Compact objects in entangled relativity

We describe the first numerical Tolman-Oppenheimer-Volkoff solutions of compact objects in entangled relativity, which is an alternative to the framework of general relativity that does not have any additional free parameter. Assuming a simple polytropic equation of state and the conservation of the rest-mass density, we notably show that, for any given density, compact objects are always heavier (up to $\sim 8\%$) in entangled relativity than in general relativity—for any given central density within the usual range of neutron stars’ central densities, or for a given radius of the resulting compact object.

Figure 1

Diagram of the mass $m_{*}$ of the compact object with respect to its central density, for central densities between 100 and $8200\mathrm{Mev}/{\mathrm{fm}}^3$.

Figure 2

Diagram of the radius of the compact object with respect to its central density, for central densities between 100 and $8200\mathrm{Mev}/{\mathrm{fm}}^3$.

Figure 3

Diagram of the mass $m_{*}$ of the compact object with respect to its radius in both theories, for central densities between 100 and $8200\mathrm{Mev}/{\mathrm{fm}}^3$.

Figure 4

Diagram of the masses $m_{*}$ and ${\mathfrak{M}}_{\mathrm{ADM}}$ of the compact object with respect to its radius in entangled relativity, for central densities between 100 and $8200\mathrm{Mev}/{\mathrm{fm}}^3$.

Figure 5

Scalar field and its derivative profiles for the two solutions in entangled relativity with $M=1.25M_{\odot }$, with densities $400\mathrm{MeV}/{\mathrm{fm}}^3$ or $4150\mathrm{MeV}/{\mathrm{fm}}^3$ ($R_{*}=17.0$ or $R_{*}=8.3\mathrm{km}$ respectively). The vertical lines mark the radius of the solutions.

Figure 6

Product of the metric’s components $g_{00}{g}_{rr}$ of the two solutions of an object of mass $M=1.25M_{\odot }$ in general relativity and entangled relativity. The vertical lines mark the radius of the solutions. In the parenthesis are displayed the central density for each solution, in $\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 7

Shapiro potential with respect to the radius for each solution of mass $M=1.25M_{\odot }$ in both theories. The vertical lines mark the radius of the solutions. In the parenthesis are displayed the central density for each solution, in $\mathrm{MeV}/{\mathrm{fm}}^3$.