How Long to Read Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes

How Long Does it Take to Read Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes?

It takes the average reader 2 hours and 9 minutes to read Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes by Thierry Daudé

Assuming a reading speed of 250 words per minute. Learn more

Description

In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)—that the Dirac equation can be separated into radial and angular ordinary differential equations—to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, the authors are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.

How long is Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes?

Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes by Thierry Daudé is 126 pages long, and a total of 32,256 words.

This makes it 43% the length of the average book. It also has 39% more words than the average book.

How Long Does it Take to Read Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes Aloud?

The average oral reading speed is 183 words per minute. This means it takes 2 hours and 56 minutes to read Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes aloud.

What Reading Level is Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes?

Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes?

Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes by Thierry Daudé is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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