开更多
The objective of this paper is to investigate the thermodynamic properties of Mc Vittie universe. It turns out that the Einstein field equations are obtained by using Clausius equation near apparent horizon of Mc Vitt...The objective of this paper is to investigate the thermodynamic properties of Mc Vittie universe. It turns out that the Einstein field equations are obtained by using Clausius equation near apparent horizon of Mc Vittie universe.For the existence of horizons, different conditions in terms of Mc Vittie parameters are discussed. Diverse cases of surface gravity are studied and conditions in terms of parameters for which surface gravity is positive, zero and negative are obtained and analyzed. It is shown that the generalized second law(GSL) holds near the apparent horizon if˙RA > 0.Our results show that the heat capacity, CP, of the universe is always negative for matter dominated phase having P = 0. On the other hand, when P > 0, the heat capacity CP > 0 provided RA >√2/√8πP- 3H2 and negative otherwise. Furthermore, when P > 0, the temperature of the universe is minimum at Rmin =√2/√8πP- 3H2 while its heat capacity diverges.展开更多
In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V ...In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.展开更多
We construct various cases for validity of the generalized second law(GSL)of thermodynamics by assuming the logarithmic correction to the horizon entropy of an evolving wormhole.It is shown that the GSL is always resp...We construct various cases for validity of the generalized second law(GSL)of thermodynamics by assuming the logarithmic correction to the horizon entropy of an evolving wormhole.It is shown that the GSL is always respected forα0≤0,whereas forα0>0 the GSL is respected only ifπr2A+/ℏ<α.展开更多
There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon ca...There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics.Using the idea of foliation,we develop a simpler procedure toobtain such results.We considerγ=constant slices,for the Schwarzschild and Reissner-Nordstrom black hole spacetimes.The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces.As expected,it is found that the field equations of the induced metric corresponding to the horizon can be written as afirst law of black hole thermodynamics.It is to be mentioned here that our procedure is much easier,to obtain such results,as here one has to essentially deal with(n-1)-dimensional induced metric for an n-dimensional spacetime.展开更多
基金Supported by the Research Consultancy Institute(RCI),Effat University,Jeddah,Kingdom of Saudi Arabia.
文摘We deal with the thermodynamic properties of the Bardeen regular black hole with reference to their respective horizons.It is argued here that the expression of the heat capacity at horizons is positive in one parameter region and negative in the other,and between them the heat capacity diverges where the black hole undergoes the second-order phase transition.
文摘The objective of this paper is to investigate the thermodynamic properties of Mc Vittie universe. It turns out that the Einstein field equations are obtained by using Clausius equation near apparent horizon of Mc Vittie universe.For the existence of horizons, different conditions in terms of Mc Vittie parameters are discussed. Diverse cases of surface gravity are studied and conditions in terms of parameters for which surface gravity is positive, zero and negative are obtained and analyzed. It is shown that the generalized second law(GSL) holds near the apparent horizon if˙RA > 0.Our results show that the heat capacity, CP, of the universe is always negative for matter dominated phase having P = 0. On the other hand, when P > 0, the heat capacity CP > 0 provided RA >√2/√8πP- 3H2 and negative otherwise. Furthermore, when P > 0, the temperature of the universe is minimum at Rmin =√2/√8πP- 3H2 while its heat capacity diverges.
文摘In the paper [M. Akbar and R.G. Cai, Commun. Theor. Phys. 45 （2006） 95], a complete classification is provided with at least one component of the vector field V is zero. In this paper, I consider the vector field V with all non-zero components and the static space times with maximal symmetric transverse spaces are classified according to their Ricci collineations. These are investigated for non-degenerate Ricci tensor det R ≠0. It turns out that the only collineations admitted by these spaces can be ten, seven, six or four. It also covers our previous results as a spacial case. Some new metrics admitting proper Ricci collineations are also investigated.
文摘We construct various cases for validity of the generalized second law(GSL)of thermodynamics by assuming the logarithmic correction to the horizon entropy of an evolving wormhole.It is shown that the GSL is always respected forα0≤0,whereas forα0>0 the GSL is respected only ifπr2A+/ℏ<α.
文摘There has been lots of interest in exploring the thermodynamic properties at the horizon of a black hole spacetime.It has been shown earlier that for different spacetimes,the Einstein field equations at the horizon can be expressed as the first law of black hole thermodynamics.Using the idea of foliation,we develop a simpler procedure toobtain such results.We considerγ=constant slices,for the Schwarzschild and Reissner-Nordstrom black hole spacetimes.The Einstein field equations for the induced 3-dimensional metrics of the hypersurfaces are expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces.As expected,it is found that the field equations of the induced metric corresponding to the horizon can be written as afirst law of black hole thermodynamics.It is to be mentioned here that our procedure is much easier,to obtain such results,as here one has to essentially deal with(n-1)-dimensional induced metric for an n-dimensional spacetime.
