The Volume of a Capped Interior: Linear Growth in Mass Instead of Cubic Growth in Radius

For ten solar masses the capped volume is 2.046e-27 cubic metres against a horizon ball of 1.079e+14 cubic metres, a ratio of 1.896e-41. For a billion solar masses the capped volume reaches 2.046e-19 cubic metres yet the ratio falls to 1.896e-57. The capped volume grows linearly with mass while the horizon ball grows with the cube of mass, so the interior is, in this precise sense, mostly not at the cap: the ceiling governs a small central region and the rest of the interior lies at lower densities. This reframes the interior problem. Computed from stated assumptions, not measured.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24125848
Primary Topic
Cosmology and Gravitation Theories
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
article

The Volume of a Capped Interior: Linear Growth in Mass Instead of Cubic Growth in Radius

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
article

The Volume of a Capped Interior: Linear Growth in Mass Instead of Cubic Growth in Radius

William Alexander Aldred
article en

Abstract

For ten solar masses the capped volume is 2.046e-27 cubic metres against a horizon ball of 1.079e+14 cubic metres, a ratio of 1.896e-41. For a billion solar masses the capped volume reaches 2.046e-19 cubic metres yet the ratio falls to 1.896e-57. The capped volume grows linearly with mass while the horizon ball grows with the cube of mass, so the interior is, in this precise sense, mostly not at the cap: the ceiling governs a small central region and the rest of the interior lies at lower densities. This reframes the interior problem. Computed from stated assumptions, not measured.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon