In the Euclidean flat space-time
, the coordinates are represented by [z.sup.A] = ([x.sup.a], [[theta].sup.I]).
(6) The diagram shown is for flat space-time
Moreover, an EH always exists in black hole asymptotically flat space-time under a weak cosmic censorship condition and is represented by a Killing horizon such that the space-time is analytic and the stress tensor obeys the weak energy condition.
In , they considered a conformal transformation [bar.g] = [[OMEGA].sup.2]g to a stationary, asymptotically flat space-time (M, g) admitting a Killing horizon H.
According to this theory, dynamical phenomena occurring in a curved space-time like black holes can be described by a theory on a flat space-time
, just as a hologram can record the information of 3D objects on a plane.
The teleparallel equivalent of general relativity allows the curvature of a metric to be rephrased as contorsion in a flat space-time due to a tetrad field .
This results in a flat space-time with an index of refraction.
and we identify the mass M of the sphere under study as constant, in flat space-time
(M = 4/3[pi][rho][r.sup.3]).
In the second case, it reduces to flat space-time
of special relativity.
This solution has the same thermodynamic characteristics as the black hole solution in asymptotically flat space-time
; that is, the black hole entropy is equal to a quarter of the event horizon area, while the corresponding thermodynamics quantity satisfies the law of thermodynamics of black hole.