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It is shown that, for spherically symmetric static backgrounds, a simplereduced Dirac equation can be obtained by using the Cartesian tetrad gauge inCartesian holonomic coordinates. This equation is manifestly covariant underrotations so that the spherical coordinates can be separated in terms ofangular spinors like in special relativity, obtaining a pair of radialequations and a specific form of the radial scalar product. As an example, weanalytically solve the anti-de Sitter oscillator giving the formula of theenergy levels and the form of the corresponding eigenspinors.Comment: 16 pages, Late

THE DIRAC PARTICLE ON CENTRAL BACKGROUNDS AND THE ANTI-DE SITTER OSCILLATOR