The Holographic Solution -why General Relativity Must Be Understood in Terms of Strings

This paper discusses the so called holographic solution, in short ”holostar”. The holostar is the simplest exact, spherically symmetric solution of the original Einstein field equations with zero cosmological constant, including matter. The interior matter-distribution follows an inverse square law ρ = 1/(8πr). The interior principal pressures are Pr = −ρ and P⊥ = 0, which is the equation of state for a collection of radial strings with string tension μ = −Pr = 1/(8πr). The interior space-time is separated from the exterior vacuum space-time by a spherical two-dimensional boundary membrane, consisting out of (tangential) pressure. The membrane has zero mass-energy. Its stress-energy content is equal to the holostar’s gravitational mass. The total gravitational mass of a holostar can be determined by a proper integral over the Lorentz-invariant trace of the stress-energy tensor. The holostar exhibits properties similar to the properties of black holes. The exterior space-time of the holostar is identical to that of a Schwarzschild black hole, due to Birkhoff’s theorem. The membrane has the same properties (i.e. the same pressure) as the fictitious membrane attributed to a black hole according to the membrane paradigm. This guarantees that the dynamical action of the holostar on the exterior space-time is identical to that of a black hole. The holostar possesses an internal temperature proportional to 1/ √ r and a surface redshift proportional to √ r, from which the Hawking temperature and entropy formula for a spherically symmetric black hole are derived up to a constant factor. The holostar’s interior matter-state is singularity-free. It can be interpreted as the most compact spherically symmetric (i.e. radial) arrangement of classical strings: The radially outlayed strings are densely packed, each string occupies exactly one Planck area in its transverse direction. This maximally dense arrangement is the reason why the holostar does not collapse to a singularity and why the number of interior degrees of freedom ∗email: [email protected]