Black hole thermodynamics for higher derivative theories of gravity

It is well known that black holes in Einstein's gravity 
satisfy the laws of thermodynamics. And we also know that Einstein's 
theory of gravity cannot be the final theory. In this context it becomes 
an interesting question to explore what other terms we could add to 
gravity Lagrangian without spoiling the thermodynamic nature of its 
black hole solution. In these three lectures I shall discuss my current 
understanding of this topic purely from the point of view of classical 
physics. First we shall develop a new technique of boost weight 
analysis, based on the symmetries of any null hypersurface like the 
event horizon. We shall use this technique to prove the Zeroth, First 
and the Second law at a linearized level for arbitrary higher derivative 
theories of gravity. Next we shall connect it with the famous covariant 
phase space formalism of Wald and the construction of Wald's entropy for 
such theories. And finally we shall discuss the still unsolved question 
of the Second law at nonlinear order.