Normal Phase Space Research Articles

Phase structures and critical behavior of rational non-linear electrodynamics Anti de Sitter black holes in Rastall gravity

This research paper presents a black hole solution with a rational nonlinear electrodynamics source within the Rastall gravity framework. The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior. The phase structure is examined using the extended first law of thermodynamics, with the cosmological constant Λ serving as pressure P. The isotherms exhibit van der Waals behavior at small values of horizon r +. The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the re-entrant phase transition occurs and disappears. We also explore the prevalent microstructure of black holes in Ruppeiner geometry, uncovering significant deviations in the nature of particle interactions from conventional practice. Moreover, the thermodynamic geometry is analyzed using the Ruppeiner formalism, with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity, and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar. The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures. Thus, there is an absolute correspondence.

Step-barrier dynamical system

The step-barrier dynamical system is discussed in detail. The behavior of particles captured in the barrier bucket remarkably varies depending on their initial conditions. The intrinsic nature of motion observed in the fully normalized area-preserving mapping simulations is simply clarified by a value of energy or momentum of particle at the initial stage. A rational initial value of y in the normalized phase space (x, y) at beginning leads to the periodic solution. Meanwhile, an irrational value of y gives the oscillation in amplitude with multi-frequency, resulting in broad tracks in the phase space. Effectively, the barrier bucket size is reduced due to these broad tracks. We arrive at the concept of effective stable region, which is defined by the contour of the averaged step-barrier Hamiltonian and useful in actual applications.

Hawking radiation from a Reissner-Nordstrom-AdS black hole with integral monopoles in extended phase space

In recent years, thermodynamics and phase transitions of black holes in extended phase space have been extensively studied. The results show that the original first law of thermodynamics needs revising and new phase transitions will appear. However, so far, Hawking tunneling radiation has not been widely studied in the extended phase space. In particular, whether the tunneling radiation probability changes at this time is still uncertain. This work focuses on this topic, that is, to calculate the specific value of the tunneling probability in the extended phase space and ascertains whether the results obtained in the normal phase space are consistent with those in the extended phase space. The methods used herein are described below. Taking Reissner-Nordstrom-AdS black holes with global monopole for example, the cosmological parameters are regarded as dynamic variables, which is different from previous treatment methods that regard them as constants and ignore their contributions to the tunneling probability. In particular, cosmological parameters are introduced and regarded as thermodynamic pressure when the tunneling probability is calculated, and their contribution to the tunneling probability is considered. In the work the tunneling process of mass particles is mainly studied. The outgoing particles are viewed as spherical de Broglie waves, and then the relative phase velocity and group velocity are calculated. The geodesic equation is obtained according to the relationship between the two velocities, and the tunneling probability is calculated from the geodesic equation. It is concluded that the results show that the tunneling probability of the ingoing particles is proportional to the difference in the Bekenstein-Hawking entropy of the black hole before and after the particles tunnel, and the radiation spectrum deviates from the pure thermal spectrum, which is exactly the same as the case that the cosmological parameters are treated as constants. This means that the tunneling probability of particles can be obtained in the extended phase space, and the tunneling process does not depend on thermodynamic parameters. In addition, it is found that although the global monopole affects the dynamical behavior and thermodynamic quantity of the particle, it does not affect the entropy change or tunneling rate. In other words, the conclusion that the tunneling probability in extended phase space is exactly the same as that in normal phase space does not depend on the space-time topology.

Beam-based reconstruction of the shielded quench-heater fields for the LHC main dipoles

Small orbit oscillations of the circulating particle beams have been observed immediately following quenches in the LHC’s superconducting main dipole magnets. Magnetic fields generated during the discharge into the quench heaters were identified as the cause. Since the resulting, shielded field inside the beam screen cannot be measured in-situ, the time evolution of the field has to be reconstructed from the measured beam excursions.In this paper, the field-reconstruction method using rotation in normalized phase space and the optimized fitting algorithm are described. The resulting rise times and magnetic field levels are presented for quench events that occurred during regular operation as well as for dedicated beam experiments. Finally, different approaches to model the shielding behavior of the beam screen are discussed.

Multidimensional system geomonitoring of groundwater in water in-takes areas (on the example of Poltava city). Part 1. Identification of system development of hydrogeological process

Formulation of the problem. The paper is the beginning of scientific papers series of authors on an actual environmental topic – multidimensional system geomonitoring of groundwater in water intakes areas. The purpose of article is a substantiation of application possibility of the method of objects trajectory modeling in the normalized phase space, which has been developed at V. N. Karazin Kharkiv National University for socio-geographical monitoring tasks, for hydrogeological objects geomonitoring. Materials and methods. The research is based on the method of objects trajectory modeling in the normalized phase space. To achieve the purpose of this study, geomonitoring data of five water intakes in Poltava city, which operate Cenomanian-Lower Cretaceous aquifer, has been used. Changes in the average chemical composition of groundwater for each water intake have been analyzed according to 12 indicators: pH, hardness, dry residue, ammonium, fluorine, chlorine, sulfates, bicarbonates, calcium, magnesium, sodium+potassium, ferrous iron. The initial data have been collected from 1981 to 2008 according to an irregular pattern in time (39 points in time). Research results. The following indicators of systemic development of hydrogeological system have been calculated for each water intake: a) for each period of time – the path length traveled by the water intake hydrogeological system, which characterizes the intensity of changes in the groundwater chemical composition; b) for each control time – the projection of current trajectory point on the optimal trajectory (main diagonal), the deviation of point from the optimal trajectory, the progress coefficient (the ratio of point projection to the length of main diagonal). The main trends in the systemic development of hydrogeological system for all studied water intakes have been identified: - the intensity of changes in the groundwater chemical composition at water intakes Nos. 1-5 decreases over time, which can be explained by the reduction of water withdrawal and hydrodynamic factors associated with the formation of depression funnel, in particular the spreading of quasi-stationary filtration regime; - according to the absolute values of changes intensity in the groundwater chemical composition, the water intake No. 3 is highlighted, the value of which is significantly less than the values of other water intakes; - groundwater at the water intake No. 1 has the greatest variability in the changes intensity of chemical composition over time both in amplitude and in absolute values; - there is a very noticeable synchronization of movement intensity graphs of water intakes hydrogeological systems in the normalized phase space and the average intensity of changes in the groundwater chemical composition, but a detailed analysis reveals some deviations from this pattern, which may be due to abrupt changes in operation mode of water intakes.

Remarks on the weak cosmic censorship conjecture of RN-AdS black holes with cloud of strings and quintessence under the scalar field

In this paper, we investigate the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black hole with the cloud of strings and quintessence by the scattering of a scalar field. The variations of the thermodynamic variables are calculated in the normal and extended phase spaces. In the normal phase space, where the cosmological constant is considered as a constant, the first and second laws of thermodynamics are satisfied. In the extended phase space, where the cosmological constant and the parameters related to the cloud of strings and quintessence are treated as variables, the first law of thermodynamics is still satisfied and the second law of thermodynamics is indefinite. Moreover, we find that the weak cosmic censorship conjecture is valid for the extremal and near-extremal black holes in both phase spaces.

Simulation of the solenoid scan method used in overlapping field for thermal emittance measurement

In one high repetition frequency X-ray free electron laser (XFEL) equipment, the electron gun and compensate solenoid have special structure in the photoinjector, thus the electric field and the magnetic field overlaps near the cathode. The thermal emittance of the cathode should be measured in the experiment. The solenoid scan method used to measure the thermal emittance is not suitable for the overlapping field, because it works effectively only when the rms emittance keeps constant. As the normalized phase space can avoid the influence of the electric field, we tried to use the solenoid scan method in normalized phase space. Using simulation code to do simulations and analysis, we finally demonstrate that this method is feasible for measurement of thermal emittance of the photoinjector which has overlapping field.

Thermodynamics and weak cosmic censorship conjecture in Born-Infeld-anti-de Sitter black holes * *Supported by the National Natural Science Foundation of China (11875095, 11675140, 11705005), and Basic Research Project of Science and Technology Committee of Chongqing (cstc2018jcyjA2480)

In this study, we examine the laws of thermodynamics and the weak cosmic censorship conjecture in the normal and extended phase spaces of Born-Infeld-anti-de Sitter black holes by considering a charged particle absorption. In the normal phase space, the first and second laws of thermodynamics as well as the weak cosmic censorship are still valid. However, in the extended phase space, the second law of thermodynamics is violated for double-horizon black holes and part of single-horizon black holes. The first law of thermodynamics and the weak cosmic censorship conjecture are still valid for all types of black holes. In addition, we found that the shift of the metric function, which determines the locations of the horizons, takes the same form at the minimum point in both the normal and extended phase spaces, indicating that the weak cosmic censorship conjecture is independent of the thermodynamic phase space.

Testing thermodynamic laws and weak cosmic censorship conjecture of conformal anomaly corrected AdS black hole

By dropping particles into black hole, we have employed recently the new assumption (Hu et al. in Phys Rev D100:104022, 2019. https://doi.org/10.1103/PhysRevD.100.104022 ) that the change of the black hole mass(enthalpy) should be the same amount as the energy of an infalling particle ( $$\omega = \mathrm{d}M$$ ), to carefully test the laws of thermodynamics and the weak cosmic censorship conjecture of a conformal anomaly corrected AdS black hole in different phase spaces. Using the energy–momentum relation, the result shows that the first law, second law and weak cosmic censorship conjecture of black hole are all valid in the normal phase space; no violations occur. In the extended phase space, it firstly shows that the first law of black hole thermodynamics is always true in our case. Then, we interestingly find that if the condition $${\mathrm{d}\ell } > -\left( P^r \ell ^3\right) /{r_+^3}$$ satisfied, the variation of entropy is always positive, which means there would be no violation of the second law in the extend phase spaces. Also, it is true that there are always horizons by which the singularity is also covered. So, the configurations of the extremal and near-extremal black holes will not be changed, and there has no violation of the weak cosmic censorship conjecture. Finally, all of those conclusions are independent of the scalar curvature parameter k and the conformal anomaly parameter $${\tilde{\alpha }}$$ .

Thermodynamics and weak cosmic censorship conjecture in the Kerr-AdS black hole

We investigate the laws of thermodynamics and weak cosmic censorship conjecture in the normal and extended phase space of a Kerr-AdS black hole by analyzing the energy-momentum relation of the absorbed fermion dropping into the horizon. In the normal phase space, the first law, second law as well as the weak cosmic censorship conjecture are found to be valid in all the initial states of the black hole. However, in the extended phase space, although the first law and weak cosmic censorship conjecture are still valid, the second law becomes more subtle. We find that the validity or violation of the second law depends on the spin parameter, the radius of the AdS spacetime, and their variations. In addition, in the extended phase space, the configurations of the extremal and near-extremal Kerr-AdS black holes are unchanged as the fermions are absorbed since the final and initial states are the same.

Thermodynamics and weak cosmic censorship conjecture of 4D Gauss-Bonnet-Maxwell black holes via charged particle absorption * *Supported in part by the NSFC (11875196, 11375121, 11005016, 11947225)

Recently, the non-trivial solutions for 4-dimensional black holes of Einstein-Gauss-Bonnet gravity had been discovered. In this paper, considering a charged particle entering into a 4-dimensional Gauss-Bonnet-Maxwell black hole, we calculate the black hole thermodynamic properties using the Hamilton-Jacobi equation. In the normal phase space, the cosmological constant and Gauss-Bonnet parameter are fixed, the black hole satisfies the first and second laws of thermodynamics, and the weak cosmic censorship conjecture (WCCC) is valid. On the other hand, in the case of extended phase space, the cosmological constant and Gauss-Bonnet parameter are treated as thermodynamic variables. The black hole also satisfies the first law of thermodynamics. However, the increase or decrease in the black hole's entropy depends on some specific conditions. Finally, we observe that the WCCC is violated for the near-extremal black holes in the extended phase space.

Revisiting black hole thermodynamics in massive gravity: charged particle absorption and infalling shell of dust * * Supported by the Natural Science Foundation of China (11705161, 11675139, 11875220). Xiao-Mei Kuang is also partly Supported by Natural Science Foundation of Jiangsu Province (BK20170481) and Fok Ying Tung Education Foundation (171006). Shi-Qian Hu is also Supported by the Postgraduate Reaearch & Practice

In this study, we apply two methods to consider the variation of massive black holes in both normal and extended thermodynamic phase spaces. The first method considers a charged particle being absorbed by the black hole, whereas the second considers a shell of dust falling into it. With the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space; however, in the extended phase space, the first law is satisfied but the validity of the second law of thermodynamics depends upon the model parameters. With the latter method, both laws are valid. We argue that the former method's violation of the second law of thermodynamics may be attributable to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we demonstrate that the event horizon always ensures the validity of weak cosmic censorship in both phase spaces; this means that the violation of the second law of thermodynamics, arising under the aforementioned assumption, does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method is responsible for the violation and requires deeper treatment.

Testing the weak cosmic censorship conjecture in torus-like black hole under charged scalar field

We investigate weak cosmic censorship conjecture in charged torus-like black hole by the complex scalar field scattering. Using the relation between the conserved quantities of a black hole and the scalar field, we can calculate the change of the energy and charge within the infinitesimal time. The change of the enthalpy is connected to the change of energy, then we use those results to test whether the first law, the second law as well as the weak cosmic censorship conjecture are valid. In the normal phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid, and the second law of thermodynamics is not violated. For the specific black hole under scalar field scattering we consider, in the extended phase–space, the first law of thermodynamics and the weak cosmic censorship conjecture are valid. However, the second law of thermodynamics is violated when the black hole’s initial charge reaches a certain value.

Thermodynamics and weak cosmic censorship conjecture in (2+1)-dimensional regular black hole with nonlinear electrodynamics sources

We study the dynamical behavior of spinor particles and get the energy–momentum relation of charged particles by solving the Dirac equation. Based on the energy–momentum relation, we investigate the laws of thermodynamics and the weak cosmic censorship conjecture for the (2 + 1)-dimensional regular black hole with nonlinear electrodynamics sources in the normal phase space and extended phase space. Our results show that the first law of thermodynamics as well as the weak cosmic censorship conjecture are valid in both the phase spaces. However, the second law of thermodynamics is violated in the extended phase space, implying that the first law and weak cosmic censorship conjecture do not depend on the phase space while the second law depends. In addition, in the extended phase space, we find the configurations of the extremal and near-extremal black holes does not change for the final states and initial states are the same.

Minimal Length Effect on Thermodynamics and Weak Cosmic Censorship Conjecture in Anti-de Sitter Black Holes via Charged Particle Absorption

In this paper, we investigate the minimal length effects on the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black hole via charged particle absorption. We first use the generalized uncertainty principle (GUP) to investigate the minimal length effect on the Hamilton-Jacobi equation. After the deformed Hamilton-Jacobi equation is derived, we use it to study the variations of the thermodynamic quantities of a RN-Ads black hole via absorbing a charged particle. Furthermore, we check the second law of thermodynamics and the weak cosmic censorship conjecture in two phase spaces. In the normal phase space, the second law of thermodynamics and the weak cosmic censorship conjecture are satisfied in the usual and GUP-deformed cases, and the minimal length effect makes the increase of entropy faster than the usual case. After the charge particle absorption, the extremal RN-AdS black hole becomes nonextremal. In the extended phase space, the black hole entropy can either increase or decrease. When T>2Pr+, the second law is satisfied. When T<2Pr+, the second law of thermodynamics is violated for the extremal or near-extremal black hole. Finally, we find that the weak cosmic censorship conjecture is legal for extremal and near-extremal RN-Ads black holes in the GUP-deformed case.

Weak cosmic censorship conjecture in the nonlinear electrodynamics black hole under the charged scalar field

In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the nonlinear electrodynamics black hole under the scattering of a charged complex scalar field. According to the energy and charge fluxes of the scalar field, the variations of this black hole’s energy and charge can be calculated during an infinitesimal time interval. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.

Weak cosmic censorship conjecture and thermodynamics in quintessence AdS black hole under charged particle absorption * * Supported by the National Natural Science Foundation of China (11875095) and Basic Research Project of Science and Technology Committee of Chongqing (cstc2018jcyjA2480)

Considering the cosmological constant as the pressure, this study addresses the laws of thermodynamics and weak cosmic censorship conjecture in the Reissner-Nordström-AdS black hole surrounded by quintessence dark energy under charged particle absorption. The first law of thermodynamics is found to be valid as a particle is absorbed by the black hole. The second law, however, is violated for the extremal and near-extremal black holes, because the entropy of these black hole decrease. Moreover, we find that the extremal black hole does not change its configuration in the extended phase space, implying that the weak cosmic censorship conjecture is valid. Remarkably, the near-extremal black hole can be overcharged beyond the extremal condition under charged particle absorption. Hence, the cosmic censorship conjecture could be violated for the near-extremal black hole in the extended phase space. For comparison, we also discuss the first law, second law, and the weak cosmic censorship conjecture in normal phase space, and find that all of them are valid in this case.

Thermodynamics and weak cosmic censorship conjecture in the charged RN-AdS black hole surrounded by quintessence under the scalar field

In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the RN-AdS black hole surrounded by the quintessence under the scattering of a charged complex scalar field. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, and the entropy of a black hole decreases with time. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.

Weak cosmic censorship conjecture with pressure and volume in the Gauss-Bonnet AdS black hole

With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the basis of the energy-momentum relation at the event horizon, we investigate the first law, second law, and weak cosmic censorship conjecture in both the normal phase space and extended phase space. Our results show that the first law, second law as well as the weak cosmic censorship conjecture are valid in the normal phase space for all the initial states are black holes. However, in the extended phase space, the second law is violated for the extremal and near-extremal black holes, and the weak cosmic censorship conjecture is violable for the near-extremal black hole, though the first law is still valid. In addition, in both the normal and extended phase spaces, we find the absorbed particle changes the configuration of the near-extremal black hole, while don't change that of the extremal black hole.

Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space * *Supported by National Natural Science Foundation of China (11875095) and Basic Research Project of Science and Technology Committee of Chongqing (cstc2018jcyjA2480, cstc2019jcyjA2091)

As a charged fermion drops into a BTZ black hole, the laws of thermodynamics and the weak cosmic censorship conjecture are investigated in both the normal and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics, and the weak cosmic censorship are found to be valid. In the extended phase space, although the first law and weak cosmic censorship conjecture remain valid, the second law is dependent on the variation of the renormalization energy dK. Moreover, in the extended phase space, the configurations of extremal and near-extremal black holes are not changed, as they are stable, while in the normal phase space, the extremal and near-extremal black holes evolve into non-extremal black holes.