The critical and the saturation content of magnetic monopoles in rotating relativistic objects

Abstract

Both the critical content ζ _c (ζ ≡N _m /N _B , whereN _m ,N _B are the total numbers of monopoles and nucleons, respectively, contained in the object), and the saturation content ζ _s of monopoles in a rotating relativistic object are found in this paper. The results are:

$$\zeta _c = \zeta _{c0} \left( {1 - \frac{{4a^2 }}{{R_g^2 }}} \right)^{1/2} ,{\text{ }}\zeta _{c0} \equiv {{Gm_B } \mathord{\left/ {\vphantom {{Gm_B } {g_m }}} \right. \kern-\nulldelimiterspace} {g_m }} = 4.365 \times 10^{ - 21} $$

((1))

wherea is the specific angular momentum of the object;R _g the Schwarzschild radius of the object;g _m , the magnetic charge of a stable colourless monopoleg _m =3hc/4πe.

• (2) For a non-rotating object (a=0).

  $$\zeta _s = \zeta _n \left( {1 - {{R_g } \mathord{\left/ {\vphantom {{R_g } R}} \right. \kern-\nulldelimiterspace} R}} \right)^{ - {\text{ }}1/2} $$

  when

  $$\left( {{R \mathord{\left/ {\vphantom {R R}} \right. \kern-\nulldelimiterspace} R}_g } \right)^2 \gg {\text{ 1 or }}\zeta _s = \sqrt 2 {\text{ }}\beta ^{ - {\text{ }}1/2} \sqrt {\frac{R}{{R_g }}} \zeta _n {\text{ when }}{R \mathord{\left/ {\vphantom {R R}} \right. \kern-\nulldelimiterspace} R}_g< 1 + \beta $$

  whereR is the radius of the object; ζ _n , the Newtonian saturation content² of like monopole,

  $$\begin{gathered} \zeta _n = {{Gm_B m_m } \mathord{\left/ {\vphantom {{Gm_B m_m } {g_m^2 = 1.9 \times 10^{ - 25} \left( {{{m_m } \mathord{\left/ {\vphantom {{m_m } {10^{16} m_B }}} \right. \kern-\nulldelimiterspace} {10^{16} m_B }}} \right),}}} \right. \kern-\nulldelimiterspace} {g_m^2 = 1.9 \times 10^{ - 25} \left( {{{m_m } \mathord{\left/ {\vphantom {{m_m } {10^{16} m_B }}} \right. \kern-\nulldelimiterspace} {10^{16} m_B }}} \right),}} \hfill \\ \beta {\text{ = }}{{\zeta _n } \mathord{\left/ {\vphantom {{\zeta _n } {\zeta _{c0} }}} \right. \kern-\nulldelimiterspace} {\zeta _{c0} }} = 4.3 \times 10^{ - 5} \left( {{{m_m } \mathord{\left/ {\vphantom {{m_m } {10^{16} m_B }}} \right. \kern-\nulldelimiterspace} {10^{16} m_B }}} \right) \hfill \\ \end{gathered} $$

  . Although the critical content cannot be reached, the induced nucleon decay by monopoles will prevent the massive objects (e.g., galactic nuclei and quasars) from collapsing into black holes (Penget al., 1986a, b).

• (3) For a rotating object, although the saturation content of monopoles is the same as above, the value of the critical content is greatly decreased for a fast rotating object. Due to the induced nucleon decay by monopoles, neither the horizon nor the central singularity exists for a collapsed object withR≤1/2R _g which is rotating so fast that the conditiona>GM/c ² [1 − (ζ/ζ _cO )²]^1/2 is satisfied. Those objects mainly radiate infrared radiation with rather strong γ-ray and X-ray.