Negative mass bubbles in de Sitter spacetime

We study the possibility of the existence of negative mass bubbles within a de Sitter spacetime background with matter content corresponding to a perfect fluid. It is shown that there exist configurations of the perfect fluid that satisfy everywhere the dominant energy condition, the Einstein equations and the equations of hydrostatic equilibrium which asymptotically approach the exact solution of Schwarzschild—de Sitter spacetime with a negative mass.

Figure 1

$m(r)$ for the parameters $x=.1$, $\mathrm{\Lambda }=.001$, $M=.01$, $y\approx 245$.

Figure 2

Density $\rho (r)$ for the parameters $x=.1$ $G=1$, $\mathrm{\Lambda }=.001$, $M=.01$, $y\approx 245$.

Figure 3

Pressure $p(r)$ for the parameters $x=.1$ $G=1$, $\mathrm{\Lambda }=.001$, $M=.01$, $y\approx 245$.

Figure 4

$\ln AB$ for the parameters $x=.1$ $G=1$, $\mathrm{\Lambda }=.001$, $M=.01$, $y\approx 245$.

Figure 5

$p(r)/\rho (r)$ for the parameters $x=.1$ $G=1$, $\mathrm{\Lambda }=.001$, $M=.01$, $y\approx 245$.