Generalization of the Geroch-Held-Penrose formalism to higher dimensions

Abstract

Geroch, Held and Penrose invented a formalism for studying spacetimes admitting one or two preferred null directions. This approach is very useful for studying algebraically special spacetimes and their perturbations. In the present paper, the formalism is generalized to higher-dimensional spacetimes. This new formalism leads to equations that are considerably simpler than those of the higher-dimensional Newman-Penrose formalism employed previously. The dynamics of p-form test fields is analyzed using the new formalism and some results concerning algebraically special p-form fields are proved.

24 pages

References in corpus (3)

• A field-theory motivated approach to symbolic computer algebra
• Type D Einstein spacetimes in higher dimensions
• Type II Einstein spacetimes in higher dimensions

Cited by in corpus (30)

• Algebraic classification of higher dimensional spacetimes based on null alignment
• Causality and Hyperbolicity of Lovelock Theories
• Ultraspinning instability of rotating black holes
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Greybody factors for rotating black holes in higher dimensions
• Kerr-Schild spacetimes with (A)dS background
• On a five-dimensional version of the Goldberg-Sachs theorem
• Perturbations of higher-dimensional spacetimes
• Spinor classification of the Weyl tensor in five dimensions
• Renormalization of conformal infinity as a stretched horizon
• On higher dimensional Einstein spacetimes with a warped extra dimension
• Static and radiating p-form black holes in the higher dimensional Robinson-Trautman class
• Charging Kerr-Schild spacetimes in higher dimensions
• Refinements of the Weyl tensor classification in five dimensions
• Asymptotic behaviour of Maxwell fields in higher dimensions
• Algebraic classification of five-dimensional spacetimes using scalar invariants
• On the Goldberg-Sachs theorem in higher dimensions in the non-twisting case
• Kerr-Schild double copy for Kundt spacetimes of any dimension
• Classification of Gravitational Waves in Higher-dimensional Space-time and Possibility of Observation
• On the Weyl Tensor Classification in All Dimensions and its Relation with Integrability Properties
• Exact Solutions of General Relativity and Quadratic Gravity in Arbitrary Dimension
• The small sphere limit of quasilocal energy in higher dimensions along lightcone cuts
• The Newman-Penrose formalism in quadratic gravity
• Instability in near-horizon geometries of even-dimensional Myers-Perry black holes
• Cosmology on a cosmic ring
• Algebraically special solutions in AdS/CFT
• New frontiers in Numerical Relativity
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
• The Smarr formula within the Geroch-Held-Penrose formalism
• Asymptotic properties of gravitational and electromagnetic fields in higher dimensions