Monotonicity of Causal Killing Vectors and Geometry of ADM Mass Minimizers

2025/10/11 by Hirsch, Sven, Huang, Lan-Hsuan
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2510.10306

Abstract

We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed into strongly stationary vacuum spacetimes, thereby confirming the Bartnik stationary vacuum conjecture. A key ingredient is a new monotonicity formula for the Lorentzian length of a causal Killing vector field, which, among other applications, yields a strong maximum principle for the length.

Citations

• Regularity and temperature of stationary black hole event horizons
• Initial data sets with vanishing mass are contained in pp-wave spacetimes
• Equality in the spacetime positive mass theorem II
• The case of equality for the spacetime positive mass theorem
• Scalar curvature deformation and mass rigidity for ALH manifolds with boundary
• Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
• Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations
• Ellipticity of Bartnik boundary data for stationary vacuum spacetimes
• Phase space for the Einstein equations
• Mass and 3-metrics of non-negative scalar curvature
• On the Asymptotics for the Vacuum Einstein Constraint Equations
• Regularity of Horizons and The Area Theorem
• A new proof of the positive energy theorem
• On the proof of the positive mass conjecture in general relativity

Related

• Bartnik mass minimizing initial data sets and improvability of the dominant energy scalar
• On mass-minimizing extensions of Bartnik boundary data
• Proof of Positivity of Mass for Maximally Sliced, Asymptotically Flat Spacetimes
• The spacetime positive mass theorem in dimensions less than eight
• Equality in the spacetime positive mass theorem II