Thermodynamics And Shadow Observational Characteristics Of Black Holes In Different Gravity Spacetimes

Black holes have always been a hot topic of extensive discussion.In 2005,the journal “Science” published a list of the 125 most important scientific questions globally,which included “What is the essence of black holes?” In recent years,the thermodynamics and shadows of black holes have been continuously explored in the fields of astrophysics,making it one of the focal points of research.This article focuses on the thermodynamics and shadows of black holes,exploring a series of important questions related to black holes.Firstly,the importance of black hole thermodynamics is emphasized,and the thermodynamic behavior of the regular black hole is deeply studied.By applying the Clausius-Clapeyron-Ehrenfest equation,the phase transition level of the Bardeen-Ad S black hole is rigorously demonstrated.Furthermore,the black hole is analogized to ferromagnetic materials using the Landau continuous phase transition theory,providing a microscopic perspective on the black hole’s phase transition level.The results reveal that,whether viewed from a macroscopic or microscopic perspective,the phase transition of the BardeenAd S black hole is a second-order phase transition.Additionally,by comparing the thermodynamic properties of the Bardeen-Ad S black hole and the HaywardAd S black hole,differences are found in terms of phase transition direction,critical universal constants,etc.,and it is pointed out that the Bardeen-Ad S black hole is closer to the Van der Waals system.Different behaviors under conditions of cold-hot phase transitions are revealed by plotting isenthalpic curves and inversion curves.Furthermore,through the study of black hole engine efficiency,it is found that the efficiency of the Hayward-Ad S black hole increases with increasing pressure and magnetic charge,while that of the Bardeen-Ad S black hole exhibits the opposite trend.These analyses not only demonstrate the characteristics of regular Ad S black hole phase transitions and engines but also reveal the influence of singularities on black hole thermodynamic phase transitions.From macroscopic and microscopic perspectives,the possibility of singularities altering the type of phase transition and affecting the microscopic structure is discussed,emphasizing the importance of singularity disappearance for black hole phase transitions and providing some methods for understanding the thermodynamic properties of black holes.Secondly,this paper explores a novel perspective by introducing the concept of shadow radius when studying black hole thermodynamics.In addition to the conventional notions of event horizon and photon circular orbit radius,the shadow radius is reintroduced as a third parameter,elucidating its positive correlation with the event horizon radius.This implies that the black hole temperature can be characterized through the shadow radius,offering a new descriptive approach to black hole thermodynamics.By establishing the relationship between the shadow radius and thermodynamic quantities,thermal profiles are delineated,revealing the isoperimetric law and black hole heat capacity under the shadow radius.The results indicate specific trends in the temperature variations of black holes at different temperatures.Furthermore,through the establishment of shadow thermodynamics,the black hole shadow emerges as a valuable tool for probing phase structures,thereby furnishing additional thermodynamic insights.This study not only lays a new theoretical foundation for black hole thermodynamics but also presents novel methods and avenues for future investigations into the properties and behaviors of black holes.Relying on general relativity and accretion models,we have developed numerical codes based on Mathematica to simulate black hole shadows in different accretion environments.By combining theoretical models and numerical simulations,we comprehensively explore the characteristics of black hole shadows.Firstly,this paper introduces the method for deriving arbitrary black hole shadows and photon rings,and derives the solutions of regular Bardeen and Hayward black holes based on field equations.By analyzing the photon trajectories around these two types of regular black holes,we independently developed numerical programs for studying black hole shadows and phenomenologically displayed the trajectories of light near the two black holes.The results indicate that the light density around regular black holes differs from that around Schwarzschild black holes.Even if the observed shadow radii are equal,the presence of a magnetic charge leads to different observed light intensities in these two spacetimes.This paper also considers the issue of black hole singularities,attempting to eliminate singularities by improving the internal matter distribution of black holes.By considering the black hole’s magnetic charge,the black hole becomes more dense,resulting in greater curvature of the surrounding light rays.This paper further investigates the optical appearance of black holes under different accretion backgrounds,such as spherical accretion and disk accretion,revealing the influence of accretion models and geometric backgrounds on the shadows and optical appearance of black holes.For distant observers,black holes are illuminated by different light sources,resulting in varying observed luminosities.By considering different accretion backgrounds,possible observational appearances of regular black holes are demonstrated.Investigation into toy models of two spherical illumination accretions reveals that changes in the accretion background affect the observed intensity,particularly forming intriguing intensity curves near the photon ring.In geometrically thin optical emission disk accretion models,possible observational features of Hayward and Bardeen black holes are discussed.The results show that,unlike in spherical accretion models,in disk accretion scenarios,there not only exists a dark central region but also photon rings and lens rings outside the black hole shadow.The photon ring region is narrow and highly magnetized,while the lens ring can only provide a minimal fraction of the total observed flux.In the Novikov-Thorne model,it is found that black hole accretion disks exhibit a hat-shaped optical appearance,with a remarkably high correlation between the radiation flux of the accretion disk and the black hole’s magnetic charge.Additionally,this paper extends the research results to thinshell wormholes,one of the black hole mimickers,revealing the unique lens bands and photon ring structures of wormholes.These structural signatures may serve as characteristic indicators for identifying different types of black holes using next-generation high-resolution EHT telescopes.Finally,the optical appearances of black holes is considered under two additional modified gravity scenarios: Euler-Heisenberg black holes and charged black holes in Rastall gravity theory.The former arises from nonlinear electromagnetic fields,which affect the motion of photon null geodesics from the perspective of effective geometry problems in spacetime backgrounds.For the latter,the matter carried by spacetime itself may serve as a significant indicator influencing observational outcomes.The research findings indicate that the black hole’s charge and environmental parameters affect the size,brightness,and optical characteristics of its shadow.In the case of spherically symmetric accretion,irrespective of the modified gravity theory model,the size and position of the shadow and photon ring remain unchanged,demonstrating that the black hole shadow is a spacetime geometric feature,unaffected by the motion state of accreting matter,only altering the luminosity of the shadow.Due to the Doppler effect,the shadow’s luminosity corresponding to moving accreting matter is dimmer.For thin accretion disks,parameters such as the position,thickness,emission form,and observational inclination angle of the accretion disk can alter the size and luminosity of the shadow.Whether through direct emission or the photon ring,the details of emission modes have a significant impact on the appearance and optical characteristics of black holes.The research findings not only contribute to understanding black holes,the most mysterious celestial objects in the universe but also provide new identification and characterization methods for future astrophysical observations.