Research
Peer-reviewed work in general relativity, quantum gravity and kinetic theory. Open an abstract to read it in place, or view and download the PDF.
Publications
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Kinetic theory of stimulated Brillouin scattering with velocity-dependent collisional relaxation
Abstract
In this work, we develop a kinetic theory of stimulated Brillouin scattering (SBS) based on a generalized Bhatnagar-Gross-Krook (BGK) model incorporating a velocity-dependent collision frequency. Starting from the Boltzmann equation, we derive an analytic expression for the SBS gain coefficient that explicitly captures the coupling between velocity-dependent relaxation and acoustic response. We show that this modification leads to a systematic reshaping of the gain spectrum, including broadening, peak enhancement, and pressure-dependent frequency shifts that are not captured by conventional BGK theory. Our results demonstrate improved agreement with experimentally measured gain coefficients, identifying velocity-resolved relaxation as a key physical mechanism underlying SBS in rarefied and intermediate collisional regimes. This framework provides a physically grounded extension of kinetic SBS theory and introduces a parameter for controlling and optimizing Brillouin gain in high-power laser systems.
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Unified Microscopic Foundations of the Quantum Boltzmann Equation
Abstract
The quantum Boltzmann equation (QBE), originally formulated as the quantum extension of Boltzmann's classical transport theory by Uehling and Uhlenbeck and subsequently developed within the nonequilibrium Green-function formalisms of Kadanoff–Baym and Keldysh, provides the central kinetic framework for describing relaxation and transport in weakly interacting quantum many-body systems. Although its formal structure is well established, conventional derivations often obscure the microscopic equivalence between operator and nonequilibrium Green-function approaches. Wick factorization is typically applied without explicitly enumerating real-time contractions, while Green-function treatments encode the same physics in Born-level self-energies that conceal their operator origin. In this paper, we present a pedagogical microscopic derivation of the quantum Boltzmann equation that makes this equivalence fully explicit. Starting from the ladder-operator formulation, we enumerate all fifteen Wick pairings of the second-order six-field correlator, identifying three Hartree–Fock contributions and twelve real-time Born scattering channels generated by a quartic, number-conserving interaction Hamiltonian. We then establish a one-to-one correspondence between these twelve operator contractions and the Keldysh components of the second-order Born self-energy, demonstrating explicitly how the Uehling–Uhlenbeck collision integral emerges after Wigner transformation and quasiparticle projection. Under controlled Born–Markov and quasiparticle approximations, this work offers a transparent synthesis of operator and Green-function formulations, and clarifies how kinetic fluctuations can be understood as emergent under coarse-graining.
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Erratum: “Unified Microscopic Foundations of the Quantum Boltzmann Equation”
Summary
We have identified sign- and factor-level errors in the intermediate steps of the Green-function derivation of Sec. 3, together with a factor-of-two error in the Markov step of Appendix A that propagated into the coefficient of the final rate expressions. All equation, figure, and page numbers below refer to the published article. None of the corrections affects the structure of the Uehling–Uhlenbeck collision integral, the quantum-statistical factors, the equilibrium solutions, the H-theorem, or any conclusion of the article.
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The Validity of the Ehrenfest Theorem in Quantum Gravity Theory
Abstract
The Ehrenfest theorem is a well-known theoretical result of quantum mechanics. It relates the dynamical evolution of the expectation value of a quantum operator to the expectation value of its corresponding commutator with the Hermitian Hamiltonian operator. However, the proof of validity of the Ehrenfest theorem for quantum gravity field theory has remained elusive, while its validation poses challenging conceptual questions. In fact, this presupposes a number of minimum requirements, which include the prescription of quantum Hamiltonian operator, the definition of scalar product, and the identification of dynamical evolution parameter. In this paper, it is proven that the target can be established in the framework of the manifestly covariant quantum gravity theory (CQG theory). This follows as a consequence of its peculiar canonical Hamiltonian structure and the commutator-bracket algebra that characterizes its representation and probabilistic interpretation. The theoretical proof of the theorem for CQG theory permits to elucidate the connection existing between quantum operator variables of gravitational field and the corresponding expectation values to be interpreted as dynamical physical observables set in the background metric space-time.
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An Intrinsic Coordinate Reference Frame Procedure I: Tensorial Canonical Weyl Scalars
Abstract
The canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space time into a 3 + 1 formalism. Such a simplification appears to come at the cost of general covariance. This quantization procedure requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as “intrinsic coordinates” (or a dynamical reference frame) that depend only on the spatial metric (gab) and the conjugate momenta (pcd), allows for an alternative approach to canonical quantization of gravity. In this paper, we present the tensorial solution of the set of Weyl scalars in terms of canonical phase-space variables.
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An Invariant Characterization of the Levi-Civita Spacetimes
Abstract
In the years 1917–1919 Tullio Levi-Civita published a number of papers presenting new solutions to Einstein's equations. This work, while partially translated, remains largely inaccessible to English speaking researchers. In this paper we review these solutions, and present them in a modern readable manner. We will also compute both Cartan–Karlhede and Carminati–McLenaghan invariants such that these solutions are invariantly characterized by two distinct methods. These methods will allow for these solutions to be totally and invariantly characterized. Because of the variety of solutions considered here, this paper will also be a useful reference for those seeking to learn to apply the Cartan–Karlhede algorithm in practice.
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Curvature Invariants for the Accelerating Natário Warp Drive
Abstract
A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants—the Ricci scalar, r1, r2, and w2. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natário warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble.
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Curvature Invariants for Lorentzian Traversable Wormholes
Abstract
The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).
Projects
Ongoing computational work lives on the Simulations and Modules pages.