# A Theory of Black Holes

If we assume there is a singularity at the centre of a black hole:

For an observer at the centre of a black hole (of mass M) the force on a small mass (m0) approaching from infinity when at distance r from the centre

 F = - GMm r2

 Where m = mo by special relativity, which is towards the centre. (1 - v2/c2)½

 - d  r = - GMm dt r  m

 and - dr = - GM dt r  dt

 or - dr = - GM = GM = GM dt r  dr r ro

 and dr = - GM -  as ro  o dt ro

The kinetic energy  =

and the added mass  =     /c    +  mo

so that the black hole has infinite mass, which is clearly not true by observation

If on the other hand the mass of the black hole is contained in a neutron star at absolute zero, with radius ro;

If a particle of rest mass mo arrives from infinity

 Force (F) = - GMm r

 Where m = mo invoking special relativity, and (1 - v2/c2)½

d   r/dt    =  -GMm/r   m/r   m

 So - dr = GM dt r  dt

 and - dr = GM = - GM = - GM dt r  dr r ro

Particle arrives at r0 with kinetic energy moGM/2ro and the added mass  is  moGM/2ro c    +  mo

Note that dr/dt can exceed the velocity of light if M is large enough
And -dr/dt  = vo say.

For example, for G =  6.67X10-11 , M = 4×1033  kg and ro= 1.343×106m the particle arrives at the neutron surface at c

The value for r0 requires some justification.
If a neutron has a cross section of one barn its radius is 5.64×10-5m assuming it is incompressible.
A spherical neutron star of mass M with hexagonal close packing has a radius of (5.656 M / mo)1/3×5.64×10-5 = 1.343×106m.

An alternative way of calculating the escape velocity from ro allowing for r inside the neutron star is as follows:

F =  -GMm/r    .r   /ro    when r <  ro

and d   r/dt    =  -GM/r   r   /ro

 - dr = GMr dt ro  dt

 dr = GMr = GMr = GM dt ro  dr 2ro 2ro

 Therefore - dr = GM = - vo giving the same value for vo as before. dt 2ro

J F Fleming  24 February 2011