Cosmic no‐hair conjecture and conformal vector fields

Seungsu Hwang and Gabjin Yun

Mathematische Nachrichten, 2025, vol. 298, issue 9, 3061-3074

Abstract: In this paper, we investigate cosmic no‐hair properties mathematically when a given Riemannian manifold admits a nontrivial closed conformal vector field. Let (Mn,g)$(M^n, g)$ be a compact Riemannian n$n$‐manifold with connected non‐empty boundary ∂M$\partial M$. Assume that there exists a smooth function f$f$ on M$M$ with f>0$f>0$ in M∖∂M$M \setminus \partial M$ and ∂M=f−1(0)$\partial M = f^{-1}(0)$ satisfying the static vacuum equation. We prove that if (Mn,g)$(M^n, g)$ admits a nontrivial closed conformal vector field, then M$M$ must be isometric to a hemisphere S+n${\mathbb {S}}_+^n$. We also discuss a static triple (Mn,g,f)$(M^n, g, f)$ admitting a nontrivial conformal vector field which is not necessarily closed.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.70025

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:298:y:2025:i:9:p:3061-3074

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().