Narrow Results

We obtain the energy of a conformal scalar dyon black hole (CSD) by using the energy–momentum complexes of Tolman and Möller. The total gravitational energy is given by the CSD charge in both prescriptions.

We consider an anti de Sitter universe filled by quantum CFT with classical phantom matter and perfect fluid. The model represents the combination of a trace-anomaly annihilated and a phantom driven anti de Sitter universes. The influence exerted by the quantum effects and phantom matter on the AdS space is discussed. Different energy conditions in this type of universe are investigated and compared with those for the corresponding model in a de Sitter universe.

We give three different spherically symmetric spacetimes for the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. One of these contains an arbitrary function and generates the others. These spacetimes give the Reissner–Nordström metric black hole. We then calculated the energy associated with these spacetimes using the superpotential method. We find that unless the time-space components of the tetrad field go to zero faster than at infinity, one gets different results for the energy.

An exact charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters "the gravitational mass M, the charge parameter Q and the rotation parameter a" and its associated metric gives Kerr–Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then calculate the total energy using the gravitational energy–momentum. The energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no energy is shared by the exterior of the Kerr–Newman black hole.

We study energy distribution in the context of teleparallel theory of gravity, due to matter and fields including gravitation, of the universe based on the plane-wave Bianchi VII_δ spacetimes described by the Lukash metric. For this calculation, we consider the teleparallel gravity analogs of the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz. We find that Einstein and Bergmann–Thomson prescriptions agree with each other and give the same results for the energy distribution in a given spacetime, but the Landau–Lifshitz complex does not. Energy density turns out to be nonvanishing in all of these prescriptions. It is interesting to mention that the results can be reduced to the already available results for the Milne universe when we write ω = 1 and Ξ² = 1 in the metric of the Lukash spacetime, and for this special case, we get the same relation among the energy–momentum formulations of Einstein, Bergmann–Thomson and Landau–Lifshitz as obtained for the Lukash spacetime. Furthermore, our results support the hypothesis by Cooperstock that the energy is confined to the region of nonvanishing energy–momentum tensor of matter and all non-gravitational fields, and also sustain the importance of the energy–momentum definitions in the evaluation of the energy distribution associated with a given spacetime.

This review gives some recollections on the recent history of the concepts of vacuum and mass and the search for higgs. According to the widely spread terminology, the Higgs field permeates vacuum and serves as the origin of masses of all fundamental particles including the Higgs boson — the higgs.

Some new results are presented and recent developments are reviewed on the study of Time in quantum physics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the Hermitian (more precisely, maximal Hermitian, but non-self-adjoint) operator for Time which appears: (i) for particles, in ordinary nonrelativistic quantum mechanics; and (ii) for photons (i.e. in first-quantization quantum electrodynamics). In conclusion, various recent and possible future applications of the time quantum analysis for tunnelling processes, nuclear collisions and systems with (quasi)discrete energy spectra are indicated.

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters: M (mass), Q (charge), a (rotation) and L (NUT). We then calculate the total exterior energy using the energy–momentum complex given by Møller in the framework of Weitzenböck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only nonvanishing components of the angular momentum is in the Z direction.

A quasilocal framework of stationary and dynamical untrapped hypersurfaces is introduced to generalize the notions of energy and angular momentum of isolated and dynamical trapping horizons to general strong gravitating systems.

We show that for every qubit of quantum information, there is a well-defined notion of "the amount of energy that carries it," because it is a conserved quantity. This generalizes to larger systems and any conserved quantities: the eigenvalue spectrum of conserved charges has to be preserved while transferring quantum information. It is possible to "apparently" violate these conservations by losing a small fraction of information, but that must invoke a specific process which requires a large scale coherence. We discuss its implication regarding the black hole information paradox.

The D-instantons in $(p,p+1)$ theory can contribute to the string effective action. The relation with the D-instanton term in Type IIB string theory will be clarified. The equation of the scalar field is projected to the two-dimensional worldsheet, on which a $(p,q)$ conformal field theory may be formulated. The energies of primary states in a minimal $(p,p+1)$ theory coupled to a $G_2$ topological string are evaluated and compared with the particle spectrum.

In this paper, using Einstein, Landau and Lifshitz's energy–momentum complexes both in general relativity and teleparallel gravity, we calculate the total energy distribution (due to matter and fields, including gravitation) associated with locally rotationally symmetric (LRS) Bianchi type II cosmological models. We show that energy densities in these different gravitation theories are the same, so they agree with each other. We obtain the result that the total energy is zero. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, Aydogdu and Saltı. Moreover, our result supports the viewpoints of Albrow and Tryon.

The Møller energy (due to matter and fields including gravity) distribution of the gamma metric is studied in teleparallel gravity. The result is the same as those obtained in general relativity by Virbhadra in the Weinberg complex and Yang–Radincshi in the Møller definition. Our result is also independent of the three teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.

We give two classes of spherically symmetric exact solutions of the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function H(R,t). The second solution depends on a constant parameter η. These solutions reproduce the same metric, i.e. the Reissner–Nordström metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition, which Møller required for a consistent energy–momentum complex, namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than for R → ∞. It is also shown that the second exact solution meets the Møller's condition.

Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild–de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild–de Sitter space–times with the cosmological parameter y = Λ M²/3 ≤ 10^-6.

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit different notions of energy as defined by different observers. As is well-known, the existence of a timelike isometry allows for the notion of total conserved energy to be well defined. We use this well-known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the $\mathrm{\Lambda }>0$ Schwarzschild–de Sitter (SdS) case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle’s total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.