Surface stress tensor and junction conditions on a rotating null horizon

Journal Article · Mon Jan 03 00:00:00 EST 2022 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.105.024001· OSTI ID:1874174

Beltracchi, Philip ^[1]; Gondolo, Paolo ^[2]; Mottola, Emil ^[3]

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1. Univ. of Utah, Salt Lake City, UT (United States)
2. Univ. of Utah, Salt Lake City, UT (United States); Tokyo Institute of Technology (Japan); Univ. of Tokyo (Japan)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Japan Society for the Promotion of Science (JSPS); National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1874174
• Report Number(s): LA-UR-20-30222
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 2 Vol. 105; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
astronomy and astrophysics
atomic
nuclear and particle physics
general relativity
horizons
junction conditions
null surfaces