Regular Black Holes with Cosmological Constant

We present a class of regular black holes with cosmological constant A in nonlinear electrodynamics. Instead of usual singularity behind black hole horizon, all fields and curvature invariants are regular everywhere for the regular black holes. Through gauge invariant approach, the linearly dynamical stability of the regular black hole is studied. In odd-parity sector, we find that the A term does not appear in the master equations of perturbations, which shows that the regular black hole is stable under odd-parity perturbations. On the other hand, for the even-parity sector, the master equations are more complicated than the case without the cosmological constant. We obtain the sufficient conditions for stability of the regular black hole. We also investigate the thermodynamic properties of the regular black hole. and find that those thermodynamic quantities do not satisfy the differential form of first law of black hole thermodynamics. The reason for violating the first law is revealed.

Preliminary analyses of the dynamics and thermodynamics of rotating regular black holes

We investigate the dynamic and thermodynamic laws governing rotating regular black holes.By analyzing dynamic properties,i.e.,the interaction between scalar particles and rotating regular black holes,we establish the criteria that determine whether such black holes satisfy the laws of thermodynamics.In addition,we provide the general form of conserved quantities related to rotating regular black holes,including the relevant flows associated with neutral scalar particles.Meanwhile,we reexamine the relationship between the third law of thermodynamics and weak cosmic censorship conjecture for rotating regular black holes.Based on the abovementioned criteria,we discuss the laws of thermodynamics for three models of rotating regular black holes:Rotating Hayward black holes,Kerr black-bounce solutions,and loop quantum gravity black holes.Our findings indicate that none of the three models satisfies the first law of thermodynamics.In particular,the first and third models fail to comply with the three laws of thermodynamics,whereas the second model satisfies only the second and third laws of thermodynamics.Finally,we attempt to rescue the laws of thermodynamics by modifying entropy or extending the phase space.However,the two scenarios cannot ensure the three laws of thermodynamics in the three models,which reveals an unusual property of rotating regular black holes.

Singularities of regular black holes and the monodromy method for asymptotic quasinormal modes

We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits.We find that,for regular black holes with spherical symmetry and a single shape function,the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.

Regular black holes with improved energy conditions and their analogues in fluids

On the premise of the importance of energy conditions for regular black holes,we propose a method to remedy those models that break the dominant energy condition,e.g.,the Bardeen and Hayward black holes.We modify the metrics but ensure their regularity at the same time,so that the weak,null,and dominant energy conditions are satisfied,with the exception of the strong energy condition.Likewise,we prove a no-go theorem for conformally related regular black holes,which states that the four energy conditions can never be met in this class of black holes.In order to seek evidences for distinguishing regular black holes from singular black holes,we resort to analogue gravity and regard it as a tool to mimic realistic regular black holes in a fluid.The equations of state for the fluid are solved via an asymptotic analysis associated with a numerical method,which provides a modus operandi for experimental observations,in particular,the conditions under which one can simulate realistic regular black holes in the fluid.

Superradiance of massive scalar particles around rotating regular black holes

Regular black holes,as part of an important attempt to eliminate the singularities in general relativity,have been of wide concern.Because the superradiance associated with rotating regular black holes plays an indispensable role in black hole physics,we calculate the superradiance related effects,i.e.,the superradiance instability and the energy extraction efficiency,for a scalar particle with a small mass around a rotating regular black hole,where the rotating regular black hole is constructed by the modified Newman-Janis algorithm.We analytically give the eigenfrequency associated with instability and the amplification factor associated with energy extraction.For two specific models,i.e.,the rotating Hayward and Bardeen black holes,we investigate how their regularization parameters affect the growth of instability and the efficiency of energy extraction from the two rotating regular black holes.We find that the regularization parameters give rise to different modes of the superradiance instability and the energy extraction when the rotation parameters vary.There are two modes for the growth of superradiance instability and four modes for the energy extraction.Our results show the diversity of superradiance in the competition between the regularization parameter and the rotation parameter for rotating regular black holes.

Astrophysical observables for regular black holes with sub-Planckian curvature

We investigate the photon sphere and marginally stable circular orbit of massive particles over the re-cently proposed regular black holes with sub-Planckian curvature and a Minkowskian core.We derive the effective potential for geodesic orbits and determine the radius of circular photon orbits,with an analysis of the stability of these orbits.We extend our analysis to the background of a compact massive object(CMO)without a horizon,whose mass is below the lowest bound for the formation of a black hole.For massive particles,marginally stable cir-cular orbits become double-valued in the CMO phase.Through a comparison with Bardeen and Hayward black holes,we also find that the locations of the photon sphere and marginally stable circular orbit in the CMO phase with a Minkowskian core are evidently different from those in the CMO phase with a dS core,which potentially provides a way to distinguish between these two types of black holes by astronomical observation.Finally,we present the ob-servational constraint on the deviation parameter for such regular black holes using observed data from the black hole M87^(*).

Modified regular black holes with time delay and 1-loop quantum correction

We develop the regular black hole solutions by incorporating the 1-loop quantum correction to the Newton potential and a time delay between an observer at the regular center and one at infinity. We define the maximal time delay between the center and the infinity by scanning the mass of black holes such that the sub-Planckian feature of the Kretschmann scalar curvature is preserved during the process of evaporation. We also compare the distinct behavior of the Kretschmann curvature for black holes with asymptotically Minkowski cores and those with asymptotically de-Sitter cores, including Bardeen and Hayward black holes. We expect that such regular black holes may provide more information about the construction of effective metrics for Planck stars.

Accretion onto the Magnetically Charged Regular Black Hole

We investigate the accretion process for static spherically symmetric geometry, i.e., magnetically charged regular black hole with isotropic fluid. W＇e obtain generalized expressions for the velocity （u（r））, speed of sound （cs2）, energy density （ρ（r） ） and accretion rate （M） at the critical point near the regular black hole during the accretion process. We also plot these physical parameters against fixed values of charge, mass and different values of equation of state parameter to study the process of accretion. We find that radial velocity and energy density of the fluid remain positive and negative as well as rate of change of mass is increased and decreased for dust, stiff, quintessence fluid and phantom-like fluid, respectively.

Regular Magnetic Black Hole Gravitational Lensing

The Bronnikov regular magnetic black hole as a gravitational lens is studied. In nonlinear electrodynamics, photons do not follow null geodesics of background geometry, but move along null geodesics of a corresponding effective geometry. To study the Bronnikov regular magnetic black hole gravitational lensing in the strong deflection limit, the corresponding effective geometry should be obtained firstly. This is the most important and key step. We obtain the deflection angle in the strong deflection limit, and further calculate the angular positions and magnifications of relativistic images as well as the time delay between different relativistic images. The influence of the magnetic charge on the black hole gravitational tensing is also discussed.

Comparison of thermodynamic behaviors of two regular-AdS black holes

Considering the negative cosmological constant of an anti-de Sitter(AdS)background as a positive thermodynamic pressure in the extended phase space,we investigate the P-υ critical behavior and of the cooling-heating phase transition of the regular Hayward-AdS(HAd S)black hole(BH),and compare the difference of some thermodynamic processes in both the HAdS BH and the BardeenAdS(BAdS)BH.We found that the phase transition of the BAdS BH tends to be more the van der Waals(vdW)phase transition.For the cooling-heating phase transition,we obtained the inversion curves of the HAdS BH are always higher than the BAdS BH under the same pressure and magnetic charge.We also compare the smallest existence mass,the zero-temperature remnant,and the critical magnetic charge for these two BHs.The results suggested that the inner horizon and the outer horizon of the Hayward BH are easier to merge,and the singularity is easier to expose.

Polarization distribution in the image of a synchrotron emitting ring around a regular black hole

The polarized images of a synchrotron emitting ring are studied in the regular Hayward and Bardeen black hole spacetimes.These regular black holes carry a magnetic field in terms of gravity coupled to nonlinear electrodynamics.Results show that the main features of the polarization images of the emitting rings are similar in these two regular black hole spacetimes.As the magnetic charge parameter increases,the polarization intensity and the electric vector position angle in the image plane increase in Hayward and Bardeen black hole spacetimes.Moreover,the polarization intensity and electric vector position angle in the image of the emitting ring in the Hayward black hole spacetime are closer to those in the Schwarzschild case.The effects of the magnetic charge parameter on the Strokes Q-U loops are also slightly smaller in the Hayward black hole spacetime.This information stored in the polarization images around Hayward and Bardeen black holes could help understand regular black holes and the gravity coupled to nonlinear electrodynamics.

Neutral regular black hole solution in generalized Rastall gravity

We investigate the static, spherically symmetric regular black hole solutions in the generalized Rastall gravity. In particular, the prescription of Rastall gravity implies that the present approach does not necessarily involve nonlinear electrodynamics. Subsequently, the resulting regular black hole solutions can be electrically and magnetically neutral. The general properties of the regular black hole solutions are explored. Moreover, specific solutions are derived and discussed, particularly regarding the parameter related to the degree of violation of the energy-momentum conservation in the Rastall theory.

Joule-Thomson expansion of the regular(Bardeen)-AdS black hole

We study the Joule-Thomson expansion of the regular black hole in an anti-de Sitter background,and obtain the inversion temperature for the Bardeen-AdS black hole in the extended phase space.We investigate the isenthalpic and inversion curves for the Bardeen-AdS black hole in the T-P plane and find that the intersection points between them are exactly the inversion points discriminating the heating from the cooling process.The inversion curve for the regular(Bardeen)-AdS black hole is not closed and there is only a lower inversion curve,in contrast to the Van der Waals fluid.Most importantly,we find that the ratio between the minimum inversion temperature and the critical temperature for the regular(Bardeen)-AdS black hole is 0.536622,which is larger than any known ratio for the singular black hole.The large ratio for the Bardeen-AdS black hole may be due to the repulsive de Sitter core near the origin of the regular black hole.

Dynamics of Particles Around a Regular Black Hole with Nonlinear Electrodynamics

We investigate the dynamics of a charged particle being kicked off from its circular orbit around a regular black hole by an incoming massive particle in the presence of magnetic field. The resulting escape velocity, escape energy and the effective potential are analyzed. It is shown that the presence of even a very weak magnetic field helps the charged particles in escaping the gravitational field of the black hole. Moreover the effective force acting on the particle visibly reduces with distance. Thus particle near the black hole will experience higher effective force as compared to when it is far away.

New black-to-white hole solutions with improved geometry and energy conditions

We construct new black-to-white hole solutions which connect the geometry of spacetime at some gluing surface inside the horizon.The continuity of the metric can be guaranteed up to the arbitrary order which is controlled by the power factor n.This sort of black-to-white holes is characterized by the sub-Planckian scalar curvature,independent of the mass of black-to-white holes.More importantly,we show that the energy condition is only violated within a small region near the gluing surface.The geodesics of particles within the region from black hole to white hole is also analyzed.It turns out that the matter falling into the black hole may pass through the center without singularity and come out from the white hole.This scenario provides novel ideas for understanding the information loss paradox in traditional black hole physics.

Shadow thermodynamics of the Hayward-AdS black hole

In this paper,the phase structure of the Hayward-anti-de Sitter(AdS)black hole(BH)is studied using shadow formalism.It has been found that the shadow radius is a monotonic function of the horizon radius and can therefore play an equivalent role to the horizon radius in characterizing the thermodynamics of the Hayward-AdS BH.The thermodynamic phase transition(PT)of the Hayward-AdS BH is investigated with the shadow radius.It is shown that as the magnetic charge increases,the shadow radius becomes larger,while the coexistence temperature becomes lower.The thermal profile of the Hayward-AdS BH is established by combining the temperature diagram and the shadow cast diagram,which shows that for a fixed magnetic charge,the temperature of the Hayward-AdS BH increases with the pressure whereas the region of the thermal profile decreases with the pressure.In particular,the temperature of the Hayward-AdS BH follows an N-type change trend when it is smaller than the critical temperature.It implies that the BH shadow may be used to investigate the thermodynamics of the Hayward-AdS BH.