The holographic solution - Why general relativity must be understood in terms of strings

TL;DR

This paper explores a specific exact solution to Einstein's equations, called the holographic solution, which models matter as densely packed strings and suggests that understanding general relativity requires string theory concepts.

Contribution

It introduces the holographic solution as a simple, matter-including solution to Einstein's equations that aligns with string theory principles and provides new insights into the geometric structure of spacetime.

Findings

The interior matter density follows an inverse square law.

The solution models matter as densely packed strings with a specific equation of state.

The membrane bounding the strings has zero energy density, consistent with string theory.

Abstract

This paper is a significantly expanded version of gr-qc/0306066. It discusses the geometric properties of the so called holographic solution, an exact, spherically symmetric solution to the Einstein field equations with zero cosmological constant. The holographic solution can be regarded as the simplest solution of the field equations including matter. Its interior matter-density follows an inverse square law: e = 1 / (8 pi r2). The interior principle pressures are P_r = - e in the radial direction and P_tan = 0 in the tangential direction. This is the equation of state of a radial arrangement of strings. The interior string type matter state is densely packed, each string occupying a transverse extension of exactly one Planck area, and bounded by a membrane consisting out of tangential pressure. The membrane's energy density is zero, as expected from string theory. Despite its simple structure, the results that can be derived from this solution are far from trivial. It is not possible to give a fair account of all relevant results in a 20-line abstract. The reader is referred to the abstract in the paper, which summarizes some of the more important results. The author appreciates any comments, critique or suggestions of new material.