A note on circular geodesics and phase transitions of black holes

Abstract

The circular motion of charged test particles in the gravitational field of a Reissner-Nordström black hole in Anti de Sitter space-time is investigated, using a set of independent parameters, such as charge Q, mass M and cosmological constant Λ = −3/l 2 of the space-time, and charge to mass ratio = q/m of the test particles. Classification of different spatial regions where circular motion is allowed, is presented, showing in particular, the presence of orbits at special limiting values, M = 4/ √ 6Q and l = 6Q. Thermodynamically, these values are known to occur when the black hole is on the verge of a second order phase transition, there by, giving an interesting connection between thermodynamics and geodesics of black holes. We also comment on the possibility of such a connection for black holes in flat spacetime in a box. 1 chandrasekhar@iitbbs.ac.in 2 sm32@iitbbs.ac.in 1 arXiv:1805.05088v3 [hep-th]

Probing correlation between photon orbits and phase structure of charged AdS black hole in massive gravity background

“…In this sense, a variety of technics have born to consolidate this analogy, such as thermodynamical geometry [30,31], quasi-normal modes [32,33] and non-local observables [34,35]. More recently, many endeavors have been performed to achieve connection between the thermodynamic behaviors and the geodesics of test particles [36][37][38]. The purpose of the present paper is to study the unstable circular orbits of photons in the vicinity of charged black holes in asymptotically AdS space in the theory of massive gravity.…”

Null geodesics, quasinormal modes, and thermodynamic phase transition for charged black holes in asymptotically flat and dS spacetimes *

“…More interestingly, there exists a universal critical exponent of for the changes of the radius and the minimum impact parameter near the critical point, that is also independent of the dimension of the spacetime [32]. Such a study was also generalized to a rotating Kerr-AdS black hole [33]. In addition, another new issue was examined, and the result shows that the temperature and pressure corresponding to the extremal points of the radius or the angular momentum of the light rings exactly agree with that of the metastable curves from the thermodynamic side.…”

“…Moreover, we conducted a study that explored the relation between the photon sphere (light ring) and the Van der Waals-type phase transition [31] for a charged or rotating black hole in anti-dS (AdS) spacetime [32,33]. For a charged AdS black hole, non-monotonic behaviors of the photon sphere radius and the minimum impact parameter when the pressure and temperature are below their critical values were found, and the behaviors disappear when the parameters exceed their critical values [32].…”

“…Our recent work [32,33] showed the existence of a relation between the black hole's null geodesics and the thermodynamic phase transition of a liquid/gas type in AdS spacetime. Motivated by this, we expected to apply it to a charged RN black hole to investigate the relation between null geodesics and the Davies point.…”