Hawking Temperature and the Quantum Pressure of the Schwarzschild Black Hole

There is no term for pressure ( P∇V) in the first law of black hole thermodynamics. To address this question, we study the first law of black hole thermodynamics and derive an expression for it. We report that this pressure corresponds to the Hawking temperature and is inversely proportional to the quartic of the Schwarzschild radius. It implies that a lighter and smaller black hole exerts more pressure on its surrounding environment. It might shed light on the other thermodynamic aspects of the black hole.

The Hawking Hubble Temperature as the Minimum Temperature, the Planck Temperature as the Maximum Temperature, and the CMB Temperature as Their Geometric Mean Temperature

Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble temperature and the maximum Planck temperature of the expanding universe over the course of cosmic time. This mathematical discovery suggests a re-consideration of Rh=ctcosmological models, including black hole cosmological models, even if it possibly could also be consistent with the Λ-CDM model. Most importantly, this paper contributes to the growing literature in the past year asserting a tightly constrained mathematical relationship between the CMB temperature, the Hubble constant, and other global parameters of the Hubble sphere. Our approach suggests a solid theoretical framework for predicting and understanding the CMB temperature rather than solely observing it.1.

Hawking temperature of Kerr anti-de-Sitter black hole affected by Lorentz symmetry violating

We studied the correction of the quantum tunneling radiation of fermions with spin 1/2 in Kerr anti-de-Sitter black hole.First,the dynamic equation of spin 1/2 fermions was corrected using Lorentz’s violation theory.Second,the new expressions of the fermions quantum tunneling rate,the Hawking temperature of the black hole and the entropy of the black hole were obtained according to the corrected fermions dynamic equation.Our results show that Hawking temperature increases with the enhancement of both the coupling strength and the radial component of ether-like field,but is independent of non-radial components of ether-like field.At last,some comments are made on the results of our work.

Dirac Particles' Tunneling Radiation from Dilaton Space-time with Squashed Horizons

The aim of this paper is to investigate Hawking radiation of Dirac particles from the Dilaton space-time with squashed horizons by improving the method of Kerner and Man’s tunneling analysis.We construct appropriate matrices for general covariant Dirac equation,and derive the tunneling probability and Hawking temperature.The results show that both Dirac particles and scalar particles radiate at the same Hawking temperature.

On the Thermodynamical Black Hole Stability in the Space-Time of a Global Monopole in f(R)-Gravity

In this work, we re-assess a class of black hole solutions in a global monopole spacetime in the framework of an f(R)-gravity model. Our main line of investigation consists in considering a region close enough to the black hole, but such that the weak field approximation is still valid. The stability of the black hole is studied in terms of its thermodynamical properties, with the radial coordinate written as a power-law function with the status of the main factor underneath the stability of the model. We obtain the explicit expressions for the thermodynamical quantities of the black hole as functions of the event horizon, by considering both the Hawking and the local temperatures. The phase transitions that may occur in this system, including the Hawking-Page phase transition, are inspected with particular attention. We work out and contemplate a solution of special interest in which one of the parameters is related to the cosmological constant. Our main result sets out to establish a comparison between both the Hawking and the local formalisms for the black hole in the framework of the f(R)-gravity in the particular space-time adopted here.

Charged Fermions Tunneling from a Rotating Charged Black Hole in 5-Dimensional Gauged Supergravity

Recent research shows that Hawking radiation from black hole horizon can be treated as a quantum tunneling process, and fermions tunneling method can successfully recover Hawking temperature. In this tunneling framework, choosing a set of appropriate matrices γ^μ is an important technique for fermions tunneling method. In this paper, motivated by Kerner and Man＇s fermions tunneling method of 4 dimension black holes, we further improve the analysis to investigate Hawking tunneling radiation from a rotating charged black hole in 5-dimensional gauged supergravity by constructing a set of appropriate matrices γ^μ for general covariant Dirac equation. Finally, the expected Hawking temperature of the black hole is correctly recovered, which takes the same form as that obtained by other methods. This method is universal, and can also be directly extend to the other different-type 5-dimensional charged black holes.

Fermion tunneling from squashed black holes in the Gdel universe and charged Kaluza Klein space time

This paper is devoted to the investigation the fermion tunneling radiation of squashed black holes in the G6del universe and charged Kaluza-Klein space-time. For black holes with different dimensions, establishing a set of appropriate matrices γμ for the general covariant Dirac equation plays an important role in the semi-classical tunneling method. By constructing two sets of γμ matrices, we have successfully derived the tunneling probability and Hawking temperature of the black holes.

Invariant expression for tunneling rate under canonical transformations

The original formula to calculate the tunneling rate through event horizons is apparently dependent on the type of coordinates used. In this paper, we propose an invariant expression under canonical transformations to study the tunneling effect. Moreover, the problem of factor 2 is solved naturally. As an application of this expression, we obtain the same tunneling rate both in the Schwarzschild and the Painlev6 coordinates. It is shown that once the suitable formula to calculate tunneling rate is correctly identified, the tunneling method is manifestly covariant.

Maxwell's equal area law for Vaidya-Bonner-de Sitter black hole under Lorentz invariance violation

In this study,we investigate the tunneling of fermions with arbitrary spin near the event horizon of a nonstationary Vaidya-Bonner-de Sitter(VBdS)black hole under Lorentz invariance violation(LIV).The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation,Feynman prescription,and Wentzel-Kramers-Brillouin approximation.By considering the cosmological constant as a thermodynamic pressure in the extended phase space,we construct a Maxwell's equal area law under LIV and study the phase transitions of VBdS black hole in P-v,P-V,and T-S planes.The LIV increases the length of the liquid-gas coexistence region.The thermodynamic quantities such as the entropy,heat capacity,Helmholtz free energy,internal energy,enthalpy,and Gibbs free energy of the VBdS black hole are discussed.These quantities tend to increase under LIV.The stability of the black hole is also discussed in the presence of LIV.

Charged fermions tunneling radiation from the charged Gdel black hole in minimal five-dimensional gauged supergravity

In this paper,we extend fermions tunneling radiation to the case of five-dimensional charged black holes by introducing a set of appropriate matrices γμ for general covariant Dirac equation of 1/2 spin charged Dirac particles in the electromagnetic field.It is expected that our result can strengthen the validity and power of the tunneling method.We take the charged Gdel black holes in minimal five-dimensional gauged supergravity for example in order to present a reasonable extension of the tunneling method.As a result,we get fermions tunneling probability of the black hole and the Hawking temperature near the event horizon.

Quantum tunnelling radiation from static and rotating black lenses in five dimensions

Black lenses with L(n,1) horizon topology in five dimensions have many unusual properties shared by neither Myers-Perry black holes with event-horizon topology S 3,nor 5-dimensional black rings with event-horizon topology S 2 × S 1.In this work,by constructing appropriate matrices γμ for the general covariant Dirac equation,we further extend the fermion tunnelling method to 5-dimensional static and rotating black lenses.As a result,it is interesting to find as in black hole cases,fermions tunnelling can also result in correct Hawking temperatures for the static and rotating black lenses.