The oscillating gravitational field of an oscillaton of finite mass M causes it to lose energy by emitting classical scalar field waves, but at a rate that is nonperturbatively tiny for small $\mu \equiv GMm/ħc,$ where m is the scalar field mass: $dM/dt\approx -3797{437.776(c}^3/G\left){\mu }^{-2}{e}^{-39.433795197/\mu }\right[1+O\left(\mu \right)].$ Oscillatons also decay by the quantum process of the annihilation of scalarons into gravitons, which is only perturbatively small in $\mu ,$ giving by itself $dM/dt\approx -0.008513223{935(m}^2{c}^2/ħ\left){\mu }^5\right[1+O\left({\mu }^2\right)].$ Thus the quantum decay is faster than the classical one for $\mu \lesssim 39.4338/\left[\ln \right(ħ{c/Gm}^2)+7\mathrm{}\ln (1/\mu )+19.9160\mathrm{}].$ The time for an oscillaton to decay away completely into free scalarons and gravitons is $t_{\mathrm{decay}}\sim 2{ħ}^6{c}^3{/G}^5{m}^{11}\sim {10}^{324}\mathrm{yr}(1\mathrm{}\mathrm{meV}{/mc}^2{)}^{11}.$ Oscillatons of more than one real scalar field of the same mass generically asymptotically approach a static-geometry $U\left(1\right)\mathrm{}$ boson star configuration with $\mu ={\mu }_0,$ at the rate ${d(GM/c}^3)/dt\approx [(C/{\mu }^4{)e}^{-\alpha /\mu }{+Q(m/m}_{\mathrm{Pl}}{)}^2{\mu }^3]\left({\mu }^2-{\mu }_0^2\right),$ with ${\mu }_0$ depending on the magnitudes and relative phases of the oscillating fields, and with the same constants C, $\alpha ,$ and Q given numerically above for the single-field case that is equivalent to ${\mu }_0=0.\mathrm{}$

• Received 2 October 2003

DOI:https://doi.org/10.1103/PhysRevD.70.023002