Be used to make any lagrangian invariant under

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Unformatted text preview: any Lagrangian invariant under general coordinate diffeomorhpisms, the same group under which GR is invariant. Thus general coordinate invariance cannot be the defining feature of GR. Similarly, the principle of equivalence, which demands that all mass and energy gravitate with the same strength, is not unique to GR. It can be satisfied even in scalar field theories, if one chooses the interactions properly. For example, this can be achieved by iteratively coupling a canonical massless scalar to its own energy momentum tensor. Such a theory in fact solves all the problems Einstein set out to solve; it provides a universally attractive force which conforms to the principles of special relativity, reduces to Newtonian gravity in the nonrelativistic limit, and satisfies the equivalence principle.1 By introducing diffeomorphism ¨ invariance via the Stuckelberg trick, it can even be made to satisfy the principle of general coordinate invariance. The real underlying principle of GR has nothing to do with coordinate invariance or equivalence principles or geometry, rather it is the statement: General relativity is the theory of a nontrivially interacting massless helicity 2 particle. The other properties are consequences of this statement, and the implication cannot be reversed. As a quantum theory, GR is not UV complete. It must be treated as an effective field theory valid at energies up to a cutoff at the Planck mass MP , beyond which unknown high energy effects will correct the Einstein-Hilbert action. For a given background such as the spherical solution around a heavy source of mass M such as the Sun, GR has three distinct regimes. There is a classical linear regime, where both nonlinear effects and quantum effects can be ignored. This is the regime in which r is greater than the 2 Schwarzschild radius r > rS $ M=MP . For M the mass of the Sun, we have rS $ 1 km, so the classical linear approximation is good nearly everywhere in the Solar System. There is the quantum regime r < 1=MP , very near the singularity of the black hole, where the effective field theory description breaks down. Most importantly, there is a well-separated 1 This theory is sometimes known as the Einstein-Fokker theory, ¨ first introduced in 1913 by Nordstrom (1913a, 1913b), and later in a different form (Freund and Nambu, 1968; Deser and Halpern, 1970). It was even studied by Einstein when he was searching for a relativistic theory of gravity that embodied the equivalence principle (Einstein and Fokker, 1914). Kurt Hinterbichler: Theoretical aspects of massive gravity middle ground, a classical nonlinear regime 1=MP < r < rS , where nonlinearities can be summed up without worrying about quantum corrections, the regime which can be used to make controlled statements about what is going on inside a black hole. One of the challenges of adding a mass to the graviton, or any modification of gravity, is to retain calculable yet interesting regimes such as this....
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This document was uploaded on 09/28/2013.

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