Probing the existence of a minimal length through compact binary inspiral

TL;DR

This paper investigates how a minimal length in spacetime affects gravitational wave signals from binary black hole inspirals, revealing potential observational constraints on quantum gravity effects through waveform modifications.

Contribution

It demonstrates that a minimal length introduces a minimum frequency and alters the GW waveform, providing a new way to test quantum properties of black holes with gravitational wave data.

Findings

Minimal length causes a minimum frequency in GW signals.

Waveform modifications appear at 2.5 post Newtonian order.

Detection of classical-like BH inspirals constrains minimal length to be near the Planck scale.

Abstract

Existence of a minimal length in spacetime geometries avoids several singular situations involving quantum theory and gravity. In this work, we show that the existence of such a minimal length also affects the gravitational wave (GW) waveform of any inspiraling binary black hole (BH) system by introducing a minimum frequency, below which the BHs behave as perfectly reflecting compact objects, while above they are identical to classical BHs. This leads to a significant imprint on the tidal heating term, appearing in the GW waveform at 2.5 post Newtonian order. Based on these modifications to the inspiraling waveform, it turns out that the detection of highly spinning and highly absorbing, almost classical BH like compact objects, inspiraling around each other, would be in tension with the quantum properties of BH geometries. The same would also be true if the zero point length exceeds the Planck length by a significant amount, suggesting that the zero point length, if it exists, must be of the same order as the Planck length, or smaller, purely from GW observations.