44 3 Afield
guide
to the (2+l)'dimensional
spacetimes
have already computed the quantity v
1
 appearing in (2.56); combining
this result with the expression (3.9) for the canonical momentum, we see
that the total boundary diffeomorphism generator is
V]
= ^
j^
d<j>
[(2

2B)l + 7AI+], (3.35)
where I have again restored the constants.
In particular, a diffeomorphism that is asymptotically a time translation
has £ = 1, giving # = (}/$nG. We thus confirm that /? is the conserved
quantity associated with time translations at spatial infinity, that is, the
mass.
Similarly, an asymptotic rotation is described by * = 1 and
\ = A/B. (The time translation component reflects the 'timehelical'
structure of the metric, and is chosen so that the coordinate f in (3.24) is
left invariant.) The associated charge is then # = A/4GB, which is thus
the angular momentum, the conserved quantity associated with rotations
at infinity. Equivalent expressions for the mass and angular momentum
may be found by computing the quasilocal mass of Brown and York
associated with a surface at infinity [43].
The mass and angular momentum, constructed as integrals at spatial
infinity, are the (2+l)dimensional analogs of the ADM mass and an
gular momentum in standard general relativity. Similar integrals exist
for any isolated system of sources. Note, however, that because of the
asymptotically conical structure of our solutions, there are no asymptotic
symmetries representing spatial translations or boosts, and thus no analog
of the full ADM momentum vector. One way to understand this is to
observe that while the metric (3.21) admits local solutions of the Killing
equation corresponding to the full Poincare group, most of the resulting
wouldbe Killing vectors are not preserved under the identifications (3.25);
only the Killing vectors corresponding to rotations and time translations
are globally defined.
It is also instructive to examine the conserved charges in the firstorder
formalism. A suitable triad for the metric (3.21) is
e°
= dt
(A/B)d</>
e
1
=df
2
(3.36)
and it is easily checked that the only nonvanishing component of the spin
connection (2.63) is
co°
=
Bdcj),
(3.37)
for which the field equations (2.62) and (2.65) are clearly satisfied. There