Trapping of null geodesics in slowly rotating spacetimes
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Regular Article - Theoretical Physics
Trapping of null geodesics in slowly rotating spacetimes Jaroslav Vrba1,a , Martin Urbanec2,b , Zdenˇek Stuchlík1,c , John C. Miller3,d 1
Research Centre for Theoretical Physics and Astrophysics, Institute of Physics in Opava, Silesian University in Opava, Bezruˇcovo námˇestí 13, 74601 Opava, Czech Republic 2 Research Centre for Computational Physics and Data Processing, Institute of Physics in Opava, Silesian University in Opava, Bezruˇ covo námˇestí 13, 74601 Opava, Czech Republic 3 Department of Physics (Astrophysics), University of Oxford, Keble Road, Oxford OX1 3RH, UK
Received: 5 October 2020 / Accepted: 2 November 2020 © The Author(s) 2020
Abstract Extremely compact objects containing a region of trapped null geodesics could be of astrophysical relevance due to trapping of neutrinos with consequent impact on cooling processes or trapping of gravitational waves. These objects have previously been studied under the assumption of spherical symmetry. In the present paper, we consider a simple generalization by studying trapping of null geodesics in the framework of the Hartle–Thorne slow-rotation approximation taken to first order in the angular velocity, and considering a uniform-density object with uniform emissivity for the null geodesics. We calculate effective potentials and escape cones for the null geodesics and how they depend on the parameters of the spacetimes, and also calculate the “local” and “global” coefficients of efficiency for the trapping. We demonstrate that due to the rotation the trapping efficiency is different for co-rotating and retrograde null geodesics, and that trapping can occur even for R > 3G M/c2 , contrary to what happens in the absence of rotation.
1 Introduction Recently, there has been increasing interest in “ultra” compact objects (ones which could mimic black holes), in connection with the detection of gravitational waves coming from mergers [1]. Also, a general correlation has been suggested between quasinormal modes and the parameters of unstable circular null geodesics [2], although there could be some exceptions to this [3–6]. a e-mail:
[email protected] (corresponding author)
b e-mail:
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c e-mail:
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On the other hand, extremely compact objects are important also because of the possible existence of regions of trapped null geodesics that could be relevant for the trapping of gravitational waves [7] or neutrinos [8]. The trapping region is always centered around a stable circular null geodesic whose existence represents a necessary condition for the existence of the trapping zone. Null geodesics inside extremely compact neutron stars may govern the motion of neutrinos, if the neutron stars are sufficiently cool [8], and neutrino trapping can be important for several reasons: it can modify (decrease) the neutrino flow that reaches distant observers during the birth of a neutron star and just aft
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