klein gordon equation in curved spacetime

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Last Post; May 8, 2010; Replies 1 Views 2K. Our main tool is the method of (nonautonomous) evolution equations on Hilbert spaces. Our main goal is a construction of various kinds of propagators needed in quantum field theory. The form of the Klein Gordon equation takes many different forms, but for the purpose of this project the equation took the form of: ! 2. from the existence of a line element field $ (a^ {\beta},-a^ {\beta}) $ on a four-dimensional time oriented lorentzian manifold with metric, the klein-gordon equation in curved spacetime, $ \nabla_ {\mu}\nabla^ {\mu}\psi=k^ {2}\psi $, can be constructed from one of the pair of regular vectors in the line element field, its covariant derivative We develop a theory of the KleinGordon equation on curved spacetimes. In the rst one we give a The De Sitter metric has a coordinate sin-gularity corresponding to an event horizon. View 4 peer reviews of The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole on Publons Download Web of Science My Research Assistant : Bring the power of the Web of Science to your 5. The De Sitter metric is a solution for the Einstein equation with positive cosmological constant, modelling an expanding universe. Our main tool is the method of (nonautonomous) evolution equations on Hilbert spaces. equation, such as the KleinGordon (KG) equation or the Diracequation. The physical properties of this horizon are studied. 1 #% & (% ) #%&) *+=0 where g is the determinant of the matrix and the partial derivatives in the equations are their respectable parts of the metric. Its theoretical relevance is similar to that of the Dirac 2- Gravitation and Spacetime by Ohanian, W. W Norton & Company, 1963. p 434. Images should be at least 640320px (1280640px for best display). Topics Theories of equilibrium and non-equilibrium critical phenomena and methods to study fluctuating systems selected from the following list of topics: Percolation, scaling theory, phase transitions, Landau-Ginzburg theory, lattice models, Monte Carlo methods, renormalization group, self-organized criticality, theory of random graphs; Brownian motion, random walks and 2 and the discretized equation with SPS in Sec. For simplicity, we consider the former. It is second-order in space and time and manifestly Lorentz-covariant. Standard separation of variables, as = ( t) Rl ( r) Ylm ( , ) with Ylm the usual spherical harmonics, yields. Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of a charged, rotating Kerr-Newman-(anti) de Sitter black hole In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation We summarize this paper in Sec. EJDE-2018/17 KLEIN-GORDON EQUATION IN CURVED SPACETIME 5 with f2C1(Rn+1) is given by Yagdjian-Galstian [9, 10] as follows ( x;t) = 2e nt=2 Z t 0 db Z e b e t 0 dren 2 bv(x;r;b)E(r;t;0;b;M); (3.7) where v(x;t;b) is the solution to the following initial value problem for the wave equation v tt v= 0; v(x;0;b) = f(x;b); v t(x;0;b) = 0; (x;t) 2Rn (0;1); (3.8) where b>0. where is the KleinGordon field, and m is its mass. The complex conjugate of is written . If the scalar field is taken to be real-valued, then = , and it is customary to introduce a factor of 1/2 for both terms. Klein-Gordon equation in curved space-time. The Spacetime Structure of Open Quantum Relativity [ PDF ] Yefremov A., Smarandache F., and Christianto V. Yang-Mills Field from Quaternion Space Geometry, and its Klein-Gordon Representation [ PDF ] Panchelyuga V. A. and Shnoll S. E. On the Dependence of a Local-Time Effect on Spatial Direction [ PDF ] Panchelyuga V. A. and Shnoll S. E. The solution of the KG equation in a Furthermore, in quantum field theory, every component of every quantum field must satisfy the free KleinGordon equation, making the equation a generic expression of quantum fields. The KleinGordon equation can be generalized to describe a field in some potential V() as : 12 It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.The equation is named after Erwin Schrdinger, who postulated the equation in 1925, and published it in 1926, forming the basis Diverse theories of quantum gravity expect modifications of the Heisenberg's uncertainty principle near the Planck scale to a so-called Generalized uncertainty principle (GUP). In the first one, the space is assumed where the metric is written in the usual inertial frame of reference. The Klein-Gordon Equation in Curved Spacetime Field Quantization Relativistic Wave Equations At the present time, our best theory for describing nature is Quantum Field Theory. Password requirements: 6 to 30 characters long; ASCII characters only (characters found on a standard US keyboard); must contain at least 4 different symbols; Linear instability of the Cauchy horizon in subextremal Reissner-Nordstrm spacetime under scalar perturbations. Bug reports and feature requests link split "Always out-of-date and rarely update list of open source contributions by Ciro Santilli" 0 In Sec. In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. We report the methods and results of a computational physics project on the solution of the relativistic Klein-Gordon equation for a light particle gravitationally bound to a heavy central mass. arXiv:1602.04830v2 [gr-qc] Related Threads on The gravitational Klein-Gordon Equation Newtonian limit of Gravitational Klein-Gordon Equation. Upload an image to customize your repositorys social media preview. The Klein-Gordon equation in curved spacetime has the following form: ( + m 2) = [ 1 g ( g g ) + m 2] = 0 In the case of the Schwarzschild Metric, g 00 and g 11 are dimensionless, while g 22 and g 33 are not. S [ , g ] = g d 4 x ( 1 2 g 1 2 m 2 2), since is just a scalar. instructors 25%. physics 24%. In Section 3, we introduce interactions of the scalar field with some vector potentials. Last Post; Jun 4, 2010; Replies 3 Green's function for Klein-Gordno equation in curved spacetime. It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. You will be redirected to the full text document in the repository in a few seconds, if not click here.click here. Abstract: We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. In section 3, we have obtained the transition probabilities due to virtual transi-tion for an atom falling into the event horizon of a generic black hole metric. This approach allows us to treat low regularity of the metric, of the electromagnetic potential and of the scalar potential. Vol. Abstract. Abstract. wave equations 18%. arXiv:1709.03911v2 [math-ph] 20 Sep 2017 An Evolution Equation Approach to the KleinGordon Operator on Curved Spacetime Jan Derezinski, Daniel Siemssen Department of Mathemat In Section 2, we derive the Klein-Gordon equation for free fields in a curved space time from purely geometrical considerations. AN EVOLUTION EQUATION APPROACH TO THE KLEINGORDON OPERATOR ON CURVED SPACETIME JAN DEREZINSKI AND DANIEL SIEMSSEN We develop a theory of the KleinGordon equation on curved spacetimes. Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of an electrically charged, rotating Kerr-Newman-(anti) de Sitter black hole are investigated. L ( ) = g g and L = g m 2 . Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of a charged, rotating Kerr-Newman- (anti) de Sitter black hole are investigated. Together they form a unique fingerprint. The structure of this paper is as follows. View The Klein-Gordon equation in the spacetime of a charged and rotating black hole.pdf from MEDICAL LA 123 at Lagos State University. We develop a global approach based on functional analytic methods from the theory of non-autonomous evolution equations, as developed by Kato in [24]. What I have missed? Bosons and Fermions in Curved Spacetime Dag-Morten Sjstrm Physics Supervisor: Kre Olaussen, IFY Department of Physics J. We are not allowed to display external PDFs yet. We conclude in section 5. perturbation theory 16%. Very often some extra terms containing the curvature scalar Rare arbitrarily added to Equati on (23) in the literatur [14] . By solving the GUP corrected equations, the authors arrived at quantization not only 4. The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole Item Preview 3. Each spin has a relativistic wave equation describing the propagation of free particles. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Nevertheless, ultimately they are not satisfactory because they do not permit a description of fields in a principled quantum-mechanical way. Upload an image to customize your repositorys social media preview. The Klein-Gordon equation is generalized for curved spacetime, and solved in We report the methods and results of a computational physics project on the solution of the relativistic Klein-Gordon equation for a light particle gravitationally bound to a heavy central mass. Solutions for the KleinGordon oscillator are found considering two configurations of this space-time. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Mathematical Problems in General Relativity, Stony Brook, NY, USA. the covariant Klein-Gordon eld equation with and with-out considering conformal symmetry. Free Scalar Fields where E2 is the separation constant, chosen such that E is the total energy and E E m, the binding energy. equation in 1926. 6 CONTENTS These lectures provide an introduction to quantum eld theory on curved backgrounds. The KleinGordon equation (KleinFockGordon equation or sometimes KleinGordonFock equation) is a relativistic wave equation, related to the Schrdinger equation.It is second-order in space and time and manifestly Lorentz-covariant.It is a quantized version of the relativistic energymomentum relation (= + ()).Its solutions include a quantum scalar or pseudoscalar Then. It is a quantized version of the relativistic energymomentum relation ( | equation= ). The course is divided into three parts. Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle Sort by Weight Alphabetically Physics & Astronomy. We extend the 'analogue spacetime' program by investigating a condensed-matter system that is in principle capable of simulating the massive Klein-Gordon equation in curved spacetime. students 19%. We review the canonical equation of the Klein-Gordon equation in the de Sitter spacetime in Sec. Klein-Gordon equation in curved space-time. event horizon 23%. 2.Semi-classical gravity: still treat the background as classical, but now take the back-reaction into account. In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and Exact solutions of the KleinGordonFock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of an electrically charged, rotating KerrNewman (anti) de Sitter black hole are investigated. gx g x( )=det( )(22 ) It leads to the Klein Gordon equation ( )22 2 1 0 mc gg g + = 23 ) ( in curved space times. We extend the analogue spacetime programme by investigating a condensed-matter system that is in principle capable of simulating the massive KleinGordon equation in curved spacetime. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. Energy dispersed large energy solutions to the (4+1) dimensional Maxwell-Klein-Gordon equation, with D. Tataru, Amer. In section 4, we obtained the HBAR entropy for the GHS black hole. View The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter BH.pdf from SCIENCE 234 at Lagos State University. Images should be at least 640320px (1280640px for best display). We ignore the back-reaction of the matter on space-time. arXiv:1312.4823v1 [gr-qc] 17 Dec 2013 The Klein-Gordon equation 1.Quantum eld theory in curved space-time: the background space-time is classical, meaning we work in zeroth order in ~. The KleinGordon equation (KleinFockGordon equation or sometimes KleinGordonFock equation) is a relativistic wave equation, related to the Schrdinger equation. Math. 140 (2018), no. Dive into the research topics of 'Klein-Gordon equation in curved space-time'. In Section 4, we discuss our results and in Section 5 we give our conclusions. We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. The Klein-Gordon equation is the linear partial differential equation which is the equation of motion of a free scalar field of possibly non-vanishing mass m on some (possibly curved) spacetime ( Lorentzian manifold ): it is the relativistic wave equation with inhomogeneity the mass m2. Metrics are considered for an impenetrable sphere, a soft sphere of uniform density, and a soft sphere However, in the equation we need every term to have the same dimensions. For the lowest three This paper is devoted to the study of the KleinGordon equation on a rather general (non-static) spacetime. Since many elementary particles have mass, this is an We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. Klein-Gordon equation 100%. The solution for is, of course, trivial: = e iEt, and we do not consider it further. The Klein-Gordon and Dirac equations, resulting from the search for relativistic analogues of the Schrdinger equation in the 1920s, do respect the requirement of Lorentz invariance. Finally we need the useful expression for the covariant divergence: V = 1 g ( g V ), Although it turned out that modeling the electron's spin required the Dirac equation, the KleinGordon equation correctly describes the spinless relativistic composite particles, like the pion. On 4 July 2012, European Organization for Nuclear Research CERN announced the discovery of the Higgs boson. Furthermore, any component of any solution to the free Dirac equation (for a spin-1/2 particle) is automatically a solution to the free KleinGordon equation. This generalizes to particles of any spin due to the BargmannWigner equations. Abstract. 4, we perform some simulations for confirmation of the stability and accuracy of the discretized equation. The Schrdinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. We solve the relativistic Klein--Gordon equation for a light particle gravitationally bound to a heavy central mass, with the gravitational interaction prescribed by the metric of a spherically symmetric space-time. This approach allows us to treat low regularity