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Bounds on M/R for Charged Objects with positive Cosmological constant · Around

2012

Bounds on M/R for Charged Objects with positive Cosmological constant

Andréasson, Håkan, Boehmer, Christian G., Mussa, Atifah

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We consider charged spherically symmetric static solutions of the Einstein-Maxwell equations with a positive cosmological constant $\Lambda$.

If $r$ denotes the area radius, $m_g$ and $q$ the gravitational mass and charge of a sphere with area radius $r$ respectively, we find that for any solution which satisfies the condition $p+2p_{\perp}\leq \rho,$ where $p\geq 0$ and $p_{\perp}$ are the radial and tangential pressures respectively, $\rho\geq 0$ is the energy density, and for which $0\leq \frac{q^2}{r^2}+\Lambda r^2\leq 1,$ the inequality $\frac{m_g}{r} \leq 2/9+\frac{q^2}{3r^2}-\frac{\Lambda r^2}{3}+2/9\sqrt{1+\frac{3q^2}{r^2}+3\Lambda r^2}$ holds.
We also investigate the issue of sharpness, and we show that the inequality is sharp in a few cases but generally this question is open.

Built on

H. A. Buchdahl, “General Relativistic Fluid Spheres,” Phys. Rev. 116
1959
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M. K. Mak, P. N. Dobson Jr. and T. Harko “Maximum Mass-Radius Ratios for Charged Compact General Relativistic Objects”, Europhys. Lett. 55
2001
Earlier work this paper cites.
C. G. Böhmer, “Eleven spherically symmetric constant density solutions with cosmological constant,” Gen. Rel. Grav. 36
2004
Earlier work this paper cites.
C. G. Böhmer and T. Harko, “Bounds on the basic physical parameters for anisotropic compact general relativistic objects,” Class. Quant. Grav. 23
2006
Earlier work this paper cites.

Similar

C. G. Böhmer and T. Harko, “Minimum mass-radius ratio for charged gravitational objects,” Gen. Rel. Grav. 39
2007
Cited alongside, same era.
H. Andréasson, “On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system,” Commun. Math. Phys. 274
2007
Cited alongside, same era.
H. Andréasson, “Sharp bounds on 2m/r of general spherically symmetric static objects,” J. Diff. Eq. 245
2008
Cited alongside, same era.
P. Karageorgis and J. G. Stalker, “Sharp bounds on 2m/r for static spherical objects,” Class. Quant. Grav. 25
Original
2008
Cited alongside, same era.

Then

H. Andréasson, “Sharp bounds on the critical stability radius for relativistic charged spheres,” Commun. Math. Phys. 288
Original
2009
Later among the works it cites.
H. Andréasson, M. Eklund and G. Rein, “A Numerical investigation of the steady states of the spherically symmetric Einstein-Vlasov-Maxwell system,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
H. Andréasson and C. G. Böhmer, “Bounds on 2m/r for static objects with a positive cosmological constant,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
C. G. Böhmer and A. Mussa, “Charged perfect fluids in the presence of a cosmological constant,” Gen. Rel. Grav. 43
Original
2011
Later among the works it cites.

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