Dirac Quantum Field Theory in Rindler Spacetime

The dynamical properties of Dirac particles inRindler spacetime are investigated. It is shown that thevacuum state of the Dirac field in Minkowski spacetimeappears to be a thermal state for a Rindler observer, and the usual thermal equilibriumstate of the Dirac field in Minkowski spacetime is aquasithermal equilibrium state, which is timeindependent and characterized by two quasi-temperatureparameters for a Rindler observer.     

视界和温度格林函数的生成泛函

在平衡态条件下,利用格林函数的欧氏生成泛函讨论了具有视界的Rindler时空和黑洞时空中量子场温度的几何来源。在Minkowski时空到Rindler时空的变换下,绝对零度格林函数欧氏生成泛函的路径积分表示变换为有限温度量子场的相应表示,说明Minkowski真空态和Rindler时空中的一量子混合态性质相同,导出了这个态的温度格林函数及各热力学格林函数。对于Schwarzschild,Reissner-Nordstrom和Kerr黑洞,得到了类似的结果,并获得了描写量子混合态的统计算符的具体形式。 关键词：     

Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

We review the relation between AdS spacetime in 1 $+$ 2 dimensions and the BTZ black hole (BTZbh). Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZbh. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZbh. In order to make this we use the correspondence introduced in algebraic holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism.     

Study of thermal fluctuations in five-dimensional rotating regular black hole

In this paper, we discuss the effects of thermal fluctuations on thermodynamics of rotating regular black hole in five-dimensional spacetime. We first evaluate thermodynamic quantities such as Hawking temperature, entropy, angular velocity and electric potential of the considered model. To discuss the effects of thermal fluctuations, we compute the logarithmic correction terms to entropy around the equilibrium state. We also check the validity of the first law of thermodynamics in the presence of these correction terms. Finally, we determine stability of the system through specific heat and Hessian matrix. It is concluded that logarithmic corrections originated from thermal fluctuations yield a stable model.     

HORIZONS AND GENERATING FUNCTIONALS FOR THE TEMPERATURE GREEN FUNCTIONS

The generating functional approach to Green functions in the thermal equilibrium is used to explore the geometrical origin of the temperatures of the quantum fields in the Rindler space-time and black hole spacetimes. It is shown that under the transformation from Minkowski space to the Rindler space the path integral representation for the Euclidean generating functionals of Green functions at zero temperature would transform into the corresponding ones of the quantum fields at a certain finite temperature, and the Minkowski vacuum state would have the same properties as that of the quantum mixed state at the same temperatfire. All thermal Green functions for the mixed state are given. Similar results would be obtained for the Schwarzschild, the Reissner-NordstrOm and the Kerr black holes and whereupon the Hawking temperature for the black holes would have geometrical origin as well as that in the Rindler spacetime. The various density operators of the mixed states at the Hawking temperature for the black hole sacetimes are specified.     

Concept of temperature in multi-horizon spacetimes: analysis of Schwarzschild–De Sitter metric

In case of spacetimes with single horizon, there exist several well- established procedures for relating the surface gravity of the horizon to a thermodynamic temperature. Such procedures, however, cannot be extended in a straightforward manner when a spacetime has multiple horizons. In particular, it is not clear whether there exists a notion of global temperature characterizing the multi-horizon spacetimes. We examine the conditions under which a global temperature can exist for a spacetime with two horizons using the example of Schwarzschild–De Sitter (SDS) spacetime. We systematically extend different procedures (like the expectation value of stress tensor, response of particle detectors, periodicity in the Euclidean time etc.) for identifying a temperature in the case of spacetimes with single horizon to the SDS spacetime. This analysis is facilitated by using a global coordinate chart which covers the entire SDS manifold. We find that all the procedures lead to a consistent picture characterized by the following features: (a) In general, SDS spacetime behaves like a non-equilibrium system characterized by two temperatures. (b) It is not possible to associate a global temperature with SDS spacetime except when the ratio of the two surface gravities is rational. (c) Even when the ratio of the two surface gravities is rational, the thermal nature depends on the coordinate chart used. There exists a global coordinate chart in which there is global equilibrium temperature while there exist other charts in which SDS behaves as though it has two different temperatures. The coordinate dependence of the thermal nature is reminiscent of the flat spacetime in Minkowski and Rindler coordinate charts. The implications are discussed.     

Quantum statistical entropy for Kerr－de Sitter black hole

Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n 2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole‘s entropy which contains two horizons (a black hole‘s horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole‘s horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole‘s entropy and horizon‘s area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.     

Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation

In this Letter we make a critique of, and comparison between, the anomaly method and WKB/tunneling method for obtaining radiation from non-trivial spacetime backgrounds. We focus on Rindler spacetime (the spacetime of an accelerating observer) and the associated Unruh radiation since this is the prototype of the phenomena of radiation from a spacetime, and it is the simplest model for making clear subtle points in the tunneling and anomaly methods. Our analysis leads to the following conclusions: (i) neither the consistent and covariant anomaly methods gives the correct Unruh temperature for Rindler spacetime and in some cases (e.g. de Sitter spacetime) the consistent and covariant methods disagree with one another; (ii) the tunneling method can be applied in all cases, but it has a previously unnoticed temporal contribution which must be accounted for in order to obtain the correct temperature.     

Finite temperature quantum fields in expanding universes

The thermodynamics of an ideal relativistic quantum gas in expansion is studied. It is found that only for conformally invariant fields in conformally static spacetime can thermal equilibrium be strictly maintained. A finite temperature theory can be defined under the condition of quasi equilibrium when the background expansion is nearly adiabatic. The high temperature expansion of the energy density for massive nonconformal fields in Robertson-Walker universes and for conformal fields in Bianchi Type-I universes are calculated. The importance of these results on phase transition and quantum processes in the early universe is discussed.     

Generalized Uncertainty Relation of One-Dimensional Rindler Oscillator

General Minkowski vacuum state is seen to be equivalent to a thermal bath for a Rindler uniformly accelerated observer. This paper calculates the generalized uncertainty relation of one-dimensional Rindler oscillator in the coordinate representation. The calculations show that for a Rindler uniformly accelerated observer there is not only general quantum fluctuation but also thermal fluctuation related to his acceleration.     

Modular inclusion,the Hawking temperature,and quantum field theory in curved spacetime

A recent result by Borchers connecting geometric modular action, modular inclusion and spectrum condition, is applied in quantum field theory on spacetimes with a bifurcate Killing horizon (these are generalizations of black-hole spacetimes, comprising the familiar black-hole spacetime models). Within this framework, we give sufficient, model-independent conditions ensuring that the temperature of thermal equilibrium quantum states is the Hawking temperature.     

The energy-momentum tensor near a black hole

The energy-momentum tensor for a conformally invariant scalar field near a Schwarzschild black hole in thermal equilibrium with radiation is found by a combination of analytical and numerical techniques. Calculations are performed in the Euclidean section of the spacetime, and divergences isolated using the heat kernel expansion. It is found that the results agree well with those of Candelas [1], but that there are significant differences from the Gaussian approximation of Page [2].     

A nondispersive de Broglie wave packet

It is assumed that the motion of a particle in spacetime does not depend on the motion relative to it of any observer or of any frame of reference. Thus if the particle has an internal vibration of the type hypothesized by de Broglie, the phase of that vibration at any point in spacetime must appear to be the same to all observers, i.e., the same in all frames of reference. Each observer or reference frame will have its own de Broglie wave for the particle. The phase of the particle's vibration must, by definition, be the same as that of all possible de Broglie waves at the point where the particle is. By superimposing all these possible de Broglie waves, a wave packet is formed centered in space on the particle. The formation of such a packet is discussed with the help of spacetime diagrams; the packet does not spread with time. The relevance of this packet to the wave mechanics of Schrödinger is discussed; it is also pointed out that any vibration can lead to such a packet.     

Cosmic string in the NUT-Kerr-Newman spacetime

We study the equilibrium configurations of a cosmic string described by the Nambu action in the NUT-Kerr-Newman spacetime which includes as special cases the Kerr-Newman black hole spacetime as well as the NUT spacetime which is considered as a cosmological model. In this study it is interesting to note that one can obtain parallel results for the Kerr-Newman black hole as well as the NUT spacetime.     

Nonequilibrium thermodynamics of spacetime

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.     

An empirical,purely spatial criterion for the planes ofF-simultaneity

The claim that distant simultaneity with respect to an inertial observer is conventional arose in the context of a space-and-time rather than a spacetime ontology. Reformulating this problem in terms of a spacetime ontology merely trivializes it. In the context of flat space, flat time, and a linear inertial structure (a purely space-and-time formalism), we prove that the hyperplanes of space for a given inertial observer are determined by a purely spatial criterion that depends for its validity only on the two-way light principle, which is universally regarded as empirically verified. All (empirically determined) spacetime entities, such as the conformal structure or light surface equation, are used in a purely mathematical manner that is independent of and hence isneutral with respect to the ontological status that is ascribed to them. In this regard, our criterion is significantly stronger than thespacetime criterion recently advanced by D. Malament, which appeals explicitly to the conformal orthogonality of spacetime vectors and to the invariance of the conformal-orthogonal structure of spacetime under the causal automorphisms of spacetime. Once the hyperplanes of space for a given inertial observer have been determined by our empirical and purely spatial criterion, the following holds: there exists one and only one -synchronization procedure, namely the standard procedure proposed by Einstein, such that the planes of common time are thesame as the nonconventional hyperplanes of space for the inertial observer. It follows that our criterion provides an empirical even if indirect method for determining that the one-way speed of light is the same as the average two-way speed of light. In addition, two inertial observers that are not at rest with respect to each other necessarily havedifferent hyperplanes of space, and consequently their respective spatial views cannot be encompassed in a single three-dimensional space. Hence, our purely spatial criterion provides an empirical motivation for adopting the more comprehensive spacetime ontology.     

Geometric phase under the Unruh effect with intermediate statistics

Utilizing the geometric phase (GP) acquired in a quantum evolution, we manifest the thermality and quantum nature of the Unruh effect of an accelerating detector. We consider an UDW detector coupling to a conformal field in Minkowski spacetime, whose response spectrum exhibits an intermediate statistics of (1+1) anyon field. We find that comparing to an inertial moving detector, the GP in accelerating frame is modified after the nonunitary evolution of the detector due to the Unruh effect. We show that such modification can distinguish the different thermalizing ways of the detector, which depends on the scaling dimension of the conformal primary field. Finally, we estimate the difference between the GP under the Unruh radiation and that in a thermal bath for a static observer, which reveals the quantum origin of the Unruh effect rather than a conventional thermal noise.     

A Non-Singular Universe with Vacuum Energy

A model for the universe based on the back-reaction effects of quantum fields at finite temperature in the background of Robertson-Walker spacetime and in the presence of a non-zero cosmological constant is constructed. We discuss the vacuum regime in the light of the results obtained through previous studies of the back-reaction of massless quantum fields in the static Einstein universe, and we argue that an adiabatic vacuum state and thermal equilibrium is achieved throughout this regime. Critical density is maintained naturally from the very early stages as a consequence of back-reaction effect of the vacuum fluctuations of quantum fields. Results show that such a model can explain many features of the early universe as well as the present universe. The model is free from the basic problems of the standard Friedmann cosmology, and is non-singular but involves a continuous creation of energy at a rate proportional to the size of the universe, which is lower than that suggested by the steady-state cosmology.