1. Overview: General relativity is a theory of many faces. Take the Einstein field equations to be its standard representation. Then there are many other representations of more or less the same physics. Historically, an alternative re-representation was its action formulation in terms of the Einstein-Hilbert action. Current representations include the geometric trinity.
One notes a plethora of different precise representations GENERALLY FORMAL – Hamiltonian (e.g. ADM formulation) vs. Lagrangian formulation; first vs. second order formalism (Palatini) – field redefinition into background and dynamic field
MORE SPECIFIC GEOMETRIC: curvature vs. torsion vs. non-metricity (geometric trinity)
Analogies: – thermodynamic-hydrodynamic analogies – electrodynamic-gauge-theory analogies
Mechanisms for the arisal of gravity from high energies – from a quantum theory (and thus simply the limit of some form of quantisation) – calculably induced (the gravitational theory is a mean-field theory which may not even have to be quantised)
Mechanisms for the arisal of gravity in some regime – dynamical self-coupling (but is this not a weak gravitational weak point — at least gravitational effects needs to be isolatable — but is this a necessary condition?
2. What to make of these different faces? When are some reformulations more helpful than others?
3. We consider three rather spectacular cases but also highly controversial ones: 3.1 thermodynamic gravity 3.2 spin-2 3.3. induced gravity
TO DO: induced gravity section (tonight)
One notes a plethora of different precise representations GENERALLY FORMAL – Hamiltonian (e.g. ADM formulation) vs. Lagrangian formulation; first vs. second order formalism (Palatini) – field redefinition into background and dynamic field
MORE SPECIFIC GEOMETRIC: curvature vs. torsion vs. non-metricity (geometric trinity)
Analogies: – thermodynamic-hydrodynamic analogies – electrodynamic-gauge-theory analogies
Mechanisms for the arisal of gravity from high energies – from a quantum theory (and thus simply the limit of some form of quantisation) – calculably induced (the gravitational theory is a mean-field theory which may not even have to be quantised)
Mechanisms for the arisal of gravity in some regime – dynamical self-coupling (but is this not a weak gravitational weak point — at least gravitational effects needs to be isolatable — but is this a necessary condition?
2. What to make of these different faces? When are some reformulations more helpful than others?
3. We consider three rather spectacular cases but also highly controversial ones: 3.1 thermodynamic gravity 3.2 spin-2 3.3. induced gravity
TO DO: induced gravity section (tonight)