Narrow Results

The kinematics of massive particles moving in rainbow spacetime is studied. We derive the equation of geodesics when the semiclassical effect of moving particles on the background is taken into account. In particular we show that in rainbow flat spacetime the trajectory of a freely falling particle remains unchanged which is still a straight line in energy-independent coordinate system. The implication to the Unruh effect in rainbow flat spacetime is also discussed.

It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is meaningful. For the sake of simplicity, we can construct these observers' world lines by comparing with the observers in the Hawking effect and Unruh effect, whose world lines are both hyperbolic curves in the appropriate coordinates. We do it after defining a certain special null hypersurface in the Kruskal coordinates. Our result shows that these accelerating observers defined in our paper can also detect the radiation with the analogy of the Unruh effect, though locally. Furthermore, we conjecture that, for any null hypersurface in any spacetime, the corresponding observers who can at least locally detect the radiation from it can be found.

We give an interpretation of the temperature in de Sitter universe in terms of a dynamical Unruh effect associated with the Hubble sphere. As with the quantum noise perceived by a uniformly accelerated observer in static spacetimes, observers endowed with a proper motion can in principle detect the effect. In particular, we study a "Kodama observer" as a two-field Unruh detector for which we show the effect is approximately thermal. We also estimate the back-reaction of the emitted radiation and find trajectories associated with the Kodama vector field are stable.

In this paper, we investigate how a uniformly accelerated detector responds to vacuum state of a Dirac field in the κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under κ-Poincaré algebra, we derive κ-deformed Wightman function for Dirac field, which is valid up to first-order in the deformation parameter a. Using this, we calculate the response function of the uniformly accelerated detector, which is coupled to massless Dirac field in κ-spacetime. From this, we obtain the modification to Unruh effect for the κ-deformed Dirac field, valid up to first-order in the deformation parameter.

In this paper, we modify the geometry of Rindler space so as to include an upper limit on the acceleration. Caianiello and his collaborators, in a series of papers, have analyzed the corrections to the classical spacetime metrics due to the existence of a maximal acceleration. Our goal is to derive, in this context, in a very simple way, the so-called Unruh temperature.

We obtain a (5+1)-dimensional global flat embedding of modified Schwarzschild black hole in rainbow gravity. We show that local free-fall temperature in rainbow gravity, which depends on different energy $\omega$ of a test particle, is finite at the event horizon for a freely falling observer, while local temperature is divergent at the event horizon for a fiducial observer. Moreover, these temperatures in rainbow gravity satisfy similar relations to those of the Schwarzschild black hole except the overall factor $g(\omega )$, which plays a key role of rainbow functions in this embedding approach.

Starting from a nonstandard approach to the Unruh effect, we present a description of the emission of radiation from a black hole that avoids quantization of scalar fields and Bogoliubov transformations, but assumes the existence of a maximal acceleration. In this framework, the description appears closer to the original heuristic Hawking’s point of view, with respect to the standard scenario.

In this paper, within the framework of open-system dynamics, we investigate the thermalization phenomena of Unruh effect and de Sitter spacetime. It is shown that the Unruh effect, thermal effect of de Sitter spacetime and Hawking effect are similar in nature.

It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher-dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes á la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacetime, it is indeed possible to arrive at the area scaling law for black hole entropy. Thus, by using the flat spacetime field theory, one can indeed provide a thermodynamic description of black holes. Implications are also discussed.

Usual uniformly accelerated frame, in Dray–’t Hooft spacetime, does not see the any quantum imprint on Unruh effect due to localized shock wave in Minkowski spacetime. Here, we argue that such non-appearance of quantum memory is specific to those particular observers which do not incorporate the presence of wave in their trajectory. In fact, a detector, associated with a frame which is affected by the shock, cannot be trivial in terms of its response. We explicitly show that the later type of frame detects particle in the shock wave Minkowski vacuum which is the effect of shock. Therefore, this quantum memory is very special to specific class of observers as far as Dray–’t Hooft spacetime is concerned. We analyze for a null like trajectory along which the detector is moving.

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy. So, each dark particle occupies a very small area of space so-called Planck area $L_p^2$, which represents the minimum area of the whole space-time given by the spherical surface with area $4\pi R_H^2$, where $R_H$ is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of $10^{-17}\text{Hz}$ due to the slight stretching of the fabric of space-time.

We show that the Sokolov–Ternov effect — the depolarization of particles in storage rings coming from synchrotron radiation due to spin flip transitions — is physically equivalent to the Unruh effect for circular acceleration if one uses a spin-1/2 particle as the Unruh–DeWitt detector. It is shown that for the electron, with gyromagnetic number g ≈ 2, the exponential contribution to the polarization, which usually characterizes the Unruh effect, is "hidden" in the standard Sokolov–Ternov effect making it hard to observe. Thus, our conclusions are different in detail from previous work.

We use the global embedding Minkowski space geometries of a (3+1)-dimensional curved Reissner–Nordström (RN)–AdS black hole space–time into a (5+2)-dimensional flat space–time to define a proper local temperature, which remains finite at the event horizon, for freely falling observers outside a static black hole. Our extended results include the known limiting cases of the RN, Schwarzschild–AdS and Schwarzschild black holes.

A single real scalar field of spin zero obeying the Klein–Gordon equation in flat space–time under external conditions is considered in the context of the spin-statistics connection. An imposed accelerated boundary on the field is made to become, in the far future, (1) asymptotically inertial and (2) asymptotically noninertial (with an infinite acceleration). The constant acceleration Unruh effect is also considered. The systems involving nontrivial Bogoliubov transformations contain dynamics which point to commutation relations. Particles described by in-modes obey the same statistics as particles described by out-modes. It is found in the nontrivial systems that the spin-statistics connection can be manifest from the acceleration. The equation of motion for the boundary which forever emits thermal radiation is revealed.

The Unruh effect for the rate of emission and absorption of neutral massive Majorana spinor particles — plausible constituents of the Dark Matter — in a Rindler space–time is thoroughly investigated. The corresponding Bogoliubov coefficients are explicitly calculated and the consistency with Fermi–Dirac statistics and the Pauli principle is actually verified.

The energy of a particle moving on a space–time, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here, we find the explicit expressions for the coordinate transformations from rainbow Minkowski space–time to accelerated frame. The corresponding metric is also obtained which we call as rainbow Rindler metric. So far we are aware of that no body has done it in a concrete manner. Here, this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.

These pedagogical notes are dedicated to a derivation of the Unruh effect. There is a special emphasis on the transparency of the arguments and the exhibition of detailed calculations. We assume the reader has a basic knowledge of quantum mechanics and relativity. The notes can hopefully be used in a self-contained way by advanced undergraduate or beginning graduate students.

In this paper, we propose generalizations of the Sokolov–Ternov and Unruh effects, and discuss the possibility to measure them on different experiments.

We show the need of the emergence of an invariant minimum speed in the space–time. So, we propose a deformed special relativity with two limits of speed so-called Symmetrical Special Relativity (SSR). It presents a universal minimum speed V that plays the role of a preferred reference frame $S_V$ associated with vacuum. This new paradigm of space–time allows us to understand the origin of the cosmological constant ${\mathrm{\Lambda }}_0$ starting from first principles given by a new kinematic invariance at low energies, which leads us to build a space–time metric with the presence of a minimum speed, so that such metric is equivalent to a de Sitter metric. In order to do that, we use a model of spherical universe with Hubble radius $R_H$ filled by a low vacuum energy density $ϵ$ that governs the accelerated expansion of the universe with negative pressure shown by the equation of state (EOS) of vacuum given by SSR-theory ($p=-ϵ$). Thus, we realize that such spherical universe made up of dark energy works like a black body with adiabatic expansion thermalized with a kind of dark gas that plays the role of the dark energy. From this model of virtual particles of dark gas that fills the sphere with dark energy, we are able to derive the law of universal gravitation, allowing us to understand the cosmological anti-gravity according to the EOS of vacuum in the space–time with a minimum speed. So, we estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this model, as the dark universe can be thought of as a black body with Hubble radius, we obtain its power and frequency of emission of radiation for a low temperature. We conclude that such radiation is a gravitational wave with an extremely low frequency and power due to the slight stretching of the fabric of space–time, since ${\mathrm{\Lambda }}_0$ is very small.

We explore the changes of Quantum Fisher information (QFI) for an uniformly accelerating atom coupling to fluctuating massless scalar field with a perfectly reflecting boundary. We first deduce the master equation that the system obeys. For the unbounded case, the vacuum fluctuation and Unruh thermal bath can rapidly degrade the QFI. However, with a boundary, the degradation, preservation, fluctuation and enhancement of QFI are dependent on the evolution time, boundary and acceleration. In addition, the existing boundary can effectively shield QFI from the influence of the vacuum fluctuation and Unruh thermal effect. Especially, the QFI seems to be unaffected by the vacuum fluctuation and acceleration when the atom is very close to the boundary. The efficient control of the boundary and acceleration can provide the feasible scheme of improving the parameter estimation precision.