Lecturer: Prof. Nathalie Deruelle
Affiliation: APC, CNRS-Universite Paris 7
Abstract:
We describe 4-dimensional gravity
coupled to scalar and Maxwell
fields by the covariant version of
the “Gamma-Gamma − Gamma-
Gamma” part of the Hilbert action
supplemented by the divergence of
a generalized “Katz vector”. We will
see that when a long-range scalar
“hair” is present, the variation of the
action vanishes on shell only for
sub-families of asymptotically AdS
solutions of the field equations.
Computing the action on shell, we
will see next that the asymptotically
AdS black hole solutions which
obey the variational principle, and
with mass defined as a Noether
charge, satisfy the Gibbs relation,
the Katz vectors playing the role of
“counterterms”. Finally, we will see
on the specific example of dyonic
black holes that the sub-class
selected by the variational principle
satisfies the first law of
thermodynamics when their mass
is defined as a Noether charge.
Additional details of the upcoming
High Energys' seminars
can be found on the following link.