On Thermodynamical Relation Between Rotating Charged BTZ Black Holes and Effective String Theory

In this paper we study the first law of thermodynamics for the （2＋1）-dimensional rotating charged BTZ black hole considering a pair of thermodynamical systems constructed with the two horizons of this solution. We show that these two systems are similar to the right and left movers of string theory and that the temperature associated with the black hole is the harmonic mean of the temperatures associated with these two systems.

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior work of Chen and Jing(S.Chen and J.Jing,JCAP,10:002(2015))for a Schwarzschild black hole to a Kiselev black hole.For this purpose,the equation of motion for the photons coupled to the Weyl tensor,null geodesic,and equation of photon sphere in a Kiselev black hole spacetime have been formulated.It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor,but also on the polarization direction of the photons.There is a critical value of the coupling parameter,α,for the existence of the marginally circular photon orbit outside the event horizon,which depends on the parameters of the black hole and the polarization direction of the photons.Further,the polarization directions of the coupled photons and the coupling parameter,α;both modify the features of the photon sphere,angle of deflection,and functions(^ˉa and^ˉb)owing to the strong gravitational lensing in the Kiselev black hole spacetime.In addition to this,the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.

Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions

Understanding the dynamic process of black hole thermodynamic phase transitions at a triple point is a huge challenge. In this paper, we conduct the first investigation of dynamic phase behavior at a black hole triple point. By numerically solving the Smoluchowski equation near the triple point for a six-dimensional charged Gauss-Bonnet anti-de Sitter black hole, we report that initial small, intermediate, or large black holes can transit to the other two coexistent phases at the triple point, indicating that thermodynamic phase transitions can indeed occur dynamically. More significantly, we observe characteristic weak and strong oscillatory behavior in this dynamic process, which can be understood from an investigation of the rate of first passage from one phase to another. Our results further an understanding of the dynamic process of black hole thermodynamic phase transitions.

Collapsing scenario for the k-essence emergent generalized Vaidya spacetime in the context of massive gravity's rainbow

In this study,we investigate the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow.For this study,we consider that the background metric is Vaidya spacetime in massive gravity's rainbow.We show that the k-essence emergent gravity metric closely resembles the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse,where we consider the k-essence scalar field as a function solely of the advanced or the retarded time.The k-essence emergent Vaidya massive gravity rainbow mass function is also different.This new type k-essence emergent Vaidya massive gravity rainbow metric satisfies the required energy conditions.The existence of a locally naked central singularity and the strength and strongness of the singularities for the rainbow deformations of the k-essence emergent Vaidya massive gravity metric are the interesting outcomes of the present work.