Spinning Particles in Curved Spacetime

We briefly discuss the relevant equations for the motion of spinning particles in curved spacetime. We describe the generalized Killing equations for spinning spaces and derive the constants of motion. We apply the formalism to solve for the motion of a pseudoclassical spinning particle in Schwarzschild–de Sitter spacetime.     

Spinning Particles in Reissner-Nordström-de Sitter Spacetime

We study the geodesic motion of pseudo-classical spinning particles in the Reissner-Nordström-de Sitter spacetime. We investigate the generalized Killing equations for spinning space and derive the constants of motion in terms of the solutions of these equations. We discuss bound state orbits in a plane.     

Stochastic Spacetime and Brownian Motion of Test Particles

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus, one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena that can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.     

The Motion of Spinning Particles in the Spacetime of a Black Hole with a Cosmic String Topological Defect

The geodesic motion of pseudo-classical spinning particles in the spacetime of a black hole with the topological defect of a cosmic string, is analyzed. The constants of motion are derived in terms of solving the generalized killing equations for spinning space. The bound state orbits in a plane are discussed. Our results are permitted to be regarded as a semiclassical approximation to the quantum Dirac theory which holds to first order in the spin. The existence of the cosmic string factor b distinguishes the case from the one in Schwarzschild spacetime. When one chooses b = 1, our results reduce to the case of the Schwarzschild spacetime.     

Observers in Kerr spacetimes: the ergoregion on the equatorial plane

We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between “weak” and “strong ” singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak singularities as resulting from the spin variation of black holes. We also explore the main properties of zero angular momentum observers for different classes of black hole and naked singularity spacetimes.     

Spinning Particles in Spacetimes with Torsion

A novel analysis of the Mathisson-Papapetrou-Dixon equations is presented employing mathematical tools that do not rely on the torsion free geometries used in previous literature. A system of differential algebraic equations that can be used to describe the motion of spinning particles in an arbitrary geometry is derived. The curvature in these equations can involve non-Riemannian contributions. Subsequently, this particular system of equations can accommodate modification to geodesic motion from both scalar fields and the spin of the particle. PACS: 02.40.Hw, 04.20.Cv, 04.40.Nr     

Spacetime Quantization, Elementary Particles, and Cosmology

Relativistic quantum mechanics is generalized to account for a universally constant quantum of length a. Its value depends on the total convertible energy content of our universe: E_u = hc/2a. The eigenvalues of all (x,y,z,ct) coordinates are integer or half-integer multiples of a in every particular inertial frame. There are thus several spacetime lattices of lattice-constant a: the normal lattice contains the origin of the chosen frame, while inserted lattices are displaced by a/2 along one or several reference axes. States of motion are defined by possible variations of -functions on any one of these lattices. Particle states are defined by their relative phases, specified by four new quantum numbers, u_x, u_y, u_z, u_ct = 0, ±1, ±2,.... They account for all known elementary particles and yield a natural extension of the standard model. Spacetime quantization solves also the EPR paradox and other difficulties that subsisted in the usual continuum theories. It defines inertial frames and is related to cosmology.     

Particles and Scalar Waves in Noncommutative Charged Black Hole Spacetime

In this paper we have discussed geodesics and the motion of test particle in the gravitational field of noncommutative charged black hole spacetime. The motion of massive and massless particle have been discussed seperately. A comparative study of noncommutative charged black hole and usual Reissner—Nordström black hole has been done. The study of effective potential has also been included. Finally, we have examined the scattering of scalar waves in noncommutative charged black hole spacetime.     

Particles and Scalar Waves in Noncommutative Charged Black Hole Spacetime

In this paper we have discussed geodesics and the motion of test particle in the gravitational field of noncommutative charged black hole spacetime. The motion of massive and massless particle have been discussed seperately.A comparative study of noncommutative charged black hole and usual Reissner–Nordstr¨om black hole has been done.The study of effective potential has also been included. Finally, we have examined the scattering of scalar waves in noncommutative charged black hole spacetime.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

Gravity as Spacetime Curvature

Einstein's general theory of relativity conceives the phenomena of gravity as manifestations of the curvature of the spacetime manifold in which physical events take place. I sketch the line of thought that led Einstein to this conception, and I briefly discuss proposals by Jeffreys and Feynman for retaining Einstein's gravitational field equations while discarding their purportedly geometrical meaning.     

Faraday Tensor for Time-Smarandache TN Particles Around Biharmonic Particles and its Lorentz Transformations in Heisenberg Spacetime

In this paper, we characterize time-Smarandache particle around timelike biharmonic particle in \(\mathcal {H}_{1}^{4}.\) Moreover, we obtain Lorentz transformations this particles. Finally, we construct electric and magnetic fields of time-Smarandache particle with constant curvature.     

Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings

The idea that spacetime has to be replaced by Clifford space (C-space) is explored. Quantum field theory (QFT) and string theory are generalized to C-space. It is shown how one can solve the cosmological constant problem and formulate string theory without central terms in the Virasoro algebra by exploiting the peculiar pseudo-Euclidean signature of C-space and the Jackiw definition of the vacuum state. As an introduction into the subject, a toy model of the harmonic oscillator in pseudo-Euclidean space is studied.