# High Energy Radiation from Black Holes: A Summary 

C. D. Dermer 

Space Science Division, Code 7653, Naval Research Laboratory, Washington, DC 20375-5352 

Department of Mathematics and Physics, Troy University, Troy, AL 36082 

G. Menon 

Bright γ -ray flares observed from sources far beyond our Galaxy are best explained if enormous amounts of energy are liberated by black holes. The highest-energy particles in nature—the ultra- high energy cosmic rays—cannot be confined by the Milky Way’s magnetic field, and must originate from sources outside our Galaxy. Here we summarize the themes of our book, “High Energy Radi- ation from Black Holes: Gamma Rays, Cosmic Rays, and Neutrinos,” just published by Princeton University Press. In this book, we develop a mathematical framework that can be used to help es- tablish the nature of γ -ray sources, to evaluate evidence for cosmic-ray acceleration in blazars, GRBs and microquasars, to decide whether black holes accelerate the ultra-high energy cosmic rays, and to determine whether the Blandford-Znajek mechanism for energy extraction from rotating black holes can explain the differences between γ -ray blazars and radio-quiet AGNs. 

In our book [1], a mathematical formulation of high- energy radiation processes and strong-field gravity is presented. This framework provides a starting point to investigate the following hypotheses: 

1. The most energetic and powerful radiations are made by processes taking place in black-hole jets. 

2. Ultra-high energy cosmic rays (UHECRs) are accelerated by radio and γ -ray loud blazars and GRBs. 

3. Turbulence and shocks accelerate particles to high energies through Fermi processes. 

4. The energy source of black holes with relativistic jets is black-hole rotation. 

## II. ESTABLISHING THE HYPOTHESES 

We do not attempt to present a comprehensive sum- mary of the observational background to be tested in our book, which is impossible given the rapidly ex- panding empirical data base arising from multiple fa- cilities, in particular, the Fermi Gamma ray Space Telescope, the MAGIC, HESS, and VERITAS ground- based γ -ray telescopes, the Pierre Auger Cosmic Ray Observatory, and the IceCube Neutrino Observatory. Instead we present a mathematical formalism to help researchers establish or refute the hypotheses listed above. Here we mention some observations that drive the study, and related subjects dealt with in the book. 

## I. SCIENTIFIC HYPOTHESES 

## A. Black-Hole Jets as Sources of Energetic Radiations 

The Fermi telescope, building on the success of the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observa- tory, found that ∼ 100 MeV – GeV γ rays are produced by the blazar AGN class. More than 30 blazar AGNs, principally of the X-ray selected BL Lac class, have now been detected with ground-based γ - ray telescopes. At least 12 GRBs of both the long soft and short hard class have been detected with the Large Area Telescope (LAT) on Fermi. Before that, five spark chamber events and several TASC (Total Absorption Shower Counter)/BATSE (Burst and Transient Source Experiment) events on CGRO, showed that GRBs produce extremely luminous multi- MeV/GeV emissions. Galactic microquasars like LS 5039 and Cyg X-1 are also found to be γ -ray sources. Powerful extragalactic γ -ray sources are thought to be formed by black-hole jets, with the jets nearly aligned to the observer. 

To establish whether black-hole jets are the sources of luminous γ radiations, we develop the theory of relativistic flows, starting with relativistic kinemat- ics and special relativity. Compton and synchrotron processes are treated with the goal of presenting a framework from which to model the multiwavelength spectral energy distributions of high-energy radiation sources. Starting from the Compton cross section, re- lations are derived to model external Compton scat- tering involving surrounding isotropic radiation fields and anisotropic accretion disk radiation fields. The formalism applies to scattering throughout the Thom- son and Klein-Nishina regime, though δ -function ap- proximations are provided to make simple back-of-the- envelope estimates. 

Synchrotron radiation formulae are presented, and the synchrotron self-Compton and synchrotron self- 

