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Dinesh Singh

Publications and source records attributed to Dinesh Singh.

At least 55 records · Page 3Linked to original sources
arXiv2010

Tidal Dynamics in Cosmological Spacetimes

We study the relative motion of nearby free test particles in cosmological spacetimes, such as the FLRW and LTB models. In particular, the influence of spatial inhomogeneities on local tidal accelerations is investigated. The implications of our results for the dynamics of the solar system are briefly discussed. That is, on the basis of the models studied in this paper, we estimate the tidal influence of the cosmic gravitational field on the orbit of the Earth around the Sun and show that the corresponding temporal rate of variation of the astronomical unit is negligibly small.

gr-qc↗
arXiv2010

Breakdown of Casimir Invariance in Curved Space-Time

It is shown that the commonly accepted definition for the Casimir scalar operators of the Poincare group does not satisfy the properties of Casimir invariance when applied to the non-inertial motion of elementary particles while in the presence of external gravitational and electromagnetic fields, where general curvilinear co-ordinates are used to describe the momentum generators within a Fermi normal co-ordinate framework. Specific expressions of the Casimir scalar properties are presented for spin-1/2 to spin-2 particles inclusive. While the Casimir scalar for linear momentum remains a Lorentz invariant in the absence of external fields, this is no longer true for the spin Casimir scalar. Potential implications are considered for the propagation of photons, gravitons, and gravitinos as described by the spin-3/2 Rarita-Schwinger vector-spinor field. In particular, it is shown that non-inertial motion introduces a frame-based effective mass to the spin interaction, with interesting physical consequences that are explored in detail.

hep-th↗
arXiv2010

Is There an Observable Limit to Lorentz Invariance at the Compton Wavelength Scale?

The possibility of a frame-induced violation of Lorentz invariance due to non-inertial spin-1/2 particle motion is explored in detail for muon decay while in orbit near the event horizon of a microscopic Kerr black hole. It is explicitly shown that kinematic and curvature contributions to the muon's decay spectrum--in the absence of any unforeseen processes due to quantum gravity--lead to its stabilization at the muon's Compton wavelength scale. This example is emblematic of the search for unambiguous indicators to critically assess current and future approaches to quantum gravity research.

hep-th↗
arXiv2009

A Finite Multiplicity Helson-Lowdenslager-De Branges Theorem

This paper proves two theorems. The first of these simplifies and lends clarity to the previous characterizations of the invariant subspaces of $S$, the operator of multiplication by the coordinate function $z$, on $L^2(\mathbb{T};\mathbb{C}^n)$, where $\mathbb{T}$ is the unit circle, by characterizing the invariant subspaces of $S^n$ on scalar valued $L^p$ ($0<p\le\infty$) thereby eliminating range functions and partial isometries. It also gives precise conditions as to when the operator shall be a pure shift and describes the precise nature of the wandering vectors and the doubly invariant subspaces. The second theorem describes the contractively contained Hilbert spaces in $L^p$ that are simply invariant under $S^n$ thereby generalizing the first theorem.

math.FA↗
arXiv2009

Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung

This paper investigates the properties of spin-1/2 particle Zitterbewegung in the presence of a general curved space-time background described in terms of Fermi normal co-ordinates, where the spatial part is expressed using general curvilinear co-ordinates. Adopting the approach first introduced by Barut and Bracken for Zitterbewegung in the local rest frame of the particle, it is shown that non-trivial gravitational contributions to the relative position and momentum operators appear due to the coupling of Zitterbewegung frequency terms with the Ricci curvature tensor in the Fermi frame, indicating a formal violation of the weak equivalence principle. Explicit expressions for these contributions are shown for the case of quasi-circular orbital motion of a spin-1/2 particle in a Vaidya background. Formal expressions also appear for the time-derivative of the Pauli-Lubanski vector due to space-time curvature effects coupled to the Zitterbewegung frequency. As well, the choice of curvilinear co-ordinates results in non-inertial contributions in the time evolution of the canonical momentum for the spin-1/2 particle, where Zitterbewegung effects lead to stability considerations for its propagation, based on the Floquet theory of differential equations.

gr-qc↗
arXiv2009

Breakdown of Lorentz Invariance for Spin-1/2 Particle Motion in Curved Space-Time with Applications to Muon Decay

This paper explores the properties of the Pauli-Lubanski spin vector for the general motion of spin-1/2 particles in curved space-time. Building upon previously determined results in flat space-time, it is shown that the associated Casimir scalar for spin possesses both gravitational contributions and frame-dependent contributions due to non-inertial motion, where the latter represents a possible quantum violation of Lorentz invariance that becomes significant at the Compton wavelength scale. When applied to muon decay near the event horizon of a microscopic Kerr black hole, it is shown that its differential cross section is strongly affected by curvature, with particular sensitivity to changes in the black hole's spin angular momentum. In the absence of curvature, the non-inertial contributions to the decay spectrum are also identified and explored in detail, where its potential for observation is highest for large electron opening angles. It is further shown how possible contributions to noncommutative geometry can emerge from within this formalism at some undetermined length scale. Surprisingly, while the potential exists to identify noncommutative effects in muon decay, the relevant terms make no contribution to the decay spectrum, for reasons which remain unknown.

gr-qc↗
arXiv2009

Signatures of Noncommutative Geometry in Muon Decay for Nonsymmetric Gravity

It is shown how to identify potential signatures of noncommutative geometry within the decay spectrum of a muon in orbit near the event horizon of a microscopic Schwarzschild black hole. This possibility follows from a re-interpretation of J.W. Moffat's nonsymmetric theory of gravity, first published in Phys. Rev. D 19, 3554 (1979), where the antisymmetric part of the metric tensor manifests the hypothesized noncommutative geometric structure throughout the manifold. It is further shown that for a given sign convention, the predicted signatures counteract the effects of curvature-induced muon stabilization predicted by D. Singh and N. Mobed in Phys. Rev. D 79, 024026 (2009). While it is unclear whether evidence for noncommutative geometry may be found at the Large Hadron Collider (LHC) anytime soon, this approach at least provides a useful direction for future quantum gravity research based on the ideas presented here.

gr-qc↗
arXiv2008

Perturbation Method for Classical Spinning Particle Motion: II. Vaidya Space-Time

This paper describes an application of the Mathisson-Papapetrou-Dixon (MPD) equations in analytic perturbation form to the case of circular motion around a radially accreting or radiating black hole described by the Vaidya metric. Based on the formalism presented earlier, this paper explores the effects of mass accretion or loss of the central body on the overall dynamics of the orbiting spinning particle. This includes changes to its squared mass and spin magnitude due to the classical analog of radiative corrections from spin-curvature coupling. Various quantitative consequences are explored when considering orbital motion near the black hole's event horizon. An analysis on the orbital stability properties due to spin-curvature interactions is examined briefly, with conclusions in general agreement with previous work performed for the case of circular motion around a Kerr black hole.

gr-qc↗
arXiv2008

Perturbation Method for Classical Spinning Particle Motion: I. Kerr Space-Time

This paper presents an analytic perturbation approach to the dynamics of a classical spinning particle, according to the Mathisson-Papapetrou-Dixon (MPD) equations of motion, with a direct application to circular motion around a Kerr black hole. The formalism is established in terms of a power series expansion with respect to the particle's spin magnitude, where the particle's kinematic and dynamical degrees are expressed in a completely general form that can be constructed to infinite order in the expansion parameter. It is further shown that the particle's squared mass and spin magnitude can shift due to a classical analogue of radiative corrections that arise from spin-curvature coupling. Explicit expressions are determined for the case of circular motion near the event horizon a Kerr black hole, where the mass and spin shift contributions are dependent on the initial conditions of the particle's spin orientation. A preliminary analysis of the stability properties of the orbital motion in the Kerr background due to spin-curvature interactions is explored and briefly discussed.

gr-qc↗
arXiv2008

An Analytic Perturbation Approach for Classical Spinning Particle Dynamics

A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson-Papapetrou-Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle's spin magnitude, it is shown how to obtain in general form an analytic representation of the particle's kinematic and dynamical degrees of freedom that is formally applicable to infinite order in the expansion. Within this formalism, it is possible to identify a classical analogue of radiative corrections to the particle's mass and spin due to spin-gravity interaction. The robustness of this approach is demonstrated by showing how to explicitly compute the first-order momentum and spin tensor components for arbitrary particle motion in a general space-time background. Potentially interesting applications based on this perturbation approach are outlined.

gr-qc↗
arXiv2007

A Constrained Nevanlinna-Pick Interpolation Problem

We obtain necessary and sufficient conditions for Nevanlinna-Pick interpolation on the unit disk with the additional restriction that all analytic interpolating functions satisfy $f'(0)=0.$ Alternatively, these results can be interpreted as interpolation results for $H^{\infty}(V),$ where $V$ is the intersection of the bidisk with an algebraic variety. We use an analysis of C*-envelopes to show that these same conditions do not suffice for matrix interpolation.

math.OA↗
arXiv2007

The implications of noninertial motion on covariant quantum spin

It is shown that the Pauli-Lubanski spin vector defined in terms of curvilinear co-ordinates does not satisfy Lorentz invariance for spin-1/2 particles in noninertial motion along a curved trajectory. The possibility of detecting this violation in muon decay experiments is explored, where the noninertial contribution to the decay rate becomes large for muon beams with large momenta and trajectories with radius of curvature approaching the muon's Compton wavelength scale. A new spacelike spin vector is derived from the Pauli-Lubanski vector that satisfies Lorentz invariance for both inertial and noninertial motion. In addition, this spin vector suggests a generalization for the classification of spin-1/2 particles, and has interesting properties that are applicable for both massive and massless particles.

hep-th↗
arXiv2006

Dynamics of Extended Spinning Masses in a Gravitational Field

We develop a first-order approximation method for the influence of spin on the motion of extended spinning test masses in a gravitational field. This approach is illustrated for approximately circular equatorial motion in the exterior Kerr spacetime. In this case, the analytic results for the first-order approximation are compared to the numerical integration of the exact system and the limitations of the first-order results are pointed out. Furthermore, we employ our analytic results to illustrate the gravitomagnetic clock effect for spinning particles.

astro-ph↗
arXiv2006

Can Gravity Distinguish Between Dirac and Majorana Neutrinos?

We show that spin-gravity interaction can distinguish between Dirac and Majorana neutrino wave packets propagating in a Lense-Thirring background. Using time-independent perturbation theory and gravitational phase to generate a perturbation Hamiltonian with spin-gravity coupling, we show that the associated matrix element for the Majorana neutrino differs significantly from its Dirac counterpart. This difference can be demonstrated through significant gravitational corrections to the neutrino oscillation length for a two-flavour system, as shown explicitly for SN1987A.

gr-qc↗
arXiv2006

The Distinction Between Dirac and Majorana Neutrino Wave Packets Due to Gravity and Its Impact on Neutrino Oscillations

We present the possibility that Dirac and Majorana neutrino wave packets can be distinguished when subject to spin-gravity interaction while propagating through vacuum described by the Lense-Thirring metric. By adopting the techniques of gravitational phase and time-independent perturbation theory following the Brillouin-Wigner method, we generate spin-gravity matrix elements from a perturbation Hamiltonian and show that this distinction is easily reflected in well-defined gravitational corrections to the neutrino oscillation length for a two-flavour system. Explicit examples are presented using the Sun and SN1987A as the gravitational sources for the Lense-Thirring metric. This approach offers the possibility to determine the absolute neutrino masses by this method and identify a theoretical upper bound for the absolute neutrino mass difference, where the distinctions between the Dirac and Majorana cases are evident. We discuss the relevance of this analysis to the upcoming attempts to measure the properties of low-energy neutrinos by SNO and other solar neutrino observatories.

gr-qc↗
arXiv2005

The Dynamics of a Classical Spinning Particle in Vaidya Space-Time

Based on the Mathisson-Papapetrou-Dixon (MPD) equations and the Vaidya metric, the motion of a spinning point particle orbiting a non-rotating star while undergoing radiation-induced gravitational collapse is studied in detail. A comprehensive analysis of the orbital dynamics is performed assuming distinct central mass functions which satisfy the weak energy condition, in order to determine a correspondence between the choice of mass function and the spinning particle's orbital response, as reflected in the gravitational waves emitted by the particle. The analysis presented here is likely most beneficial for the observation of rotating solar mass black holes or neutron stars in orbit around intermediate-sized Schwarzschild black holes undergoing radiation collapse. The possibility of detecting the effects of realistic mass accretion based on this approach is considered. While it seems unlikely to observe such effects based on present technology, they may perhaps become observable with the advent of future detectors.

gr-qc↗