Finite energy for a gravitational potential falling slower than 1/r

The total energy of any acceptable self-gravitating physical system has to be finite. In GR, the static gravitational potential of a self-gravitating body goes as 1=r at large distances and any slower decrease leads to infinite energy. In this work we show that in modified gravity theories the situation can be much different. We show that there exist spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1=r and generically of the form r. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counter- balancing the apparently infinite energy budget.The total energy of any acceptable self-gravitating physical system has to be finite. In GR, the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinite energy. In this work we show that in modified gravity theories the situation can be much different. We show that there exist spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form r(gamma). This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget