^{1}

^{,*}

^{2}

^{,†}

^{3,4}

^{,‡}

^{3}.

We show that there are a further infinite number of, previously unknown, supertranslation charges. These can be viewed as duals of the known Bondi-Metzner-Sachs (BMS) charges corresponding to supertranslations. In Newman-Penrose language, these new supertranslation charges roughly correspond to the imaginary part of the leading term in

Recently, the relation between Bondi-Metzner-Sachs (BMS) symmetry and Newman-Penrose charges at null infinity of asymptotically flat spacetime has been made explicit in linear and nonlinear gravity

At leading order, the BMS charges can be derived from the Barnich-Brandt formalism

The supertranslation parameter describing a diffeomorphism of a physical metric should, of course, be real. It is convenient to decompose a general such parameter

To be precise, the real part of

If we consider instead an arbitrary supertranslation parameter, then

In Sec.

We begin by considering the simpler case of electromagnetism on flat Minkowski spacetime

Following Barnich and Brandt

Note that in the case of electromagnetism, the Barnich-Brandt charge is integrable. This is not the case in nonlinear gravity due to Bondi news (or more generally fake news

Contrast the above expression with the Newman-Penrose charge

As emphasized above, the Barnich-Brandt integral with

As is to be expected, the case of gravity is more intricate compared to the electromagnetic case. Starting from an asymptotically flat spacetime

The BMS charge is defined as

Given the boundary conditions

Alternatively, we may define the charge

More generally, we may allow the function

What one loses, by considering the infinity of charges corresponding to

Calculating

Noting that

It is straightforward to show that (see Appendix

In fact,

Integrating by parts,

In general, however, for an arbitrary function

We have shown that one can define new dual asymptotic charges at null infinity. These charges are the imaginary part of the charges defined in Eq.

The existence of a further infinite number of BMS charges does not seem to give rise to new soft theorems

Dualising the Barnich-Brandt prescription only works for supertranslation charges and at null infinity. In particular, for the

We would like to thank the Mitchell Family Foundation for hospitality at the Brinsop Court workshop where this work was initiated. M. G. is partially supported by Grant No. 615203 from the European Research Council under the FP7. C. N. P. is partially supported by DOE Grant No. DE-FG02-13ER42020.

In this section, we prove that the variation of the dual charge

Consider the last term in Eq.

In this appendix, we show that

Equations

In conclusion, we find that

From the perspective of the Newman-Penrose formalism, it would also make sense to define charges

We may reexpress