scholarly journals Quantum Probes of Timelike Naked Singularities in2+1-Dimensional Power-Law Spacetimes

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
O. Gurtug ◽  
M. Halilsoy ◽  
S. Habib Mazharimousavi
Keyword(s):  
Quantum Mechanics ◽  
Scalar Field ◽  
Electric Field ◽  
Power Law ◽  
Energy Conditions ◽  
Naked Singularities ◽  
Real Scalar ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Scalar Theories

The formation of naked singularities in2+1-dimensional power-law spacetimes in linear Einstein-Maxwell and Einstein-scalar theories sourced by azimuthally symmetric electric field and a self-interacting real scalar field, respectively, are considered in view of quantum mechanics. Quantum test fields obeying the Klein-Gordon and Dirac equations are used to probe the classical timelike naked singularities developed atr=0. We show that when the classically singular spacetimes probed with scalar waves, the considered spacetimes remain singular. However, the spinorial wave probe of the singularity in the metric of a self-interacting real scalar field remains quantum regular. The notable outcome in this study is that the quantum regularity/singularity cannot be associated with the energy conditions.

scholarly journals QUANTUM SINGULARITIES IN STATIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER
Keyword(s):  
Quantum Mechanics ◽  
Wave Operator ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Mathematical Framework ◽  
Physical Content ◽  
Dirac Equations ◽  
Quantum Particles ◽  
Klein Gordon ◽  
Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

Real scalar field solutions of the EKG equations including matter

2020 ◽  
pp. 2150009
Author(s):  
A. Cabo Montes de Oca ◽  
D. Suarez Fontanella
Keyword(s):  
Dark Matter ◽  
Gravitational Field ◽  
Scalar Field ◽  
Scalar Fields ◽  
Stationary Solutions ◽  
Field Interaction ◽  
Small Bodies ◽  
Real Scalar ◽  
Static Solutions ◽  
Klein Gordon

Static (not stationary) solutions of the Einstein–Klein–Gordon (EKG) equations including matter are obtained for real scalar fields. The scalar field interaction with matter is considered. The introduced coupling allows the existence of static solutions in contraposition with the case of the simpler EKG equations for real scalar fields and gravity. Surprisingly, when the considered matter is a photon-like gas, it turns out that the gravitational field intensity at large radial distances becomes nearly a constant, exerting an approximately fixed force to small bodies at any distance. The effect is clearly related with the massless character of the photon-like field. It is also argued that the gravitational field can generate a bounding attraction, that could avoid the unlimited increase in mass with the radius of the obtained here solution. This phenomenon, if verified, may furnish a possible mechanism for explaining how the increasing gravitational potential associated to dark matter, finally decays at large distances from the galaxies. A method for evaluating these photon bounding effects is just formulated in order to be further investigated.

CREATION OF SCALAR AND DIRAC PARTICLES IN THE PRESENCE OF A TIME VARYING ELECTRIC FIELD IN AN ANISOTROPIC UNIVERSE

2002 ◽  
Vol 17 (20) ◽  
pp. 2781-2781
Author(s):  
VÍCTOR M. VILLALBA
Keyword(s):  
Electric Field ◽  
Particle Distribution ◽  
Anisotropic Universe ◽  
Homogeneous Electric Field ◽  
Dirac Equations ◽  
Dirac Particles ◽  
Electric Interaction ◽  
Quasiclassical Limit ◽  
Klein Gordon ◽  
Hamilton Jacobi Equation

We compute the density of scalar and Dirac particles created by a cosmological anisotropic universe1,2 in the presence of a time dependent homogeneous electric field. In order to compute the rate of particles created we apply a quasiclassical approach that has been used successfully in different scenarios3,4. The idea behind the method is the following: First, we solve the relativistic Hamilton-Jacobi equation and, looking at its solutions, we identify positive and negative frequency modes. Second, after separating variables5,6, we solve the Klein-Gordon and Dirac equations and, after comparing with the results obtained for the quasiclassical limit, we identify the positive and negative frequency states. We show that the particle distribution becomes thermal when one neglects the electric interaction.

scholarly journals Cosmological reconstruction and energy constraints in generalized Gauss–Bonnet-scalar–kinetic–matter couplings

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Adam Z. Kaczmarek ◽  
Dominik Szczęśniak
Keyword(s):  
Scalar Field ◽  
Perfect Fluid ◽  
Power Law ◽  
Cosmological Models ◽  
Energy Conditions ◽  
Kinetic Term ◽  
De Sitter ◽  
Field Equations ◽  
Energy Constraints ◽  
Matter Fields

Abstract Recently introduced $$f(\mathcal {G},T)$$ f ( G , T ) theory is generalized by adding dependence on the arbitrary scalar field $$\phi $$ ϕ and its kinetic term $$(\nabla \phi )^2$$ ( ∇ ϕ ) 2 , to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss–Bonnet theories. The field equations for the resulting $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime are discussed for the generic function $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T . As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed $$f\left( \mathcal {G},\phi ,(\nabla \phi )^2,T\right) $$ f G , ϕ , ( ∇ ϕ ) 2 , T gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the $$f\left( \mathcal {G},\phi ,T\right) $$ f G , ϕ , T case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the $$f(R,\phi ,(\nabla \phi )^2)$$ f ( R , ϕ , ( ∇ ϕ ) 2 ) and $$f=\gamma (\phi ,X)\mathcal {G}+\mu T^{1/2}$$ f = γ ( ϕ , X ) G + μ T 1 / 2 approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.

scholarly journals Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale

2016 ◽  
Vol 31 (17) ◽  
pp. 1650096 ◽  
Author(s):  
Apollo V. Silva ◽  
E. M. C. Abreu ◽  
M. J. Neves
Keyword(s):  
Scalar Field ◽  
Quantum Electrodynamics ◽  
Minimal Length ◽  
Length Scale ◽  
Field Equations ◽  
Self Energy ◽  
Dirac Equations ◽  
Minimal Length Scale ◽  
Klein Gordon ◽  
The Green Function

The main motivation to study models in the presence of a minimal length is to obtain a quantum field theory free of the divergences. In this way, in this paper, we have constructed a new framework for quantum electrodynamics embedded in a minimal length scale background. New operators are introduced and the Green function method was used for the solution of the field equations, i.e. the Maxwell, Klein–Gordon and Dirac equations. We have analyzed specifically the scalar field and its one loop propagator. The mass of the scalar field regularized by the minimal length was obtained. The QED Lagrangian containing a minimal length was also constructed and the divergences were analyzed. The electron and photon propagators, and the electron self-energy at one loop as a function of the minimal length was also obtained.

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