- Physicists develop an analytical formula for measuring Hawking radiation on the black hole’s event horizon.
- It will help scientists test the accuracy of different quantum gravity theories.

In 1975, Stephen Hawking published a theory stating that black holes emit radiation due to the quantum effects near their event horizons. This black-body radiation, known as Hawking radiation, is named after him. It is responsible for reducing the mass and rotational energy of black holes.

The recent discovery of gravitation waves has verified Einstein’s gravitation theory, but it still doesn’t explain the nature of dark matter, dark energy, singularity, and quantum gravity.

In fact, the observations show that alternative gravitational theories may accurately describe black holes. Most of those theories include quantum parameters, and they do not contradict the data obtained from black hole mergers.

The information of matter (the total mass, charge, and angular momentum) falling into a black hole is conserved. It is generally believed that no information loss occurs, as it exists inside the black hole and can’t be accessed from the outside.

However, according to Stephan Hawking’s theory, black holes gradually evaporate by emitting Hawking radiation, and this radiation doesn’t seem to carry additional information about the matter that created the black hole. So, where does the information go?

In quantum physics, loss of information is a clear violation of an important property known as unitarity. To eliminate this paradox, several quantum gravitation theories have become more popular in the past decade.

### Analytical Formula To Calculate Hawking Radiation

One of the most promising theories is the Einstein-dilaton-Gauss-Bonnet theory (EdGB), which integrates quantum parameters with the Theory of General Relativity. It is inspired by the low-energy limit of string theory.

In this study, physicists have focused on this theory only, since it contains the Einstein part as well as the quantum curvature terms and a scalar field. They came up with an analytical formula for measuring Hawking radiation on the black hole’s event horizon.

*Reference: Physical Review D | DOI:10.1103/PhysRevD.99.124042 | RUDN University *

This formula will help scientists determine how Hawking radiation would vary with the quantum corrections to Einstein’s gravitation theory. It will also allow them to test the accuracy of different quantum gravity theories by observing black holes.

Quasinormal modes explain how black holes respond to external gravitational perturbations. Since these modes fade over time, their amplitude can be determined only for a small period.

Quasinormal modes are the modes of energy dissipation of a black hole. Their frequency is represented by a complex number, where the real part is periodic oscillation and the imaginary part is decay rate.

Courtesy of researchers

The research team examined classical (quasinormal) and quantum (Hawking) radiation for test fields in the background of 4D, asymptotically flat and spherically symmetric black hole in the EdGB theory.

The team developed the formula for the eikonal state of quasinormal modes and then utilized it to measure the quasinormal modes of Maxwell’s fields and test scalar, which eventually helped them estimate the Hawking radiation intensity for the EdGB black hole.

In summary, they applied quantum corrections to the black hole’s geometry to evaluate the intensity of the Hawking evaporation on the black hole’s event horizon.

Read: 15 Interesting Facts About Stephen Hawking

Classical radiation, such as electromagnetic waves, slightly differs from Einstein’s, which means Hawking radiation is a much more sensitive phenomenon. By further investigating the black holes formed in the early universe, physicists may better understand how to apply quantum corrections to gravity.