In this study,we observe that,in the presence of the string cloud parameter a and the quintessence parameterγ,with the equation of state parameter,ω_(q) = -2/3the radius of the shadow of the Schwarzschild black hole...In this study,we observe that,in the presence of the string cloud parameter a and the quintessence parameterγ,with the equation of state parameter,ω_(q) = -2/3the radius of the shadow of the Schwarzschild black hole increases as compared with that in the pure Schwarzschild black hole case.The existence of both quintessential dark energy and the cloud of strings increases the shadow size;hence,the strength of the gravitational field around the Schwarzschild black hole increases.Using the data collected by the Event Horizon Telescope(EHT)collaboration for M87*and Sgr A*,we obtain upper bounds on the values of a andγ.Further,we see the effects of a andγon the rate of emission energy for the Schwarzschild black hole.We notice that the rate of emission energy is higher in the presence of clouds of strings and quintessence.Moreover,we study the weak deflection angle using the Gauss-Bonnet theorem.We show the influence of a andγon the weak deflection angle.We notice that both a andγincrease the deflection angleα.展开更多
By looking at the Lovelock theorem one can infer that the gravity model given by[1]cannot be applicable for all types of 4D Einstein–Gauss–Bonnet(EGB)curved space-time.The reason for this is that in 4D space-time,th...By looking at the Lovelock theorem one can infer that the gravity model given by[1]cannot be applicable for all types of 4D Einstein–Gauss–Bonnet(EGB)curved space-time.The reason for this is that in 4D space-time,the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics.Hence,the authors of[2]presented an alternative consistent EGB gravity model instead of[1]by applying a break-of-diffeomorphism property.In this work,we use the alternative model to produce a de Sitter(dS)/Anti-de Sitter(AdS)black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings.Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the d S sector but not in the Ad S background.From this,we infer that the black hole participates in the small-to-large black hole phase transition in the dS background,while it exhibits a Hawking–Page phase transition in the AdS background.In the latter case,an evaporating black hole eventually reaches an AdS vacuum space because of its instability.展开更多
As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzsehild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar ...As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzsehild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.展开更多
In this paper, we investigate the basic equations of the motion for relativistic strings on the equatorial plane in the Schwarzsehild space-time, discuss smooth solutions of the motion equations for closed strings, an...In this paper, we investigate the basic equations of the motion for relativistic strings on the equatorial plane in the Schwarzsehild space-time, discuss smooth solutions of the motion equations for closed strings, and obtain some interesting physical results.展开更多
基金the Grant No.ZC304022919 to support his Postdoctoral Fellowship at Zhejiang Normal Universitythe support of Inha University in Tashkent and research work has been supported by the Visitor Research Fellowship at Zhejiang Normal Universitysupported by Research Grant FZ-20200929344,F-FA-2021-510 and F-FA-2021-432 of the Uzbekistan Ministry for Innovative Development。
文摘In this study,we observe that,in the presence of the string cloud parameter a and the quintessence parameterγ,with the equation of state parameter,ω_(q) = -2/3the radius of the shadow of the Schwarzschild black hole increases as compared with that in the pure Schwarzschild black hole case.The existence of both quintessential dark energy and the cloud of strings increases the shadow size;hence,the strength of the gravitational field around the Schwarzschild black hole increases.Using the data collected by the Event Horizon Telescope(EHT)collaboration for M87*and Sgr A*,we obtain upper bounds on the values of a andγ.Further,we see the effects of a andγon the rate of emission energy for the Schwarzschild black hole.We notice that the rate of emission energy is higher in the presence of clouds of strings and quintessence.Moreover,we study the weak deflection angle using the Gauss-Bonnet theorem.We show the influence of a andγon the weak deflection angle.We notice that both a andγincrease the deflection angleα.
文摘By looking at the Lovelock theorem one can infer that the gravity model given by[1]cannot be applicable for all types of 4D Einstein–Gauss–Bonnet(EGB)curved space-time.The reason for this is that in 4D space-time,the Gauss–Bonnet invariant is a total derivative and hence it does not contribute to gravitational dynamics.Hence,the authors of[2]presented an alternative consistent EGB gravity model instead of[1]by applying a break-of-diffeomorphism property.In this work,we use the alternative model to produce a de Sitter(dS)/Anti-de Sitter(AdS)black hole metric and then investigate its thermodynamic behavior in the presence of a cloud of Nambu–Goto strings.Mathematical derivations show that the resulting diagrams of pressure vs specific volume at a constant temperature are similar to that for a van der Waals gas/fluid in an ordinary thermodynamic system in the d S sector but not in the Ad S background.From this,we infer that the black hole participates in the small-to-large black hole phase transition in the dS background,while it exhibits a Hawking–Page phase transition in the AdS background.In the latter case,an evaporating black hole eventually reaches an AdS vacuum space because of its instability.
基金National Natural Science Foundation of China under Grant No.10573003the National Basic Research Program of China under Grant No.2003CB716300
文摘As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzsehild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.
基金Supported by the National Natural Science Foundation of China under Grant No. 10971190the Qiu-Shi Professor Fellowship from Zhejiang University,China
文摘In this paper, we investigate the basic equations of the motion for relativistic strings on the equatorial plane in the Schwarzsehild space-time, discuss smooth solutions of the motion equations for closed strings, and obtain some interesting physical results.
