dc.contributor.author |
Cap, Andreas |
|
dc.contributor.author |
Gover, A Rod |
|
dc.date.accessioned |
2021-10-10T21:54:26Z |
|
dc.date.available |
2021-10-10T21:54:26Z |
|
dc.identifier.citation |
Arxiv (2108.01373). 03 Aug 2021. 33 pages |
|
dc.identifier.uri |
https://hdl.handle.net/2292/56893 |
|
dc.description.abstract |
We construct a cocycle that, for a given $n$-manifold, maps pairs of
asymptotically locally hyperbolic (ALH) metrics to a tractor-valued
$(n-1)$-form field on the conformal infinity. This describes, locally on the
boundary, a relative mass difference between the pairs of ALH metrics, where
the latter are required to be asymptotically related to a given order that
depends on the dimension. It is distinguished as a geometric object by its
property of being invariant under suitable diffeomorphisms fixing the boundary,
and that act on (either) one of the argument metrics.
Specialising to the case of an ALH metric $h$ that is suitably asymptotically
related to a locally hyperbolic conformally compact metric, we show that the
cocycle detemines an absolute invariant $c(h)$. This tractor-valued
$(n-1)$-form field on the conformal infinity is canonically associated to $h$
(i.e. is not dependent on other choices) and is equivariant under the
appropriate diffeomorphisms.
Finally specialising further to the case that the boundary is a sphere and
that a metric $h$ is asymptotically related to a hyperbolic metric on the
interior, we show that the invariant $c(h)$ can be integrated over the
boundary. The result pairs with solutions of the KID (Killing initial data)
equation to recover the known description of hyperbolic mass integrals of Wang,
and Chru\'{s}ciel--Herzlich. |
|
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. |
|
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
|
dc.rights.uri |
https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html |
|
dc.subject |
math.DG |
|
dc.subject |
math.DG |
|
dc.subject |
primary: 53A55, secondary: 53C18, 53C25, 53C80, 83C30, 83C60 |
|
dc.title |
A relative mass cocycle and the mass of asymptotically hyperbolic
manifolds |
|
dc.type |
Journal Article |
|
dc.date.updated |
2021-09-06T23:33:04Z |
|
dc.rights.holder |
Copyright: The author |
en |
pubs.author-url |
http://arxiv.org/abs/2108.01373v1 |
|
dc.rights.accessrights |
http://purl.org/eprint/accessRights/OpenAccess |
en |
pubs.elements-id |
863048 |
|