The physical properties of this horizon are studied. 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. J. Together they form a unique fingerprint. It is second-order in space and time and manifestly Lorentz-covariant. Coordinate systems in De Sitter spacetime - Radboud … equation in 1926. where ψ is the Klein–Gordon field, and m is its mass. The complex conjugate of ψ is written ψ. If the scalar field is taken to be real-valued, then ψ = ψ, and it is customary to introduce a factor of 1/2 for both terms. The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. Klein-Gordon equation in curved space-time. equation The Klein-Gordon-Fock equation in the curved spacetime of the … 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. 6 CONTENTS These lectures provide an introduction to quantum eld theory on curved backgrounds. 1 #−% & ’ (% ’) #−%&) *+Φ=0 where g is the determinant of the matrix and the partial derivatives in the equations are their respectable parts of the metric. The solution of the KG equation in a … S [ φ, g μ ν] = ∫ g d 4 x ( − 1 2 g μ ν ∂ μ φ ∂ ν φ − 1 2 m 2 φ 2), since φ is just a scalar. Klein-Gordon equation in curved space-time - NASA/ADS 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 … Modified General Relativity and the Klein-Gordon Equation in … Although it turned out that modeling the electron's spin required the Dirac equation, the Klein–Gordon 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. Password requirements: 6 to 30 characters long; ASCII characters only (characters found on a standard US keyboard); must contain at least 4 different symbols; Finally we need the useful expression for the covariant divergence: ∇ μ V μ = 1 g ∂ μ ( g V μ), … Nevertheless, ultimately they are not satisfactory because they do not permit a description of fields in a principled quantum-mechanical way. The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. : 1–2 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 Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis … Klein-Gordon equation in curved space-time - CORE Reader instructors 25%. Klein Klein–Gordon equation in curved space-time - IOPscience The form of the Klein Gordon equation takes many different forms, but for the purpose of this project the equation took the form of: ! ∂ L ∂ ( ∂ μ φ) = − g g μ ν ∂ ν φ and ∂ L ∂ φ = − g m 2 φ. In Section 2, we derive the Klein-Gordon equation for free fields in a curved space time from purely geometrical considerations. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Klein-Gordon equation 100%. For simplicity, we consider the former. Very often some extra terms containing the curvature scalar Rare arbitrarily added to Equati on (23) in the literatur [14] . [1711.00735] Klein-Gordon equation in curved space-time In the rst one we give a … Progress in Physics 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). 4, we perform some simulations for confirmation of the stability and accuracy of the discretized equation. Abstract. We develop a global approach based on functional analytic methods from the theory of non-autonomous evolution equations, as developed by Kato in [24]. The Klein-Gordon-Fock equation in the curved spacetime of the … It is a quantized version of the relativistic energy–momentum relation ( | equation= ). Its theoretical relevance is similar to that of the Dirac … We summarize this paper in Sec. wave equations 18%. 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. Klein Gordon and Dirac in Curved Spacetime - [PDF Document] An evolution equation approach to the Klein Gordon operator … of an atom falling into a generic black hole Klein–Gordon equation - Wikipedia 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. event horizon 23%. 1.Quantum field theory in curved space-time: the background space-time is classical, meaning we work in zeroth order in ~. (PDF) The Klein-Gordon-Fock equation in the curved spacetime of … The solution for τ is, of course, trivial: τ = e ±iEt, and we do not consider it further. Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle … We extend the “analogue spacetime” programme by investigating a condensed-matter system that is in principle capable of simulating the massive Klein–Gordon equation in curved spacetime. 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. Furthermore, in quantum field theory, every component of every quantum field must satisfy the free Klein–Gordon equation, making the equation a generic expression of quantum fields. The Klein–Gordon equation can be generalized to describe a field in some potential V(ψ) as It was shown by some authors that the GUP gives rise to corrections to the Schrodinger , Klein-Gordon, and Dirac equations. the covariant Klein-Gordon field equation with and with-out considering conformal symmetry. The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. students 19%. The Klein-Gordon Equation Meets the Cauchy Horizon arXiv:1602.04830v2 [gr-qc] … View The Klein-Gordon equation in the spacetime of a charged and rotating black hole.pdf from MEDICAL LA 123 at Lagos State University. The Klein-Gordon-Fock equation in the curved spacetime of the … The gravitational interaction is prescribed by the metric of a spherically symmetric space-time. 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 Last Post; May 8, 2010; Replies 1 Views 2K. Vol. Solutions for the Klein–Gordon oscillator are found considering two configurations of this space-time. Abstract. The Klein-Gordon-Fock equation in the curved spacetime of the … 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. Klein-Gordon equation in curved space-time - Semantic Scholar Sort by Weight Alphabetically Physics & Astronomy. [1711.00735v1] Klein-Gordon equation in curved space-time arXiv:1709.03911v2 [math-ph] 20 Sep 2017 An Evolution Equation Approach to the Klein–Gordon Operator on Curved Spacetime Jan Derezi´nski, Daniel Siemssen Department of Mathemat 4. The Klein-Gordon equation in the spacetime of a charged and … Klein-Gordon equation in curved space time - Physics Stack … The Klein-Gordon-Fock equation in the curved spacetime of the … Upload an image to customize your repository’s social media preview. Klein-Gordon equation in curved space-time – Fingerprint — … AN EVOLUTION EQUATION APPROACH TO THE KLEIN–GORDON OPERATOR ON CURVED SPACETIME JAN DEREZINSKI´ AND DANIEL SIEMSSEN We develop a theory of the Klein–Gordon equation on curved spacetimes. The De Sitter metric is a solution for the Einstein equation with positive cosmological constant, modelling an expanding universe. What I have missed? arXiv:1312.4823v1 [gr-qc] 17 Dec 2013 The Klein-Gordon equation ... Related Threads on The gravitational Klein-Gordon Equation Newtonian limit of Gravitational Klein-Gordon Equation. Spacetime Geometry and the Laws of Physics - scirp.org Numerical simulations of semi-linear Klein-Gordon equations in … An evolution equation approach to the Klein–Gordon operator on … Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations. In the first one, the space is assumed where the metric is written in the usual inertial frame of reference. In Section 4, we discuss our results and in Section 5 we give our conclusions. You will be redirected to the full text document in the repository in a few seconds, if not click here.click here. Spacetime Geometry and the Laws of Physics In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation … Utah State University DigitalCommons@USU Math. The structure of this paper is as follows. The Klein-Gordon-Fock equation in the curved spacetime of the … This approach allows us to treat low regularity Free Scalar Fields Standard separation of variables, as Ψ = τ ( t) Rl ( r) Ylm ( θ, ) with Ylm the usual spherical harmonics, yields. The Klein–Gordon–Fock equation in the curved spacetime of the … The course is divided into three parts. 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. Klein-Gordon equation in nLab Join LiveJournal 2.Semi-classical gravity: still treat the background as classical, but now take the back-reaction into account. Images should be at least 640×320px (1280×640px for best display). Each spin has a relativistic wave equation describing the propagation of free particles. By solving the GUP corrected equations, the authors arrived at quantization not only …