%0 Generic %1 Butcher2009 %A Butcher, Luke M. %A Hobson, Michael %A Lasenby, Anthony %D 2009 %K SG gravity %T Bootstrapping gravity: a consistent approach to energy-momentum self-coupling %U http://arxiv.org/abs/0906.0926 %X It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into serious doubt 1. To remedy this confusion, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a non-vacuum background is examined, and the graviton is found to develop a non-vanishing "mass-term" in the action.

@misc{Butcher2009, abstract = { It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into serious doubt [1]. To remedy this confusion, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a non-vacuum background is examined, and the graviton is found to develop a non-vanishing "mass-term" in the action. }, added-at = {2009-06-12T11:30:48.000+0200}, author = {Butcher, Luke M. and Hobson, Michael and Lasenby, Anthony}, biburl = {https://www.bibsonomy.org/bibtex/2275bda977e21a7fd8f38be940d98cf73/tomasortin}, description = {Bootstrapping gravity: a consistent approach to energy-momentum self-coupling}, interhash = {25e39d601d598de46e5562a5308764a9}, intrahash = {275bda977e21a7fd8f38be940d98cf73}, keywords = {SG gravity}, note = {cite arxiv:0906.0926 Comment: 18 pages}, timestamp = {2009-06-12T11:30:48.000+0200}, title = {Bootstrapping gravity: a consistent approach to energy-momentum self-coupling}, url = {http://arxiv.org/abs/0906.0926}, year = 2009 }