Gerardo García: Deforming (almost) black holes from the inside and from the outside

mardi 28 nov. 2023, 11:30 → 12:30 Europe/Paris

In this talk I will reconsider the no-hair theorems trying to 
understand two main aspects. First of all, no-hair theorems are always 
formulated in vacuum. However, it is legitimate to ask about the role 
that external matter can play in the structure of black hole solutions, 
namely whether for a given external matter distribution there exists 
more than one family of black holes that are compatible with such matter 
distribution. Second, it is interesting to consider what happens if one 
substitutes the assumption of a smooth event horizon (zero redshift 
surface) by the existence of an arbitrary but small finite redshift 
surface. This sheds light on the origin of the theorems and allows one 
to consider situations in which we have an almost perfect mimicker of a 
black hole.

To address these questions, I will discuss the structure of static 
vacuum Einstein equations, putting a special emphasis on the elliptic 
problem that the redshift function obeys. Then, I will consider a 
simplified scenario, in which I restrict myself to consider axisymmetric 
spacetimes since in that case the elliptic problem reduces to a 
Laplacian problem in Euclidean 3D space. To answer the first question, I 
will first discuss how external matter content can deform the geometry 
of the horizon and discuss how the contribution of the black hole and 
the and the external matter to the multipolar structure can be in a 
precise sense decoupled. To answer the second question, I will assume 
the existence of a surface of arbitrary small redshift and see what are 
the constraints that we can obtain on the multipolar structure of the 
object if we impose that the curvature remains bounded as this minimum 
redshift tends to zero (horizon limit).