Compact stars in the braneworld: A new branch of stellar configurations with arbitrarily large mass

We study the properties of compact stars in the Randall-Sundrum type-II braneworld (BW) model. To this end, we solve the braneworld generalization of the stellar structure equations for a static fluid distribution with spherical symmetry considering that the spacetime outside the star is described by a Schwarzschild metric. First, the stellar structure equations are integrated employing the so-called causal limit equation of state (EOS), which is constructed using a well-established EOS at densities below a fiducial density, and the causal EOS $P=\rho$ above it. It is a standard procedure in general relativistic stellar structure calculations to use such EOSs for obtaining a limit in the mass radius diagram, known as the causal limit, above which no stellar configurations are possible if the EOS fulfills the condition that the sound velocity is smaller than the speed of light. We find that the equilibrium solutions in the braneworld model can violate the general relativistic causal limit, and for sufficiently large mass they approach asymptotically to the Schwarzschild limit $M=2R$. Then, we investigate the properties of hadronic and strange quark stars using two typical EOSs: a nonlinear relativistic mean-field model for hadronic matter and the Massachusetts Institute of Technology (MIT) bag model for quark matter. For masses below $\sim 1.5M_{\odot }–2M_{\odot }$, the mass versus radius curves show the typical behavior found within the frame of general relativity. However, we also find a new branch of stellar configurations that can violate the general relativistic causal limit and that, in principle, may have an arbitrarily large mass. The stars belonging to this new branch are supported against collapse by the nonlocal effects of the bulk on the brane. We also show that these stars are always stable under small radial perturbations. These results support the idea that traces of extra dimensions might be found in astrophysics, specifically through the analysis of masses and radii of compact objects.

Figure 1

Mass-radius relationship in general relativity ($\lambda \to \infty$) for the causal limit EOS matched continuously with the BPS EOS. Both EOSs are matched at different fiducial densities that lead to different values of $a={\rho }_f-p_f$. The dots over the curves indicate the maximum masses, which fall along the causal limit of Fig. 3.

Figure 2

(a) The mass-radius relationship obtained using the causal limit EOS given in Sec. 3a for some values of $a$ (in $\mathrm{MeV}/{\mathrm{fm}}^3$) and two different values of $\lambda$. (b) Same as in (a) but for a larger range of $M$ and $R$.

Figure 3

The causal limit for general relativity and the Schwarzschild limit $M=2R$. In the braneworld model, static stellar configurations fulfilling a causal EOS (sound velocity $<$ speed of light) can occupy the region between both straight lines.

Figure 4

Mass-radius relationship for (a) strange quark stars and (b) hadronic stars, using several values of the brane tension $\lambda$. These values of $\lambda$ lead to $M_5=(\frac{4}{3}\pi \lambda M_p^2{)}^{1/6}\sim 2000\mathrm{TeV}$, i.e., larger than 10 TeV, in compatibility with LHC. We also show the general relativistic and braneworld model causal limits.

Figure 5

Mass of (a) strange stars and (b) hadronic stars versus the central energy density ${\rho }_c$ for different values of brane tension $\lambda$. The labels of the curves are the same as given in Fig. 4.

Figure 6

Nonlocal energy density as a function of the radial coordinate for strange quark stars and hadronic stars. In all cases the central energy density is ${\rho }_c=2500\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 7

Stability analysis of stellar configurations in braneworld models; for simplicity we present only the curves for strange quark stars. Panels (a) and (b) correspond to a value of the brane tension, $\lambda =(551\mathrm{MeV}{)}^4$, that results in no critical points. Panels (c) and (d) correspond to a different value of the brane tension, $\lambda =(724\mathrm{MeV}{)}^4$, that results in a local maximum and a local minimum in both the $M(R)$ and $M({\rho }_c)$ curves. For the analysis of the stellar stability based on these panels, see the text.