# The spacetime positive mass theorem in dimensions less than eight

Michael Eichmair; Lan-Hsuan Huang; Dan A. Lee; Richard Schoen

Journal of the European Mathematical Society (2016)

- Volume: 018, Issue: 1, page 83-121
- ISSN: 1435-9855

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topEichmair, Michael, et al. "The spacetime positive mass theorem in dimensions less than eight." Journal of the European Mathematical Society 018.1 (2016): 83-121. <http://eudml.org/doc/277684>.

@article{Eichmair2016,

abstract = {We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality $E\ge \left|P\right|$ holds, where $(E,P)$ is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem [30, 27]. Instead of minimal hypersurfaces, we use marginally outer trapped hypersurfaces (MOTS) whose existence is guaranteed by earlier work of the first named author [14]. An important part of our proof is to introduce an appropriate substitute for the area functional that is used in the time-symmetric case to single out certain minimal hyper surfaces. We also establish a density theorem of independent interest and use it to reduce the general case of the spacetime positive mass theorem to the special case of initial data that has harmonic asymptotics and satisfies the strict dominant energy condition.},

author = {Eichmair, Michael, Huang, Lan-Hsuan, Lee, Dan A., Schoen, Richard},

journal = {Journal of the European Mathematical Society},

keywords = {positive mass theorem; marginally outer trapped surfaces; positive mass theorem; marginally outer trapped surfaces},

language = {eng},

number = {1},

pages = {83-121},

publisher = {European Mathematical Society Publishing House},

title = {The spacetime positive mass theorem in dimensions less than eight},

url = {http://eudml.org/doc/277684},

volume = {018},

year = {2016},

}

TY - JOUR

AU - Eichmair, Michael

AU - Huang, Lan-Hsuan

AU - Lee, Dan A.

AU - Schoen, Richard

TI - The spacetime positive mass theorem in dimensions less than eight

JO - Journal of the European Mathematical Society

PY - 2016

PB - European Mathematical Society Publishing House

VL - 018

IS - 1

SP - 83

EP - 121

AB - We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality $E\ge \left|P\right|$ holds, where $(E,P)$ is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem [30, 27]. Instead of minimal hypersurfaces, we use marginally outer trapped hypersurfaces (MOTS) whose existence is guaranteed by earlier work of the first named author [14]. An important part of our proof is to introduce an appropriate substitute for the area functional that is used in the time-symmetric case to single out certain minimal hyper surfaces. We also establish a density theorem of independent interest and use it to reduce the general case of the spacetime positive mass theorem to the special case of initial data that has harmonic asymptotics and satisfies the strict dominant energy condition.

LA - eng

KW - positive mass theorem; marginally outer trapped surfaces; positive mass theorem; marginally outer trapped surfaces

UR - http://eudml.org/doc/277684

ER -

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