Luke Butcher

Theoretical Physicist and Sometimes Playwright



There is no question that gravitational waves carry energy, but it has been notoriously difficult to describe where in spacetime this energy resides. This problem is so widely believed to be unsolvable that the prevailing wisdom (expressed most famously by Misner, Thorne and Wheeler in their text/telephone-book Gravitation) is that trying to localise gravitational energy is "looking for the right answer to the wrong question". I have been investigating the extent to which this statement is true: under what circumstances, and using which definitions, is it possible to make sense of local gravitational energy and momentum? Is there a right question to ask?

Recently, I developed a framework for describing the local exchange of energy and momentum between matter and (linear) gravity, which lead to an intriguing (and surprisingly simple) formula for the gravitational energy momentum tensor :
\kappa \bar{\tau}_{\mu\nu}= \frac{1}{4} \partial_{\mu}h_{\alpha\beta} \partial_{\mu}\bar{h}^{\alpha\beta}
This tensor has some very interesting properties – in particular, it describes positive energy-density and causal energy-flux for all transverse-traceless gravitational fields. Significantly, the framework in which this tensor is derived naturally leads to a program that removes the gauge ambiguity from the formula above. Interested readers should take a look at the paper.

Along with other examples, I have used this theoretical basis to produce plots of gravitational energy density outside two compact sources: an equal-mass binary, and a vibrating rod. These plots are available as an animation.


  • Localized Energetics of Linear Gravity: Theoretical Development
    L. M. Butcher, M. P. Hobson, and A. N. Lasenby, Phys. Rev. D 86, 084013 (2012) [arXiv:1210.0837]

  • Localizing the angular momentum of linear gravity
    L. M. Butcher, A. N. Lasenby, and M. P. Hobson, Phys. Rev. D 86, 084012 (2012) [arXiv:1210.0831]

  • Localizing the energy and momentum of linear gravity
    L. M. Butcher, M. P. Hobson, and A. N. Lasenby, Phys. Rev. D 82, 104040 (2010) [arXiv:1008.4061]

  • Bootstrapping gravity: A consistent approach to energy-momentum self-coupling
    L. M. Butcher, M. P. Hobson, and A. N. Lasenby, Phys. Rev. D 80, 084014 (2009) [arXiv:0906.0926]

  • The physical significance of the Babak-Grishchuk gravitational energy-momentum tensor
    L. M. Butcher, A. N. Lasenby, M. P. Hobson Phys. Rev. D 78, 064034 (2008) [arXiv:0807.0112]