We show that tunnelling between two degenerate minima, as allowed in a finite volume, leads to a non-extensive symmetric ground state. This results in Null Energy Condition violation for sufficiently low temperatures, when a continuous set of momenta in the box containing the field is assumed. Taking into account discrete momenta can modify this picture and is achieved via the addition of the Casimir energy to the tunnelling-induced ground state energy. Focusing on zero-temperature, these non-trivial effects are found to compete, depending on the typical length scales involved.
A finite volume allows tunnelling between degenerate vacua in Quantum Field Theory, and leads to remarkable energetic features, arising from the competition of different saddle points in the partition function. We describe this competition for finite temperature at equilibrium, taking into account both static and (Euclidean) time-dependent saddle points. The effective theory for the homogeneous order parameter yields a non-extensive vacuum energy at low temperatures, implying a dynamical violation of the Null Energy Condition.
The Null Energy Condition is considered the most fundamental of the energy conditions, on which several key results, such as the singularity theorems, are based. The Casimir effect is one of the rare equilibrium mechanisms by which it is breached without invoking modified gravity or non-minimal couplings to exotic matter. In this work we propose an independent dynamical mechanism by which it is violated, with the only ingredients being standard (but non-perturbative) QFT and a minimally coupled scalar field in a double-well potential. As for the Casimir effect, we explain why the Averaged Null…
We study novel type of contributions to the partition function of the Maxwell system defined on a small compact manifold ${\mathbb{M}}$ such as torus. These new terms can not be described in terms of the physical propagating photons with two transverse polarizations. Rather, these novel contributions emerge as a result of tunnelling events when transitions occur between topologically different but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that if the same system is considered in the background of…
We show through Schwinger's approach that in a static weak gravitational background, the Casimir Energy for a real massless scalar field obeying Dirichlet boundary conditions on rectangular plates is unaltered from it's flat space-time value. The result is obtained considering an rather general class of backgrounds, adding further generality and consistency test for the previous work. The proposed result has direct consequences on earlier works in the literature that found gravity related corrections for similar setups.
Tunnelling between degenerate vacuua is allowed in finite-volume Quantum Field Theory, and features remarkable energetic properties, which result from the competition of different dominant configurations in the partition function. We derive the one-loop effective potential based on two homogeneous vacuua of the bare theory, and we discuss the resulting Null Energy Condition violation in O(4)-symmetric Euclidean spacetime, as a result of a non-extensive effective action.
The discussion of vacuum energy is currently a subject of great theoretical importance, specially concerning the cosmological constant problem in General Relativity. From Quantum Field Theory, it is stated that vacuum states subject to boundary conditions may generate tensions on these boundaries related to a measurable non-zero renormalized vacuum energy: the Casimir Effect. As such, investigating how these vacuum states and energy behave in curved backgrounds is just natural and might provide important results in the near future. In this paper we revisit a model of the Casimir Effect in weak…
The principle of horizon complementarity is an attempt to extend ideas about black hole complementarity to all horizons, including cosmological ones. The idea is that the degrees of freedom necessary to describe the interior of the cosmic horizon of one observer in a given universe are in fact sufficient to account for the physics of that entire universe: the remainder is just a set of redundant copies of the interior of a single cosmic horizon. These copies must be factored out, just as one has to factor out gauge redundancies to identify the true degrees of freedom in gauge theory. Motivated…
Based on the definition of the apparent horizon in a general two-dimensional dilaton gravity theory, we analyze the tunnelling phenomenon of the apparent horizon by using Hamilton-Jacobi method. In this theory the definition of the horizon is very different from those in higher-dimensional gravity theories. The spectrum of the radiation is obtained and the temperature of the radiation is read out from this spectrum and it satisfies the usual relationship with the surface gravity. Besides, the calculation with Parikh's null geodesic method for a simple example conforms to our result in general …
We investigate quantum tunnelling methods for calculating black hole temperature, specifically the null geodesic method of Parikh and Wilczek and the Hamilton-Jacobi Ansatz method of Angheben et al. We consider application of these methods to a broad class of spacetimes with event horizons, inlcuding Rindler and non-static spacetimes such as Kerr-Newman and Taub-NUT. We obtain a general form for the temperature of Taub-NUT-Ads black holes that is commensurate with other methods. We examine the limitations of these methods for extremal black holes, taking the extremal Reissner-Nordstrom spaceti…
We review recent work on the Casimir interaction energy between cylindrical shells. We include proposals for future experiments involving cylinders, such us a null experiment using quasi-concentric cylinders, a cylinder in front a conducting plate, and a cylindrical version of the rack and pinion powered by Casimir lateral force. We also present an exact formula for the theoretical evaluation of the vacuum interaction energy between eccentric cylindrical shells, and describe improved analytical and numerical evaluations for the particular case of concentric cylinders.
A model of traversable wormhole in an extended gravity theory has been proposed. The Casimir effect and Generalised Uncertainty Principle (GUP) arising out of the concept of minimal length have been considered to obtain the shape function, radial and tangential pressure of the wormhole. The effects of the GUP parameter and the parameter of the extended gravity theory on the wormhole properties have been discussed. The energy condition violation by the exotic matter of Casimir wormhole have been shown. Also we have calculated the exotic matter content of the Casimir wormhole that violate the nu…
In this paper we study the system of a scalar quantum field confined between two plane, isotropic, and homogeneous parallel plates at thermal equilibrium. We represent the plates by the most general lossless and frequency-independent boundary conditions that satisfy the conditions of isotropy and homogeneity and are compatible with the unitarity of the quantum field theory. Under these conditions we compute the thermal correction to the quantum vacuum energy as a function of the temperature and the parameters encoding the boundary condition. The latter enables us to obtain similar results for …
We study the Casimir energy of a minimally coupled, real, massless scalar field outside a spherically symmetric background potential. We obtain a general expression for the null energy condition in d dimensions and explicit expressions for a perfectly reflecting spherical boundary in 3+1 and 2+1 dimensions. In these cases, the null energy condition is always violated for radial motion and obeyed for azimuthal motion. Nevertheless, the averaged null energy condition is always obeyed.
In recent years there has been a growing interest in the field of Casimir wormhole. In classical general relativity (GR), it is known that the null energy condition (NEC) has to be violated to have a wormhole to be stable. The Casimir effect is an experimentally verified effect that is caused due to the vacuum field fluctuations in quantum field theory. Since the Casimir effect provides the negative energy density, thus this act as an ideal candidate for the exotic matter needed for the stability of the wormhole. In this paper, we study the Casimir effect on the wormhole geometry in modified s…
In this paper, we investigate new exact and analytic solutions of the Einstein Maxwell field equations describing Casimir wormholes with and without the effect of the Generalized Uncertainty Principle (GUP). We consider a specific type of the GUP relations and study three specific models of the redshift function along with two different EoS of state. Here we obtain a class of asymptotically flat Casimir wormhole solutions with and without GUP corrections under the effect of electric charge. Furthermore we check the null, weak, strong and dominant energy conditions at the wormhole throat of rad…
The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature.
The negative energy density of Casimir systems appears to violate general relativity energy conditions. However, one cannot test the averaged null energy condition (ANEC) using standard calculations for perfectly reflecting plates, because the null geodesic would have to pass through the plates, where the calculation breaks down. To avoid this problem, we compute the contribution to ANEC for a geodesic that passes through a hole in a single plate. We consider both Dirichlet and Neumann boundary conditions in two and three space dimensions. We use a Babinet's principle argument to reduce the pr…
We consider radion stabilization in hyperbolic brane-world scenarios. We demonstrate that in the context of Einstein gravity, matter fields which stabilize the extra dimensions must violate the null energy condition. This result is shown to hold even allowing for FRW-like expansion on the brane. In particular, we explicitly demonstrate how one putative source of stabilizing matter fails to work, and how others violate the above condition. We speculate on a number of ways in which we may bypass this result, including the effect of Casimir energy in these spaces. A brief discussion of supersymme…
Connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy conditions, and quantum inequality restrictions on negative energy for free massless scalar fields. In a two-dimensional compactified Minkowski universe, we derive a covariant quantum inequality-type bound on the difference of the expectation values of the energy density in an arbitrary quantum state and in the Casimir vacuum state. From this bound, it is shown that the difference of expectation values also obeys AWEC and ANEC-type integral conditions. In contrast, it is well-known that the stress tensor…
Consider a class of relativistic rotators described by position and a single null direction. Such a rotator is called fundamental if both its Casimir invariants are intrinsic dimensional parameters independent of arbitrary constants of motion. As shown by Staruszkiewicz, only one rotator with this property exists (its partner with similar property can be excluded on physical grounds). We obtain a general solution to equations of free motion of the fundamental relativistic rotator in a covariant manner. Surprisingly, this motion is not entirely determined by initial conditions but depends on on…
The null geodesic congruence for the Lorentzian version of Hawking's wormhole is studied, in spherical Rindler coordinates. One finds that the wormhole throat expands exponentially and the "flare - out" condition is satisfied. A time reversal is equivalent with an inversion applied to the radial coordinate. The stress energy is mostly located near wormhole's throat and the anisotropic fluid is comoving with the spherical distribution of accelerating observers. Far from the throat (the light cone in Cartesian coordinates) the negative energy density acquires an expression similar with the Casim…
