Physical properties of a source of the Kerr metric: Bound on the surface gravitational potential and conditions for the fragmentation

We investigate some important physical aspects of a recently presented interior solution for the Kerr metric. It is shown that, as in the spherically symmetric case, there is a specific limit for the maximal value of the surface potential (degree of compactness), beyond which unacceptable physical anomalies appear. Such a bound is related to the appearance of negative (repulsive) gravitational acceleration that is accompanied by the appearance of negative values of the pressure. A detailed discussion on this effect is presented. We also study the possibility of a fragmentation scenario, assuming that the source leaves the equilibrium, and we bring out the differences with the spherically symmetric case.

Figure 1

Graphics of $a_r$ as function of $s$, for different values of $\tau$, with $j=0.1$, $y\equiv \cos \theta =0.5$.

Figure 2

Plot of $a_r$ as function of $s$ and $\tau$, for $j=0.1$, $y=0.2$.

Figure 3

Plot of $a_r$ as function of $\tau$ and $y$, with $j=0.1$, $s=0.3$.

Figure 4

Plot of $a_r$, as function of $s$ and $y$, with $j=0.1$, $\tau =2.1$.

Figure 5

Curves depicting $a_r$ as function of $s$, for different values of the rotation parameter $j$, with $\tau =2.24$, $y=0.5$.

Figure 6

Curves delimiting the range of values of $s$, for which the radial pressure is negative, (the curves cut the axis at $s_c$), for different values of $\tau$.