Matching Condition on the Event Horizon and the Holography Principle

TL;DR

This paper demonstrates that event horizons and $ds^2=0$ surfaces in black holes and wormholes reduce the information needed to describe spacetime, supporting the Holography principle and enabling entropy calculations via algorithm theory.

Contribution

It shows how matching metrics on $ds^2=0$ surfaces aligns with the Holography principle and introduces a method to compute black hole entropy using algorithm theory.

Findings

Event horizons reduce information for spacetime description.

Matching metrics on horizons involves only metric components, not derivatives.

Black hole entropy can be derived from algorithm theory.

Abstract

It is shown that the event horizon of 4D black hole or $ds^2 = 0$ surfaces of multidimensional wormhole-like solutions reduce the amount of information necessary for determining the whole spacetime and hence satisfy the Holography principle. This leads to the fact that by matching two metrics on a $ds^2 = 0$ surface (an event horizon for 4D black holes) we can match only the metric components but not their derivatives. For example, this allows us to obtain a composite wormhole inserting a 5D wormhole-like flux tube between two Reissner-Nordstr\"om black holes and matching them on the event horizon. Using the Holography principle, the entropy of a black hole from the algorithm theory is obtained.