arXiv subjects

Chuxiao Liu

Publications and source records attributed to Chuxiao Liu.

5 recordsLinked to original sources

arXiv2025

The Dirac and Rarita-Schwinger equations on scalar flat metrics of Taub-NUT type

We construct a scalar flat metric of Taub-NUT type whose total mass can be negative. The standard Taub-NUT metric and its negative NUT charge counterpart serve as particular examples, for which the complex 2-dimensional space of parallel spinors gives rise to $L^2$ harmonic spinors and Rarita-Schwinger fields. For the scalar flat Taub-NUT type metric, we study the Dirac and Rarita-Schwinger equations by separating them into angular and radial equations, and obtain explicit solutions in certain special cases.

math-ph↗

arXiv2025

Spherically symmetric Einstein-scalar-field equations for slowly particle-like decaying null infinity

We show that the spherically symmetric Einstein-scalar-field equations for small slowly particle-like decaying initial data at null infinity have unique global solutions.

gr-qc↗

arXiv2024

Geodesics on metrics of self-dual Taub-Nut type

Geodesic equations are solved when at least two of $τ$, $θ$, $φ$ are constant on metrics of self-dual Taub-NUT type. They can also be solved also on self-dual Taub-NUT metrics if only $r$, $θ$ or $φ$ is constant. However, the explicit solution of the geodesic equations is not available yet if only $τ$ is constant.

math.DG↗

arXiv2024

Spherically symmetric Einstein-scalar-field equations with potential for wave-like decaying null infinity

We prove the global existence and uniqueness of classical solutions with small initial data and with wake-like decaying null infinity for the spherically symmetric Einstein-scalar-field equations with potential, where the scalar potential V satisfies (1.13) and (1.14).

gr-qc↗

arXiv2022

Spherically symmetric Einstein-scalar-field equations for wave-like decaying null infinity

We show that the spherically symmetric Einstein-scalar-field equations for wave-like decaying initial data at null infinity have unique local solutions and unique global solutions for small initial data. We also generalize Christodoulou's global generalized solutions to the wave-like decaying initial data. We emphasize that this decaying condition is sharp.

gr-qc↗