FIG. 1: The infinitesimal LLT for a Kerr-Newman black hole with parameters M = 1000, a = 0 . 8 M , Q = 0 . 2 M and v = 0 . 3 , 0 . 5 , 0 . 7 and 0 . 9 for the black, thick, dashed and thick dashed lines respectively. where which turns out to be a rotation about the 2-axis though the angle ϑ $^{1}$$_{3}$( x ) = − ϑ $^{3}$$_{1}$( x ), as will be shown in Eq.(30). This is yet another tediously long equation, so we employ graphical techniques in Fig.(2) to illustrate that a singularity is evi- dent at the event horizon r$_{+}$ . This is expected since an observer at infinity can not make mea- surements at and beyond an event horizon. It is important here to note that ϑ $^{a}$$_{b}$( x ) = λ $^{a}$$_{b}$( x ) = χ $^{a}$$_{b}$( x ) = ϕ $^{a}$$_{b}$( x ), where which is a trivial change in the local inertial frame. The former set of inequalities results from the boost part of λ $^{a}$$_{b}$( x ), the acceleration and hence the force of the particle, and the curvature of the spacetime respectively. Considering now the special case when M, a, Q → 0, the Minkowski spacetime is again recovered with and and most importantly for this situation, the Thomas precession of the spin , i.e. [Eq.(23) - Eq.(22)] for v << 1, remains where a ≡ | a $^{r}$( x ) | = c $^{2}$sinh$^{2}$( $_{r}$). In this limit the change in the local inertial frame is just a We now move on to the actual gedanken exper- iment of this paper. Two observers are consid- ered at azimuthal angles ± Φ with r > r$_{+}$ and an EPR source generator at Φ = 0 as seen in Fig. (3). The observers and EPR source are static in the local inertial frame Eq.(3), i.e. they are rel- atively static. The EPR source generates a pair of maximally entangled particles at Φ = 0 which are sent in opposite directions with constant four momentum p a ± = ( m cosh ( ζ ) , 0 , 0 , ± m sinh ( ζ )). The pure state can be described by the Bell state, rotation in the 2-axis through the angle χ $^{1}$$_{3}$( x ) and the change in spin is also a rotation about the 2-axis given by ϑ $^{1}$$_{3}$( x ). The difference between the latter two terms gives the spin precession in the low velocity limit per unit dt = dτ cosh ( ζ ) γ = $^{√}$| − → p | 2 + m 2 m and i, k ∈ { 1 , 2 , 3 } (20) ϕ $^{1}$$_{3}$( x ) = − ϕ $^{3}$$_{1}$( x ) = u $^{ϕ}$( x ) (21) χ $^{1}$$_{3}$( x ) = − χ $^{3}$$_{1}$( x ) = sinh( ζ ) r (22) ϑ $^{1}$$_{3}$( x ) = − ϑ $^{3}$$_{1}$( x ) = cosh( ζ ) sinh( ζ ) r (23) $^{[}$ϑ $^{3}$$_{1}$( x ) − χ $^{3}$$_{1}$( x ) $^{]}$dτ ∼ − va 2 c $_{2}$dt (24) ζ 1 √ 2 $^{[}$| p a $_{+}$, ↑ ; 0 〉 | p a $_{−}$, ↓ ; 0 〉 − | p a $_{+}$, ↓ ; 0 〉 | p a $_{−}$, ↑ ; 0 〉 $^{]}$, (25) III. EPR CORRELATION FIG. 3: The EPR setup in the Kerr-Newman space- time. Gray circles are the observers and the gray square is the EPR source. 5 r r (a) (b) λ 0 1 λ 1 3