## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 9, Number 1 (2005), 129-172.

### A gluing construction for non-vacuum solutions of the Einstein-constraint equations

James Isenberg, David Maxwell, and Daniel Pollack

#### Abstract

We extend the conformal gluing construction of Isenberg *et al.* [19]
by establishing an analogous gluing result for field theories obtained by
minimally coupling Einstein’s gravitational theory with matter fields. We
treat classical fields such as perfect fluids and the Yang–Mills equations
as well as the Einstein–Vlasov system, which is an important example
coming from kinetic theory. In carrying out these extensions, we extend
the conformal gluing technique to higher dimensions and codify it in such
a way as to make more transparent where it can, and cannot, be applied.
In particular, we show exactly what criteria need to be met in order to
apply the construction, in its present form, to any other non-vacuum field
theory.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 9, Number 1 (2005), 129-172.

**Dates**

First available in Project Euclid: 29 March 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1143663744

**Mathematical Reviews number (MathSciNet)**

MR2193370

**Zentralblatt MATH identifier**

1101.83005

**Subjects**

Primary: 83C05: Einstein's equations (general structure, canonical formalism, Cauchy problems)

#### Citation

Isenberg, James; Maxwell, David; Pollack, Daniel. A gluing construction for non-vacuum solutions of the Einstein-constraint equations. Adv. Theor. Math. Phys. 9 (2005), no. 1, 129--172. https://projecteuclid.org/euclid.atmp/1143663744